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Development and Optimization of Spherical Neutron Polarimetry for Studying Magnetic Materials

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Title:
Development and Optimization of Spherical Neutron Polarimetry for Studying Magnetic Materials
Creator:
Silva, Nicolas
Place of Publication:
[Gainesville, Fla.]
Florida
Publisher:
University of Florida
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English
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1 online resource (128 pages)

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Nuclear Engineering Sciences
Nuclear and Radiological Engineering
Committee Chair:
Yang, Yong
Committee Co-Chair:
Enqvist, Andreas
Committee Members:
McDevitt, Christopher
Chen, Youping

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Subjects / Keywords:
neutron-polarization -- spherical-neutron-polarimetry
Nuclear and Radiological Engineering -- Dissertations, Academic -- UF
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bibliography ( marcgt )
theses ( marcgt )
born-digital ( sobekcm )
Electronic Thesis or Dissertation
Nuclear Engineering Sciences thesis, Ph.D.

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Abstract:
Spherical Neutron Polarimetry (SNP) is a highly effective tool for investigating complex magnetic structures, providing valuable insights into the contributions of neutron scattering from nuclear-magnetic interference and chiral structure in addition to separation of nuclear, magnetic, and spin-incoherent contributions. The development of the SNP device represents a significant advancement in the this field, with the potential to greatly enhance our understanding of materials and their magnetic properties. The SNP device consists of three units: incoming/outgoing neutron polarization, sample environment, and a zero-filed chamber all of which have been carefully optimized to achieve full control of neutron polarization and a near-zero magnetic field. The incoming/outgoing neutron polarization regions use high-Tc superconductiong Yttrium Barium Copper Oxide (YBCO) films and mu-metal to achieve full control of neutron polarization. The sample environment is a liquid-helium cryostat with a customized tail piece placed into the zero-field chamber. The zero-field chamber is fabricated with mu-metal to achieve a region of near-zero magnetic field. The device has been tested at the University of Missouri research reactor (MURR), then at Oak Ridge National Laboratory (ORNL) beamlines: HYSPEC, HB-1, and CG-4B. The testing demonstrates that the device functions as intended and has been entered into the user program at ORNL but can still be further optimized. The resulting optimized device is poised to significantly advance research in materials science, quantum materials, and related fields, and has the potential to drive new discoveries in these areas. ( en )
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Includes vita.
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Includes bibliographical references.
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Description based on online resource; title from PDF title page.
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This bibliographic record is available under the Creative Commons CC0 "No Rights Reserved" license. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:
Ph.D. University of Florida 2023
Local:
Advisor: Yang, Yong.
Local:
Co-advisor: Enqvist, Andreas.
Statement of Responsibility:
by Nicolas Silva.

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DEVELOPMENT AND OPTIMIZATION OF SPHERICAL NEUTRON POLARIMETRY FOR STUDYING MAGNETIC MATERIALS By NICOLAS SILVA A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 202 3

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© 202 3 Nicolas Silva

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To my family and the group of professors who continuously encouraged and supported me

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4 ACKNOWLEDGMENTS I would like to acknowledge Dr. Yong Yang for starting me on the process of getting the PhD degree and continuously supporting me and encouraging me throughout the tumultuous time. I would like to thank Dr. Chenyang Peter Jiang, Dr. Jacob Tosado, and Dr. Barry Winn for their encouragement and support and willingness to help me and offer me guidance.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ ............... 4 LIST OF TABLES ................................ ................................ ................................ ........................... 7 LIST OF FIGURES ................................ ................................ ................................ ......................... 8 LIST OF ABBREVIATIONS ................................ ................................ ................................ ........ 11 ABSTRACT ................................ ................................ ................................ ................................ ... 12 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .................. 14 Polarization Manipulation ................................ ................................ ................................ ...... 16 Polarized Neutron Scattering ................................ ................................ ................................ .. 19 Longitudinal Polarization Analysis ................................ ................................ ........................ 21 SNP Devices ................................ ................................ ................................ ........................... 23 CRYOPAD ................................ ................................ ................................ ...................... 23 MUPAD ................................ ................................ ................................ ........................... 24 SANPA ................................ ................................ ................................ ............................ 25 CRYOCUP ................................ ................................ ................................ ...................... 26 SNP Impact ................................ ................................ ................................ ............................. 27 2 DEVICE DEVELOPMENT ................................ ................................ ................................ ... 45 Incoming/Outgoing Neutron Polarization Control ................................ ................................ . 45 Nutator ................................ ................................ ................................ ............................. 45 Precession Region ................................ ................................ ................................ ........... 47 Sample Environment ................................ ................................ ................................ .............. 48 Zero Field Chamber ................................ ................................ ................................ ........ 48 Orange Cryostat ................................ ................................ ................................ ............... 49 Operation and Calibration ................................ ................................ ................................ ....... 50 CRYOPAD Calibration ................................ ................................ ................................ ... 53 SANPA Calibration ................................ ................................ ................................ ......... 53 3 EXPERIMENTAL MEAS UREMENTS ................................ ................................ ................ 68 University of Missouri Research Reactor ................................ ................................ ............... 69 Solenoid Sample ................................ ................................ ................................ .............. 69 Experimental Discussion ................................ ................................ ................................ . 69 Spallation Neutron Source, ORNL ................................ ................................ ......................... 70 Samples Measured ................................ ................................ ................................ ........... 70 Experimental Discussion ................................ ................................ ................................ . 71

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6 High Flux Isotope Reactor, ORNL ................................ ................................ ......................... 74 Samples Measured ................................ ................................ ................................ ........... 74 Experimental Discussion ................................ ................................ ................................ . 74 CG4B ................................ ................................ ................................ ................................ ...... 76 4 ADVANCING SNP ................................ ................................ ................................ ................ 97 Magnetic Shielding ................................ ................................ ................................ ................. 98 Operational Limitations ................................ ................................ ................................ ........ 100 Concept Design for HYSPEC ................................ ................................ ............................... 104 5 CONCLUSION ................................ ................................ ................................ ..................... 124 LIST OF REFERENCES ................................ ................................ ................................ ............. 125 BIOGRAPHICAL SKETCH ................................ ................................ ................................ ....... 128

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7 LIST OF TABLES Table page 1 1 Comparison of SNP devices ................................ ................................ .............................. 44 3 1 MURR theoretical polarization matrices vs their measured polarization matrices ........... 82 3 2 HYSPEC theoretical polarization matrices vs their measured polarization matrices ........ 87 3 3 HFIR theoretical polarization matrices vs. their measured polarization matrices ............. 93

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8 LIST OF FIGURES Figure page 1 1 Two schematics detailing two configur a tions for neutron scattering at a continuous neutron source (i.e. a research reactor).. ................................ ................................ ............ 30 1 2 A schematic showing an adiabatic transition on the neutron polarization. ........................ 31 1 3 A schematic showing a non adiabatic rotation. ................................ ................................ . 32 1 4 A) A schematic representation of traditional polarization analysis, note the continuous field throughout the neutron trajectory. ................................ ........................... 33 1 5 SNP setup using CRYOPAD on POLI. ................................ ................................ ............. 34 1 6 Photo of the incident nutator of D3 mounted inside the rotation unit.. ............................. 35 1 7 Photo of the hybrid precession torus of CRYOPAD. At the picture centre, we see the flat incident circuit contained in a superconducting box of Nb (frame in black).. ............ 36 1 8 A photograph of MuPAD installed on the triple axis spectrometer TASP [SRB01] at the continuous spallation neutron source ................................ ................................ ........... 37 1 9 A MuPAD precession coil is shown: (1) inner 2mm thick mu metal yoke wires, (2). ..... 38 1 10 A) A technical drawing of th e MuPAD device is shown. The mu represented by 9, ................................ ................................ ................................ ................ 39 1 11 Beamline hardware viewed from the side: (1) 3 He neutron spin polarizer, (2) incident transverse rotator, (3) incident longitudinal rotator, (4) zero field sample chamber,. ....... 40 1 12 A) Illustration of the Meissner shield construction. The length, width, and height of the outer shield are 101.6 × 76.2 × 152.4 mm 3 .. ................................ ................................ 41 1 13 A) Layout of CRYOCUP device components. B) Schematic of the rotatable guide field with the laboratory coordinates used throughout this paper [20]. ............................. 42 1 14 ecession region and sample chamber with only YBCO films and mu metal visible. B) Exploded view of a single precession region. ...... 43 2 1 A) Nutator as fabricated, B) 3 D model of the nutator, C) exploded view of the nutator ................................ ................................ ................................ ................................ 56 2 2 COMSOL simulation results for the nutator only. The magnetic flux density shown reveals that the center has a field of about 18 G ................................ ................................ 57 2 3 COMSOL simulation results for the magnetic field lines which indicate that the field between the poles and in the center is nearly vertical ................................ ........................ 58

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9 2 4 COMSOL simulation results showing the transition of the field lines as they cross through the solenoid and enter the nutator ................................ ................................ ......... 59 2 5 A) Precession region enclosed in the vacuum chamber, with the Meissner screens on, with the Meissner screens off. B) Precession region where ................................ ...... 60 2 6 Schematic showing the directions and planes each component can rotate the neutron polarization into. ................................ ................................ ................................ ................ 61 2 7 A) Zero Field Chamber as manufactured without the mu metal cradles attached. B) 3 D model of the entire ZFC, ................................ ................................ ............................. 6 2 2 8 repr esentative of the actual rotation stage. ................................ ................................ ......... 63 2 9 A) Sinusoidal nutator scan data from CRYOPAD. B) Precession scan data from CRYOPAD ................................ ................................ ................................ ........................ 64 2 10 Measurement of the shielding factor with increasing shield temperature. Black curve: The shielding factor in decibels.. ................................ ................................ ....................... 65 2 11 Calibration circles from SANPA ................................ ................................ ....................... 66 2 12 Calibration spheres from SANPA ................................ ................................ ...................... 67 3 1 Test fit and device setup on HB 1, the only missing component is the orange cryostat and associated cables ................................ ................................ ................................ ......... 78 3 2 Schematic representation of the beam setup along with the actual setup. ......................... 79 3 3 A) Test solenoid created to act as a sample for experiments at MURR, it was wound with aluminum wire and encased with s ome Mu metal. ................................ ................... 80 3 4 Precession scan showing expected sinusoidal curve ................................ ......................... 81 3 5 Full SNP setup at HYSPEC ................................ ................................ ............................... 83 3 6 Precession scan for the upstream/control precession region. ................................ ............. 84 3 7 Precession scan for the downstream/measurement precession region. The data was able to be fit and also used for the upstream/control precession region ............................ 85 3 8 The clamp for the YBCO tape was incorrectly attached and led to a poor electrical and thermal contact. ................................ ................................ ................................ ........... 86 3 9 Full SNP setup at HFIR beamline HB 1 ................................ ................................ ............ 88 3 10 Nutator scan data when sample stick containing silicon sample was added to the sample environment.. ................................ ................................ ................................ ......... 89

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10 3 12 Upstream/Control precession region scan ................................ ................................ ......... 91 3 13 Downstream/measurement precession scan ................................ ................................ ....... 92 3 14 Full SNP setup on CG 4B ................................ ................................ ................................ .. 94 3 15 Calibration data from the SNP device where all great circles are shown together to represent the sphere ................................ ................................ ................................ ............ 95 3 16 Calibration data of each plane ................................ ................................ ............................ 96 4 1 A) Redesign of the zero field chamber, B) an exploded view of the zero field chamber. ................................ ................................ ................................ ........................... 109 4 2 COMSOL simulation results showing the redesigned zero field chamber. The mu metal chamber was placed in a static magnetic field ................................ ....................... 110 4 3 COMSOL simulation results of the entire device. ................................ ........................... 111 4 4 COMSOL simulation results showing the nutator and mu metal cradle. ........................ 112 4 5 COMSOL simulation results showing the nutator and only half of the mu metal cradle. ................................ ................................ ................................ ............................... 113 4 6 COMSOL simulation results showing the nutator and none of the mu metal cradle. ..... 114 4 7 A) 3 D CAD model of the modified nutator, B) An exploded view of the modified nutator setup. ................................ ................................ ................................ .................... 115 4 8 A) 3 D CAD model of the double precession region, B) An exploded view of the precession region. ................................ ................................ ................................ ............ 116 4 9 3 D CAD model of the redesigned SNP device.. ................................ ............................. 117 4 10 3 D exploded view of the redesign vacuum assembly and the associated mu metal paneling to act as shielding. ................................ ................................ ............................. 118 4 11 COMSOL simulation results for the shorter SNP redesign. Here it can be seen that the window size act s as a barrier. ................................ ................................ ..................... 119 4 12 COMSOL simulation results for the shorter SNP redesign. Here the window size was enlarged ................................ ................................ ................................ ............................ 120 4 13 COMSOL simulation results for the shorter SNP redesign. Here t he inner mu metal shielding was removed. ................................ ................................ ................................ .... 121 4 14 Top view schematic of the setup for SNP on HYSPEC.. ................................ ................ 122 4 15 3 D CAD model of the mock up for setting the SNP device onto HYSPEC. e .............. 123

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11 LIST OF ABBREVIATIONS CAD Computer Aided Drafting CCR Closed Cycle Refrigerator CG 4B Cold Guide Hall Beamline 4B CRY OPAD Cryogenically Cooled Polarization Analysis Device HB 1 Horizontal Beamline 1 HFIR High Flux Isotope Reactor HYSPEC Hybrid Spectrometer ILL Institut Laue Langevin LPA Longitudinal Polarization Analysis MUPAD Mu metal Shielded Polarization Analysis Device MURR University of Missouri Research Reactor NIST National Institute of Standards and Technology ORNL Oakridge National Laboratory PTAX Polarized Triple Axis Spectrometer SANPA Small Angle Neutron Polarization Analysis SANS Small Angle Neutron Scattering SNP Spherical Neutron Polarimetry SNS Spallation Neutron Source YBCO Yttrium Barium Copper Oxide ZFC Zero Field Chamber

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12 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy DEVELOPMENT AND OPTIMIZATION OF SPHERICAL NEUTRON POLARIMETRY FOR STUDYING MAGNETIC MATERIALS By Nicolas Silva August 2023 Cha ir: Yong Yang Major: Nuclear Engineering Sciences Spherical Neutron Polarimetry (SNP) is a highly effective tool for investigating complex magnetic structures, providing valuable insights into the contributions of neutron scattering from nuclear magnetic interference and chiral structure in addition to separation of nuclear, magnetic, and spin incoherent contributions. The development of the SNP device represents a significant advancement in the thi s field, with the potential to greatly enhance our understanding of materials and their magnetic properties. The SNP device consists of three units: incoming/outgoing neutron polarization, sample environment, and a zero filed chamber all of which have been carefully optimized to achieve full control of neutron polarization and a near zero magnetic field. The incoming/outgoing neutron polarization regions use high Tc superconductiong Yttrium Barium Copper Oxide ( YBCO ) films and mu metal to achieve full contr ol of neutron polarization. The sample environment is a liquid helium cryostat with a customized tail piece placed into the zero field chamber. The zero field chamber is fabricated with mu metal to achieve a region of near zero magnetic field. The device h as been tested at the University of Missouri research reactor (MURR), then at Oak Ridge National Laboratory (ORNL) beamlines: HYSPEC, HB 1, and CG 4B. The testing demonstrates that the device functions as intended and has been entered into the user program at ORNL but can still be further

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13 optimized. The resulting optimized device is poised to significantly advance research in materials science, quantum materials, and related fields, and has the potential to drive new discoveries in these areas.

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14 CHAPTER 1 IN TRODUCTION Since the first experiments developed by Shull and Brockhouse, neutron scattering has proven impactful in the investigation of materials by determining the composition and dynamics of a material [1] . The technology has widely expanded to a varie ty of analysis techniques including neutron powder diffraction, small angle neutron scattering (SANS), spectroscopy, and magnetic scattering. Neutrons can interact with materials by scattering from the atomic nuclei or the magnetic moment of neutrons can i nteract with the magnetism in materials [1,2] . By using different neutron optics to select the orientation of the neutron magnetic moment one can incorporate neutron polarization into these techniques. This thesis will focus primarily on the development of the technique known as Spherical Neutron Polarimetry (SNP) which is a type of polarized neutron scattering analysis. Neutrons have widely been used for scattering experiments and analysis [2] . Compared to other techniques or radiation types (electron, x r ay, etc.) neutrons have some key advantages: the wavelength is comparable to the interatomic spacings of materials, the kinetic energy is comparable to magnetic excitations in a solid, neutrons are much more penetrating in materials, the weak interaction w ith matter helps to interpret the scattering data, and the neutron scatters from the magnetic moment of unpaired electrons [2] . The penetrating power of neutrons also allows the sample to be placed or setup in a container of appropriate materials [2] . Ulti mately, [2] . A schematic for a neutron diffractometer is shown in F igure 1 1 a and a type of neutron spectrometer commonly known as a triple axis spectrometer is shown in F igure 1 1 b . In either

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15 setup, t he neutron beam first encounters a monochromater a crystal set at a specific angle [2] : (1 1) Where is the lattice spacing for a lattice oriented towards the incident beam by the angle . Then by rotating both the detector and the sample , it can be determined how the atomic structure of the material is by the neutron diffraction pattern. and orientations of a variety of materials can be determined focusing on what the material is made of and how it is constructed. With t he addition of an analyzer another crystal or device that can select a separate final energy for the neutrons one can determine the dynamics of a material by measuring the kinetic energy changes of the neutrons in the sample [1,2] . Neutron scattering can be characterized by [2] : (1 2 ) Where the Q is the scattering/momentum transfer vector, is the wave vector of the incident neutrons and is the wave vector for the scattered neutrons. When and are equal the scattering is said to be elastic and when they are not, it is inelastic scattering [2] . During an inelastic scattering eve nt the neutron imparts some of its energy into the sample material so that and are not equal [2] . On a triple axis spectrometer this is by the analyzer ; or in the case of a time of flight spectrometer by measuring the time of flight the final neu tron energy can be determined . Another method for neutron scattering involves neutron polarization . Polarized neutron scattering has been used to study magnetism in materials [3,4] . This is largely due to the magnetic moment that a neutron exhibits which allows it to interact through magnetic scattering [3,4] .

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16 Neutron polarization refers to its magnetic moment or spin [4] . When defined with spin, S , it is the spin operator S = ( , , ), an intrinsic angular momentum with a quantum number of ½. Another expression of the spin operator is shown in the Pauli matrices = h/2 [4] : , , (1 3 ) For each neutron in the beam a vector, , with the e xpected values of the three (1 4 ) From here, the average of all the individual neutron polarizations will determine the polarization of the neutron beam [4] . (1 5 ) The polarization of the beam is a classical vector and all 3 individual components can be measured, where for a given direction i, where i can be x, y, or z on a cartesian coordinate system , can be defined as [4] : (1 6 ) Where n is the number of neutrons in accordance with the given spin (eigenstate). So that the overall beam polarization can be observed as follows [4] : (1 7 ) Polarization Manipulation The polarization of the neutrons can be controlled, directed, and guided. The polarization is referred to the neutron beam and a beam of neutrons can become polarized through the use of several devices [3,4] . Helium 3 polarizers or super mirror arrays can be used to polarize a beam of neutrons. The magnetic moment o f the neutron, , precesses in a constant magnetic field

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17 about the field direction [3,4] magnetic moment and spin in the formula shown as [3,4] : (1 8 ) Where is the magnetic moment of the neutron and is the magnetic field . The magnetic moment of the neutron can also be represented by the neutron gyromagnetic ratio and the spin vector, . T he time evolution of the spin is , which is also the rotational expression of the fundamental law of dynamics , leading to [4] : (1 9 ) Then taking the axis along the magnetic field H, the vectorial equation yield s the 3 components [3,4] : (1 10 ) (1 11) (1 12) Which leads to the solutions [3,4] : (1 13 ) (1 14) (1 15) Where the Larmor frequency is [3,4] : (1 16 ) (1 17)

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18 In the presence of varying magnetic fields, the neutron polarization can be manipulated and controlled by a spatially varying magnetic field , into different directions . If the direction of the magnetic field rate of change, , is sufficiently slow ( satisfied by ) the spin of the neutron will continue to rotate around the varying magnetic field [3,4,5,6,7 ,8 ] . Conversely if the direction of the magn etic field changes abruptly where the ratio is , then the neutron spin which was rotating around the initial field , it will then rotate around the new field when the field has changed [3,4,5,6,7 ,8 ] . These two forms of polarization control are referred to as an adiabatic and non adiabatic transition in neutron polarization and are represented in F igure 1 2 and F igure 1 3. The adiabatic transition occurs when the rate that the magnetic fields change direction is slow and smooth; whereas the n on adiabatic transition occurs when there is a sharp change in field direction. When planning for these types of transitions it is useful to develop an adiabaticity parameter, defined as E, and show in the following equations [7 ,8 ] : (1 17) (1 1 8 ) Where, in this instance, the rate of angular rotation, , of the magnetic field along the y axis is in the rest frame of the neutron to give equation 1 17 [7] . The adiabaticity parameter shows how the magnetic field changes with distance and in order to have a good adiabatic rotation without polarization loss, it is recommended to have E > 10 [7] .

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19 Polarized Neutron Scattering For polarization analysis experimen ts, the change in polarization state and intensity of the neutro ns scattered by the sample is what is measured [ 3 ] . This is represented by a polarization matrix [3,4,5,6,7] : (1 18 ) The interactions neutrons have within a sample can be both nuclear and magnetic. The Blume Maleev equations are the master equations describing polarized neutron scattering as shown in Eq. 1 19 and 1 20 [ 3 ,5 ,6,7 ] : (1 19 ) (1 20) Where, is the scattering intensity proportional to the scattering cross section, the incident neutron polarization, the final neutron polarization, the nuclear structure factor , and the magnetic interaction vector which is the projection of t he magnetic structure factor onto the plane of the scattering vector [3] . In these two equations , 1 19 is written such that the first term is paralle l to the polarization and would not rotate it [3] . The next terms , , are able to produce rotation towards the magnetic interaction vector, whereas the final term s , , are the only ones that can produce polarization towards the scattering vector [3] . For equation 1 20 the first term ( describes the nuclear scattering, the following term ( describes magnetic scattering, the next terms ( describe the nuclear magnetic interference, and the final term , , describes the chiral magnetic interactions [3] .

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20 As mentioned previously the measurements and analysis done for polarization experiments measure the change in polarization . This is represented by the following equation [3,4,6] : (1 21 ) Where, is the final polarization , , is the initial polarization, , is the polarization generated by the sample, and , is the polarization tensor. By defining 3 polarization axes as : x parallel to the momentum transfer vector , z perpendicular to the scattering plane (usually the vertical direction) and y completing the right handed coordinate system, and then measuring the scattered neutron polarization with the incident polarization along each of the polarization axes, the polarization tensor can be defined [3] : (1 21 ) (1 21 ) With I x = M 2 + N 2 + P x J yz , I y = M 2 + N 2 + P y R ny, I z = M 2 + N 2 + P z R n z , I = M 2 + N 2 + P x J yz + P y R ny + P z R nz, Where, N 2 = N N * ,

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21 M 2 = , R ij = 2 , R ij = , J ij = 2 ( , and J ni = 2 ( . Where, R ij, represents the real component and J ij, represents the imaginary component from the mathematical operations [3] . The diagonal terms of this polarization matrix represented by 1 21 give information of the traditional nuclear scattering and magnetic scattering while the off diagonal terms contain chiral contributions and nuclear magnetic interference. T raditional polarization analysis techniques can only mea sure the diagonal terms in the polarization matrix [6,7, 9 , 10 ] . SNP provides a way to access the off diagonal components and thus allows researchers to extract the complete information in the scattering. Figure 1 4 shows a schematic between a traditional te chnique vs. SNP which will be discussed in more detail in the next section . Traditional polarization analysis refers to some techniques such as half polarization analysis or longitudinal polarization analysis (LPA). The figure represents LPA since it is th e closest iteration to SNP and the jump to SNP arose from LPA. Longitudinal Polarization Analysis Longitudinal polarization analysis was developed at ORNL in 1969 by Moon, Riste and Koehler. They demonstrated that by adding a polarization analyzer and flip per after the sample it can increase the effectiveness of a polarized neutron spectrometer [ 4, 1 1 ] . The analysis for this technique is done by measuring the polarization of neutrons in the same direction as they are initially adjusted to [4,1 1 ] . That is, if the neutron polarization is aligned along z direction, the

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22 polarization on the scattering side (analysis side) is also in the z direction , either parallel or anti parallel to z [4,1 1 ] . This is primarily why this technique is called longitudinal, it is also referred to as uniaxial. By , combining the two possible states of the incident polarization and the two possible states for the scatter ed polarization, four different intensities can be measured: I ++ , I + , I + , and I [4, 9 , 10 ,1 1 ] to P i , do not change the direction of polarization, and terms proportional to P i , reverse the polarization direction. From here the terms non spin flip and spin flip are used to describe the change in polarization; where the former is when the polarization direction is not changed and the latter refers to the polarization comple [4, 9 , 10 ,1 1 ] . A general rule is that a spin flip is typically magnetic and a non spin flip can be either magnetic or nuclear. It can also be understood that magnetic components parallel to the incident polarization are non spin flip and only magnetic components perpendicular to the incident polarization affect the polarization direction [4, 9 , 10 ,1 1 ] . In LPA there is a guide field present throughout the entire neutron path to help maintain neutron polarization as shown in Figure 1 4 A . As a result LPA can only measure the final polarization that is parallel or antiparallel to the incoming polarization and the measured polarization is only the projection of the actual polarization to the direction defined by the guide field. In compar ison, SNP decouples the incoming and outgoing neutron polarizations by setting up a zero field region at the sample position seen in Figure 1 4 B , which enables measurement of all 9 components in the polarization matrix [1 2 ] . It is vital for SNP to have pre cise neutron polarization control for both incoming and outgoing neutrons which directly determines the accuracy of the results. The polarization manipulation is usually achieved through a combination

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23 of adiabatic and non adiabatic neutron polarization tra nsitions. Highly accurate neutron polarization control relies on a sharp magnetic field boundary between each transition section, i.e., the boundary between the adiabatic transition section and the non adiabatic transition section as well as the boundary b etween the non adiabatic transition section and the zero field chamber. The best solution to set up such a boundary is to use superconducting films by taking advantage of the Meissner effect. SNP Devices To date, there are only a handful of devices capabl e of performing SNP. The most successful and well known is the Cryogenically cooled Polarization Analysis Device, CRYOPAD, is an SNP device that was developed at Institut Laue Langevin (ILL) [1 3 ,1 4 ,1 5 ] . This was the first SNP device and led the way in deve lopment for the technique and technology. Since its inception there have been several iterations that have improved upon the device and have been used for a wide variety of experiments [1 3 ,1 4 ,1 5 ] . When analyzing and comparing different SNP devices there ar e some key aspects to investigate. Namely, how do the devices control or manipulate neutron polarization? How do the devices decouple the incoming and outgoing neutron polarization and associated magnetic fields? There are several other differences that ar ise because of how those questions get answered. An example of this is with the scattering range that each device can cover. Table 1 1 lists different types of SNP devices and makes some comparisons between them. CRYOPAD An overall schematic can be seen in the image below , F igure 1 5 , along with how the device looks [1 4 ] . The SNP device can be divided into the incoming neutron polarization control, outgoing neutron polarization control, and zero field chamber. T he incoming and outgoing neutron polarization control are also mirrors of each other. The polarization is controlled by

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24 adiabatic transition wi th the nutator , a rotatable magnetic field seen in F igure 1 6 [1 4 ] , and then non adiabatic transition with the Outer Meissner shield seen in F igure 1 7 [1 4 ] . The zero field region is achieved by use of niobium superconducting films that form a toroidal sh ape consisting of the Outer Meissner shield (OMS) and the Inner Meissner shield (IMS) [1 4 ] . The two Meissner shields act as both a means of magnetic shielding for a zero field region to decouple the incoming and outgoing neutron polarization but also as a way to control the polarization [1 4 ,1 5 ] . The Meissner screens can divide the magnetic fields present to create the sharp changes in magnetic field necessary for non adiabatic rotations. There is mu metal that is at the top and bottom of the device to furth er help reduce any stray magnetic field [1 5 ] . After the neutrons interact with the sample the polarization for analysis can be adjusted in any direction by adjusting the field between the IMS and OMS as well as adjusting the position of the nutator. Improv ements that have been made to CRYOPAD have included using a flat Meissner shield on the incident polarization and adding a slight curve to the nutator on the scattered beam side to help avoid misalignment of the magnetic field from the Meissner shield and the nutator [1 5 ] . MUPAD The Mu metal shielded Polarization Analysis Device, (MUPAD), was developed after CRYOPAD seen in F igure 1 8 [1 6 ] . There are several differences between this device and CRYOPAD but most notably is the approach for achieving a zero fi eld chamber. MUPAD makes use of a chamber made entirely from mu metal to decouple the incoming and outgoing neutron polarization and does not use Meissner screens at all in its design. It has a double layer of mu metal made of concentric cylinders where an orange cryostat can be placed. Additionally, MUPAD also does not use a nutator for neutron polarization control but a set of precession coils seen in F igure 1 9 [1 6 ] . It is important to note that there are also a set of

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25 cou p ling coils that connect the f ield from the outside of the device to the precession coils, this helps preserve neutron polarization and ensure good spin transport. The precession coils are built in such a way that the neutron polarization can be rotate d in every direction through only non adiabatic transitions. Going back to the zero field chamber, u sing a series of mu , seen in F igure 1 10 that can be raised and lowered the scattering arm of the device can be rotated to accommodate the scattering angle of v arious samples [16] . to the precession coils within the mu metal tunnel. SANPA The Small Angle Neutron Polarimetry Apparatus (SANPA) , shown in F igure 1 1 1 , was developed at the National Institute of Stan dards and Technology (NIST) [18,19] . Within its name it implies that this device has a much smaller scattering angle range compared to CRYOPAD and MUPAD. The device also differs further with the control of the incoming and outgoing neutron polarization, ho wever, there are some similarities with its zero field chamber. The neutron polarization control is achieved through a series of electromagnetic coils that can adiabatically adjust the polarization and that couple to a precession region for a non adiabati c rotation [18] . Note, that in F igure 1 1 1 the adiabatic rotation happens with the transverse rotator and the non adiabatic rotation with the longitudinal rotator [18] . The coils used can be seen in some more detail in F igure 1 1 2 [18] . The zero field cham ber can also be seen in some detail in F igure 1 1 2 [18] . It is made from a series of Meissner shields , specifically niobium the same superconducting material used for CRYOPAD . This design has an inner shielding region and an outer shielding region. Within the inner region there is a cap that can be removed to allow for sample placement and removal. The two outer volumes enclose the magnetic field rotators , specifically the longitudinal rotators .

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26 One of the key differences to that of the CRYOPAD design lies in the cooling system. Rather than use a liquid cryogen bath, SANPA utilizes a closed cycle refrigerator (CCR) which is capable of cooling the niobium to a nominal 3.5K [18] . Setups that use niobium have a higher demand for cooling power and use two stage cooling systems, which have longer cooling times. This also limits the use of some samples which would require lower temperatures. Additionally, the cooling of any sample material is not separated from the device, as the devices cools down the sample does also. It does not have independent cooling for any sample material. CRYOCUP CRYOCUP was developed at Indiana University and also operates as a small angle SNP device [20]. It was named cup One of the goals for this device was to improve some of the existing SNP devices by making some modifications in size and operation. The largest improvement compared to CRYOPAD or S ANPA would be the use of YBCO as the superconducting material compared to niobium [20,21] . The superconducting temperature of YBCO is about 90K [20] . As a result, the cooling system needed is significantly reduced and can be achieved with a single stage CC R that can operate at a temperature up to 25K . Similarly, to all SNP devices, polarization control occurs in a series of steps and for CRYOCUP it begins with a nutator, a rotatable magnetic field and then enters a precession region . The schematic for the device as well as the nutator is shown in F igure 1 1 3 [20] . The nutator can adjust the neutron polarization adiabatically whereas the precession region adjusts the polarization with a non adiabatic transition. Taking design elements from CRYOPAD, the prece ssion region uses two flat Meissner screens. A schematic is seen in F igure 1 1 4 where the differences between this and CRYOPAD is that the superconducting film being used is YBCO and it is also not curved [20] . Since YBCO

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27 has not been made onto curved surf aces a zero field chamber made entirely from YBCO is more difficult to develop . Also, compared to niobium, YBCO runs into size limitations . However, the use as a Meissner screen to separate magnetic fields and create the conditions ideal for non adiabatic transitions can easily be realized. Similar to MUPAD, the zero field chamber is made from mu metal [20] . The shape of this mu metal chamber was made big enough to connect the two precession regions. The overall size is quite small which does place some lim itations on what samples can be measured. This design serves as the basis for the device that was developed at ORNL. SNP Impact The use of these devices has led to many publications and discoveries, or confirmations of the crystal structure of materials. Prior to SNP theoretical models for crystallographic structures were developed by various means with limited means of confirming the true structure. Since SNP can determine the off diagonal components of the polarization tensor it can determine directional information for individual moments in complex magnetic structures such as non collinear antiferromagnetic structures and incommensurate and chiral magnetic structures (helices or cycloids) [21] . SNP also enables determination of the relative populations o f various magneto electric domains and the antiferromagnetic structure factors [21] . The magnetic character of excitations can as well be clarified using SNP. In addition, SNP is a necessary tool for measuring the magnetic form factor for some important cl asses of antiferromagnets [21] . The use of SNP also extends to the study of magnetic materials with small anisotropy, multiferroics and superconductors [21] . In particular, the chirality degree of freedom, which is realized in skyrmions and topological m at erials and becomes increasingly important in spintronics, can be observed using SNP [21] .

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28 MnSi as a material has been extensively studied and its magnetic structure has been well characterized and theorized. MnSi was suspected to have a chiral correlated p aramagnetic or spin liquid phase just above T c = 29 K [22] . Several theories came about to explain the behavior of the material within the phase; possibilities such as unpinned helical order or condensation of chiral order parameters. In the 1980s, the material was investigated thoroughly with triple axis spectroscopy but did not have the resolution to fully understand the materials behavior. SNP a long with neutron spin echo was able to provide the analysis necessary to fully understand the transition phase of MnSi [22] . Using CRYOPAD and SNP to investigate the helical magnetic moments along the helical Bragg peak along the (1,1,1) plane. The polar ization matrix measured at 25K was which is in good agreement with theory and shows a stable left handed helix [22] . It was also found that when increasing the temperature by up to 1K the polarization matrix did not change. From this data it was concluded that the previous assumption of an unpinned or fluctuating helical phase was not sufficient to describe the results [22] . By coupling this data with neutron spin echo data it is determined that a disordered Skyrmion phase, a chiral single domain and strongly fluctuating new state of matter above the helical phase of MnSi exists [22] . Aside from MnSi, the compound has also been investigated with great interest since it also has a chiral magnetic structur e. Specifically, in an investigation by Janoschek using the Mu metal Polarization Analysis Device (MUPAD) it was determined to be a chiral magnetic structure with a single chirality [23] . Several different models were created from mean field theory (MFT) t o explain the possible magnetic structure and behavior of

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29 . has a commensurate to incommensurate phase transition at T IC = 13.5 K, where the collinear antiferromagnetic structure transitions into an antiferromagnetic helix that h as a single chiral domain [23] . SNP measurements were taken above and below this transition temperature. The SNP data from the commensurate phase sugg ested which model was sufficient for explaining the magnetic structure. The measurements from the incommensurate phase faced a difficulty regarding the resolution of the device. The magnetic peak splits and broadens into two separate peaks that are near each other once the tem perature drops below the phase transition [23] . Because of this and the limitation of the resolution of MUPAD, some reasonable assumptions had to be made from the calculated data. Based off the assumptions and data collected it was determined which magneti c model would best represent the actual magnetic structure [23] . Using SNP the orientation of the magnetic moments for both the and were proven. In another investigation using CRYOPAD, Copper oxide (CuO), was investigated with greater detail. Cop per oxide has a commensurate antiferromagnetic phase below 213 K and an incommensurate antiferromagnetic phase between 213 K and 230 K [24] . Specifically, the moments of the copper ions, Cu 2+ , were confirmed to be parallel to the monoclinic b axis in the commensurate antiferromagnetic phase [24] . With the magnetic moments determined a new magnetic model was produced that also had agreement with unpolarized neutron diffraction intensities [24] . SNP has been us ed for a variety of experiments to clarify which magnetic models fully represent the material being investigated . With a device operating in the US it can provide researchers here with the opportunity to investigate magnetic materials and gain insight into their structure that would otherwise be impossible to achieve.

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30 Figure 1 1. Two schematics detailing two configur a tions for neutron scattering at a continuous neutron source (i.e. a research reactor) . A) A general schematic representing elastic neutron scattering , B) A general schematic representing inelastic neutron scattering . Neutron source Neutron source Detector Detector Sample Sample Monochromator Monochromator Analyzer A) B)

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31 P x y z Adiabatic Transition Figure 1 2. A schematic showing an adiabatic transition on the neutron polarization. When the adiabaticity parameter E, is E>10 the polarization follows the magnetic field through an adiabtic transition. In this instance the stray fields inbetween the generated fields Bx and By form a gradient field that the neutron polarization follow

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32 Figure 1 3. A schematic showing a non adiabatic rotation. The neutron polarization, in red, is aligned with the transverse magnetic field By, as it passes through a Meissner screen (yellow) the polarization will see the magnetic field Bz and rotate around it. This will reorient the polarization into the XY plane. In the configuration shown, the field beyon d the second Meissner screen is nominally zero. The adiabaticty parameter E is not met for an adiabatic transition, the sharp transition from the transverse field to the vertical field generates the conditions for a non adiabatic transition where pat h P Non Adiabatic trnsa Transition y z x

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33 Figure 1 4 . A ) A schematic representation of traditional polarization analysis, note the continuous field throughout the neutron trajectory . B ) A schematic representation of spherical neutron polarimetry, with a zero field region represented by the cylinder around the sample B B x y z x y z A ) B )

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34 Figure 1 5 . SNP setup using C RYOPAD on POLI: (1) polarizer with 3He cell, (2) incoming nutator, (3) Zero field chamber made from mu metal, (4) fixing ring, (5) outgoing nutator, (6) Decpol analyzer with 3He cell and detector, positioned on the rotating detector arm (7) [14] .

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35 Figure 1 6 . Photo of the incident nutator of D3 mounted inside the rotation unit. The curvature of the polar pieces was chosen by finite element calculations in order to minimise the spread of the field direction onto the outer Meissner screen. B oron nitride pieces are intr oduced inside the nutator for reducing the backgroud (white material) [15] .

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36 Figure 1 7 . Photo of the hybrid precession torus of C RYOPAD. At the picture centre, we see the flat incident circuit contained in a superconducting box of Nb (frame in black). On both sides, we see the ends of the outgoing coil, a toroidal solenoid which is made infinite thanks to the yoke of m metal which completely by pass the incident circuit. Inset: finite element simulation of the field lines inside t he incident coil [15] .

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37 Figure 1 8 . A photograph of MuPAD installed on the triple axis spectrometer TASP [SRB01] at the continuous spallation neutron source SINQ of Paul Scherrer Insitut , Switzerland [17] .

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38 Figure 1 9 . A MuPAD precession coil is shown: (1) inner 2mm thick mu metal yoke wires , (2) inner Al wires (3) Al wires , (4) window for neutrons , (5) secondary outer mu metal sh ield [16].

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39 Figure 1 10 . A ) A technical drawing of the MuPAD device is shown . The mu represented by 9, can be lifted and lowered in order to rotate the scattering arm. B) the hydraulic mechanism for lowering and lifting the mu by 1 and 3, where 2 and 4 are mu metal sheets [16] .

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40 Figure 1 1 1 . Beamline hardware viewed from the side: (1) 3 He neutron spin polarizer, (2) incident transverse rotator, (3) incident longitudinal rotator, (4) zero field sample chamber, (5) scattering alignment rotator, (6) scattering transverse projector, and (7) 3 He ne utron spin analyzer [18] .

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41 Figure 1 1 2 . A ) Illustration of the Meissner shield construction. The length, width, and height of the outer shield are 101.6 × 76.2 × 152.4 mm 3 . The inner shield is 63.5 × 76.2 × 146.0 mm 3 . B ) Illustration of the transverse rotator (2) and projector (6). Red arrows indicate the magnetic field produced by the Z coil pair, and blue arrows indicate the magnetic field produced by the X coil pair. The length, width, and height are 101.6 × 114.3 × 114 .3 mm 3 [18] .

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42 Figure 1 1 3 . A ) Layout of CRYOCUP device components. B ) Schematic of the rotatable guide field with the laboratory coordinates used throughout this paper [20] .

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43 Figure 1 1 4 . A ) Schematic of precession region and sample chamber with only YBCO films and mu metal visible. B ) Exploded view of a single precession region. The parts are numbered as 1 YBCO film; 2 precession region mu metal; 3 zero field chamber mu metal; 4 superconducting coil; 5 co pper coil core [20] .

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44 Table 1 1. Comparison of SNP devices ORNL SNP Device CRYOPAD MUPAD SANPA CRYOCUP Angle cover age 80 130 N/A SANS SANS Zero field characterization Mu metal chamber Niobium Meissner shield Mu metal chamber Niobium Meissner shield YBCO Meissner shields and Mu metal Nutator Rotatable magnetic field Rotatable magnetic field Coupling coil Rotatable magnetic field Rotatable magnetic field Precession region YBCO Meissner Shield Niobium Meissner Shield Precession coil Niobium Meissner Shield YBCO Meissner Shield

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45 CHAPTER 2 DEVICE DEVELOPMENT The SNP device can be separated into three different major sections: the incoming neutron polarization control, the outgoing neutron polarization control, and the sample environment. The incoming and outgoing neutron polarization control section s are effectively identical and mirror each other fro m the sample position . Incoming/Outgoing Neutron Polarization Control These sections are designed for full three dimensional polarization control and manipulation, so that the neutron polarization can theoretically be redirected into any direction, the inc oming side will be referred to as the control axis and the outgoing is referred to as the measurement axis. The control axis adjusts the neutron polarization prior to scattering with the sample whereas the measurement axis sets the polarization to be measu red after neutrons interact with the sample. Each section is comprised of two minor parts: the nutator and the precession region. The nutator is a rotatable magnetic guide field and represents the region for an adiabatic polarization transition Nutator Th e nutator mentioned above is a rotatable magnetic guide field and shown in F igure 2 1 . T his device generates a spatially varying magnetic field from two electromagnets: a solenoid and a pair of soft iron pole pieces with copper coils wound around their bas es . Seen in F igure 2 1, the nutator itself can be broken down into individual components: a solenoid, soft iron pole pieces , a mu metal ring, a rotation cylinder, and a goniometer. The s olenoid is copper wire wound around an aluminum cylinder to a total of about 74 turns . It has a 10.16 cm (4 in) inner diameter, 3 mm thickness, and is 8 cm long. The purpose of

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46 this cylinder is to generate a field in the longitudinal direction along the beam path which can couple to other components on the beam line. Typically, th ese other components would be either a Mezei flipper or an extra guide field (s) . The solenoied field also couples to the field generated by the pole pieces. Th e pole pieces themselves are two pieces. One piece being the extruded half cir cle (5.9 cm radius x 7 cm x 0.3 cm) with a rectangular core (3 cm x 6 cm x 1.5 cm) where the copper wire is wound; the second being a rectangular base (4 cm x 7cm) and a curved surface (7.4 cm radius) to contain the copper wire and fit within the mu metal ring . The pole pieces are arranged to generate a field in the transverse direction of the beam. This field is also the one that when rotated , will adjust the polarization along the transverse plane of the beam. Figure 2 2 shows the results from some magnet ic simulations showing the field strength. Additional simulation results shown in F igure 2 3 and F igure 2 4 show the direction and movement of the field along the nutator . Depending on the wavelength of the neutrons, the applied current can be adjusted to satisfy the adiabatic condition. The mu metal ring maintain s and control s the magnetic field that is generated from the pole pieces, the idea being to minimize stray field . The ring fits into the rotation cylinder having an outer radius of 7.5 cm and inner radius of 7.3 cm and is 7 cm long . The rotation cylinder houses all the components of the nutator with the exception of the goniometer. It has an inner diameter of 7.5 cm to fit the mu metal ring and an outer diameter of 7.9 cm and is 16 cm long. The goni ometer is a non magnetic HUBER ® 420 and can rotate a full 360 degrees with high precision and accuracy . The entire rotation ensures that the polarization can be directed into any direction in the transverse plane.

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47 Precession Region The precession region itself is composed of a pair of YBCO films, a copper frame, a pair of superconducting coils, and it is all cooled down by a DOMUSO ® CH 110 single stage closed circiut refrigerator (CCR). The YBCO plates are made from YBCO deposited on to sapphire and then plated with a thin film of gold. Each plate is 9 mm x 10 mm and 0. 5 mm thick. They are attached onto the copper frame to act as Meissner shields once the superconducting temperature is reached. The copper frame developed seen in F igure 2 5 has a rectangular opening (6.35 cm x 9.45 cm) and is 1.59 cm thick. Within the opening there is a layer of cryogenic mu metal and then two copper framing pieces that have additional YBCO films attached to them. Lastly, the superconducting coils are mo unted in the center of the top and bottom of the mu metal layer. The superconductiong coils were created by winding YBCO tape around copper, in total the tape has 3 turns around the copper and 3 layers of turns. Important to note, the YBCO tape was given a n additional layer of insulation by wrapping the tape with Kapton tape. This proved to be necessary as the insulation on the YBCO tape itself could more easily come off and create a short circuit by making contact with the copper frame. The YBCO films and mu metal create a zone of near zero magnetic field so the only field present would come from the superconducting coils when current is run through them. Usage of the single stage CCR highlights one of the main a dv antages to using YBCO ; as a high temperatu re s uperconductor compared to niobium , used in CRYOPAD , the cooling system is more compact and simplified. This cold head only requires the use of an air cooled compressor and reaches temperatures of about 25K, far below the critical temperature of 90K for YBCO. Looking at F igure 2 6 the nutator is what is rotating the magnetic field and polarization along the angles 1 and 2 . Also looking at F igure 2 6 the precession region rotates into the XY

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48 1 2 . This is achieved by creating a region of non adiabatic neutron polarization transition, which allows the neutron to precess around a magnetic F or full 3 dimensional polarization control a combination of the nutator and preces sion region is used . Sample Environment This major component can also be broken down into two minor components: the zero field chamber and the orange cryostat (an evaporation refrigerator). The entirety of the zero field chamber is made from Mu metal . Mu m etal being a material with the desired magnetic s . This creates a region of near zero magnetic field where the sample to be measured can reside in and is an essential component for SNP. The orange cryostat is a standard cooling system used widely throughout neutronics and neutron facilities. They use liquid helium and nitrogen as cryogens to cool down the sample material. Cooling the samples becomes necessary since the magnetic behavior of samples can often have transition temperatures. These systems can have operating temperatures ranging from 40 mK up to 300 K, depending on what is used and added onto the cryostat. Zero Field Chamber Seen in F igure 2 7 , the zero field chamber is made of several pieces, the cra dle for the precession regions and the chamber for the orange cryostat. The cradles for the precess ion reign serve as a connection to the cylindrical bridges/tunnels to ensure the neutron path has minimal field. T he cradle itself can also be fully enclosed metal sheet. This is primarily useful when cooling the system down, it creates a near zero magnetic field region within the cradle so that no magnetic field can be trapped inbetween the Meissner screens. While the system cools, the YBCO films do not act as Meissner shields so magnetic field is free

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49 to pass through the films. As the temperature passes the superconducting temperature the films will act as Meissner shields and any field that was passing through at the time ca n become trapped inbetween the shields. The presence of this stray field can add undesirable effects to the neutron polarization as it passes through. As a result of this, it is necessary to cool the precession region in a near zero field region. The cham ber for the orange cryostat is a pair of concentric cylinders with mu metal bridges/tunnels that connect to the control and measurement axes . The outer cylinder will be attached to the base plate and will be fixed in position. The inner cylinder is allowed to rotate within the desired range for observation ( 5 to +80 degrees). The measurement axis will be mounted onto a motorized platform that can freely rotate and as it moves the inner cylinder will move along with it. The tail of the orange cryostat is pl aced within the inner cylinder so that the sample itself is sitting in a region of near zero magnetic field. Orange Cryostat The orange cryostat has become a typical cooling system used in neutronics , a CAD model is shown in F igure 2 8 . They were original ly developed at ILL to be able to more precisely control the sample temperature. These are usually top loading systems and come with a sample stick. The orange cryostat uses liquid helium and their operating temperatures are roughly 1.5 300 K. This cryos tat was a custom design and purchase from AS Scientific® to have a narrow tail. The sample well is 5 cm in diameter and the sample stick is fitted with ATTOCUBE ® tilt stages and an AEROTECH ® rotation stage. The ATTOCUBE ® tilt stages can work in cryogenic t emperatures and allow for tilting of the sample to ensure a good signal or the Bragg peak can be hit. The AEROTECH ® rotation stage is attached at the top of the cryostat and allows for the entire sample stick to be rotated so that the sample can also be rotated.

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50 When comparing our device to that of others, i t takes some of the best components and is built in order to improve upon them and make a new SNP device. It utilizes polarization control similar to how CRYOPAD achieves its polarization control, a series of adiabatic and non adiabatic regions. However, a key difference is in using YBCO vs. Niobium. YBCO being the high temperature superconduc ting material that it is, allows for a simpler cooling system which makes the operation of the device a little easier. Since the cooling system is easier to realize the device also is smaller and can be transported or moved around much easier. The zero fie ld region is similar to that of MUPAD. They both utilize mu metal to create a zero field region, but their design is quite different. In our design some of t he magnetic fields generated were removed from the mu metal tunnel . The precession region is still shielded by mu metal but the nutator field was placed outside of it. I t was thought that the magnetic fields may saturate or have unintended effects on the mu metal compared to how MUPAD has many of their magnetic fields within their mu metal shielding. Th e mu metal shielding for our device was also made smaller which eases the transport and assembly of our device. So rather than cover the entire device with mu metal, only the essential regions were surrounded by mu metal. Operation and Calibration Once ins talled on a beamline the device is first vacuum pumped and the mu metal cradles are fully enclosed. Once the vacuum reaches levels of about 1x mbar the compressors are turned on to begin the cooling process. The cold heads will cool the precession regi on down and eventually plateau or stabilize at about 24 25K. At this point, the device can be operated remotely and entirely through the software program SPICE. It is a program that allows the user to control all the components, electronics, and motors ass ociated with the experiment. From the interface the user can drive the motors to rotate the nutators and sample position as well as power all the electronics to generate magnetic fields.

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51 Recall from C hapter 1 that what is measured during an experiment is the polarization matrix: (1 18 ) Where each component represents a different orientation of magnetic fields the device will be directed to and provides different information related to the magnetic structure. To measure these nine components, the device has to be able to control and manip ulate the polarization into those specific orientations to measure the polarization matrix. The process for guiding the direction of the polarization is summarized in these steps: The beam will first pass through a polarizer that will set the incident pola rization and initial orientation this depends on the polarizer being used for the experiments done. In the case for the testing done at MURR, the V cavity used set the initial polarization along the Z direction and has a polarizing power of about 99%. So that the initial polarization can be thought of as = (0,0, ), where is the magnitude of the polarization from the V cavity. The polarization then enters the first nutator where it is adiabatically rotated into the Z X plane , refer to F igure 2 7 for the direction of rotation and coordinate system . The polarization is coupled to other neutron optics via the solenoid and then the pole pieces in the nutator rotate it by an angle, , represented by ( 3 1 ) After this initial rotation, if necessary, the polarization can then be rotated by the precession region as it exits the nutator. This rotation will rotate about the Z axis and into the Y X plane through an angle, . It is a 3x3 rotation matrix ( ). The combination of and ( ) are the control axis and set the incident polarization to a desired position. ( 3 2 ) The polarization then enters the zero field chamber with its initial polarization, P i , and would interact with a sample. The sample with its own magnetic structure will scatter and modify the incident polarization to the polarization property tensor, T. From T the magnetic structure of the material can be determined and the resulting scatt ered polarization, P f , enters the measurement axis of the SNP device.

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52 ( 3 3 ) The measurement axis of the polarization would then act similarly to the control axis where the precession region and nutator would act to rotate the polarization to be measured. The polarization enters the precession region and is rotated by an angle . This is a 3x3 rotation matrix. ( 3 4 ) The polarization will then pass through the nutator and go through the final adiabatic rotation to be adjusted by a final angle , represented by: ( 3 5 ) From here the neutrons will encounter the analyzer and then the detector to measure the final state of the polarization. By adjusting the angles that the polarization will be rotated through each device the neutron polarization can be although not necessary for experimental data since the data needed is the nine components of the polarization matrix. Before taking any data or measurements or beginning the calib ration procedure, it is useful to make sure all the components are functioning as intended. In itially, raising the current beyond a certain level broke the superconductivity of one of the superconducting coils, th e diagnosis and corrections are described i n greater detail in C hapter 4. When installed on a new beamline it is best practice to calibrate the device to the beamline. Calibration entails making sure all components are functioning and that the magnetic fields are adjusting the neutron polarization in the appropriate directoins. For this device originally the calibration process followed similarly to the calibration process of CRYOPAD and then calibration process for SANPA was taken into consideration.

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53 CRYOPAD Calibration Calibration of CRYOPAD can be described in these four steps [15] : This is done by taking polarization measurements and maximizing the polarization by adjusting the relative positions of the nutators amongst themselves. Specifically, the control (incoming) nutator is rotated while the measurement (outgoing) nutator is held in a fixed position where there is no current in the precession coils. From here a sinusoidal curve is generated where the curve fit can tell the angular shift between the nutators, and th ey can be properly aligned with respect to each other shown in F igure 2 9 . The following step is to drive the nutators to a position so that the magnetic fields they produce are parallel with each other and with the vertical direction Z, see F igure 2 6 for the cartesian orientation of the beamline. Once the nutators are in position the polarization is measured while current is run through the precession coils, these are referred to as precession scans. These scans are a measurement to how much the neutron p olarization is rotating about the Z axis and into the XY plane. The resulting graphs , seen in F igure 2 10 , for each coil, can be curve fit to determine the Larmor precession in degrees per Amp and Angstrom. Next is aligning the nutators relative to the pr ecession coils. From here the nutators are rotated together while keeping them perpendicular and applying a 180° Larmor precession, or a spin flip, in one of the coils. In this orientation the polarization should be zero or near zero when the transverse gu ide field of the incident nutator is parallel to the field produced by the coil being used. The same process for 3 is applied but to the second precession coil for the final step. SANPA Calibration The calibration process for SANPA is more thorough and r obust albeit lengthier. The calibration procedure introduced by Tosado aims to fully understand neutron optics and polarization by measuring the polarization maintained and generated in every direction, so that a sphere of polarization can be generated. Fr om the measured sphere it can be determined if the components have any misalignment, tilt, distortions, or are simply not functioning as intended. The procedure follows these steps [18] : Calibration begins by determining the effectiveness of the magnetic shielding using a custom cryogenic flux magnetometer in place of the sample. Once the shield has cooled to its nominal temperature, external magnetic fields are applied and the response of the magnetometer is measured and compared to a base line measurement taking when there is no magnetic shielding. The process is detailed in F igure 2 10 where it can be seen

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54 when the niobium passes through its superconducting temperature and the magnetic f ield drops significantly. The following step is to determine the effectiveness of the longitudinal rotator and the scattering alignment rotator. These devices adjust the neutron polarization in the YZ plane in accordance with the coordinate system shown in F igure 2 6 . This step is similar to step 2 of the CRYOPAD calibration procedure where the data collected can be fit to sinuisdal curves and the Larmor precession can be calculated. Next is to align the axis of incidence with the axis of measurement. This operation is similar to how CRYOPAD aligns their nutators but is a bit more involved. Here polarization is adjusted and rotated through three orthogonal planes, the XY, XZ, and ZY planes. From this data circles of polarization are generated and fit so that a misalignment angle can be calculated shown in F igure 2 11 . After any misalignment is resolved, the following step measures a series of vectors that represent the neutron polarization throughout the entire three dimensional space. This is where a sphere of polarization is generated seen in F igure 2 12 . From this sphere further imperfections can be revealed and then corrected for. Mentioned in the calibration were steps to correct for misalignment. CRYOPAD takes similar steps and tuning and aligning the d evice does not deviate from the standard of what is done so far. The main difference comes from the presentation of the circles and when the sphere is measured. This gives much more insight into the polarization control of the device and can signify other issues that may not arise from the standard calibration procedures. This insight will be discussed further in C hapter 3 when analyzing some of the calibration data measured from the SNP device. Additionally, w hen correcting for the misalignment or distorti on it is important to also determine whether this is coming from the equipment or if this is related to noise [19] . The error should be considered when comparing the measured data against the theoretical circles due to counting statistics and the fact that each measured point is the result of several measured counts so the error gets compounded. If the deviation of the measured data is larger than the noise then aberrations from the setup are to be considered [19] . Distortions or misalignment can be adjuste d

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55 with the applied current to the devices or by adjusting the position of the equipment [19] . This is an iterative process and for further details one can refer to the work done by Tosado [19] .

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56 Figure 2 1. A) Nutator as fabricated, B) 3 D model of the nutator, C) exploded view of the nutator Goniometer Solenoid Rotation Cylinder Pole Pieces A) B) C)

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57 Figure 2 2. COMSOL simulation results for the nutator only. The magnetic flux density shown reveals that the center has a field of about 18 G, sufficient for providing an adiabatic transition

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58 Figure 2 3. COMSOL simulation results for the magnetic field lines which indicate that the field between the poles and in the center is nearly vertical

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59 Figure 2 4. COMSOL simulation results showing the transition of the field lines as they cross through the solenoid and enter the nutator

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60 Figure 2 5 . A) Precession region enclosed in the vacuum chamber, with the Meissner screens on, with the Meissner screens off . B ) Precession region where (1) Copper cover, (2) YBCO fi lm, (3) Mu metal ring, (4) Side YBCO films on copper framing, (5) Copper base for YBCO superconducting tape, (6) Copper frame A) B)

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61 Figure 2 6. Schematic showing the directions and planes each component can rotate the neutron polarization into. y Z x z x z x y x y x

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62 Figure 2 7 . A) Zero Field Chamber as manufactured without the mu metal cradles attached. B) 3 D model of the entire ZFC, note the small gap between the concentric cylinders that required the use of a removable window. C) Exploded view of the ZFC A) B) C)

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63 Figure 2 representative of the actual rotation stage.

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64 Figure 2 9. A) Sinusoidal nutator scan data from CRYOPAD. B ) Precession scan data from CRYOPAD A) B)

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65 Figure 2 10 . Measurement of the shielding factor with increasing shield temperature. Black curve: The shielding factor in decibels. Blue dashed curve: The beginning of magnetic field penetration through the shield at about 8 K. Red dashed curve: Superconducting transit ion of the shield at about 9 K. Tosado 2019.

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66 Figure 2 11 . Calibration circles from SANPA

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67 Figure 2 1 2 . Calibration spheres from SANPA

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68 CHAPTER 3 EXPERIMENTAL MEASUREMENTS The SNP device was fit and set to run on beamline HB 1 at the high flux isotope r eactor (HFIR) as seen in Figure 3 1 , however; due to the shutdown of HFIR the device was unable to be tested there at th e time. In order to test the prototype a c ollaboration was negotiated and setup with to use a beam port at the University of Missouri Research Reactor (MURR). Helmuth Kaizer kindly allowed me and Ryan Dadisman to tour the facility, examine the beam port, and take measurements. Using the measuremen ts, a table and rail system was designed and then fabricated . The entire device was packed into a cargo van and driven over to MURR. Over the course of the drive only one compressor and computer suffered some damage that would later be repaired when taken back to ORNL. Since HFIR was still unable to operate after the testing at MURR some modifications were made to both the device supports and the HYSPEC beamline for testing at HYSPEC. Barry Winn, kindly allowed the use of HYSPEC and through a group effort t he device would be able to be mounted and tested. Fortunately, at ORNL and at HYSPEC the infrastrcutre exists to allow for the use of the orange cryostat so the testing would include real samples that would be cooled down, rather than the test solenoid. Th e samples measured at HYSPEC included a silicon, manganese oxide (MnO), and Bismuth Ferrite (B i F eO 3 ). The performance of the device could be more thoroughly tested a nd understood. After the testing at HYSPEC there was some minor testing at CG 4B. At the ti me, this beamline did not have the infrastructure to support the full capabilities of the device, it could only run with no scattering angles and without the orange cryostat. From this testing preparations were made to finally run on the PTAX at HFIR, HB 1 . At HB 1 the entire device was refit and

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69 the same samples that were measured on HYSPEC were used with the addition of CYCO ( . University of Missouri Research Reactor The initial online test of the device was on the Double Axis Powder Diffractometer 2X C at the University of Missouri Research Reactor (MURR). The beamline was reconfigured to fit the SNP device. The neutron wavelength coming from the beam port is 4.3 Angstroms. On the incoming side of the neutrons was a V cavity supermirr or polarizer followed by the device and S bender supermirror was used as the analyzer. Figure 3 2 shows a schematic and how the final beam setup looks, alongside a schematic showing each component in order. Solenoid Sample Due to the limitations in infrastructure at MURR the orange cryostat could not be used, and the downstream arm was fixed so no scattering of samples could be done . Since the orange cryostat was unable to be used regular samples could not be tested ; a test solenoid was created and placed into the zero field chamber at an angle , approximately 30°, to act as a sample, demonstrated in Figure 3 3 . The solenoid itself is encased in mu metal to limit its magnetic field and generates a horizontal field. Placing the solenoid within the zero field chamber at an angle would affect the transmission of the neutron polarization. That is within the direct beam where the polarization matrix that would be measured would be: because one of the terms becomes null and drops fro m the equation. Experimental Discussion After the device was placed onto the beamline calibration for the device would begin. The calibration process for this experiment followed the CRYOPAD procedure. The device was

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70 vacuum pumped and then the CCRs were t urned on which brought the temperature to a nominal 26K on the upstream precession arm and 34k on the downstream precession arm. The first measurements made were transmission measurements with the direct beam . These measurements were the alignment of the nutator and the alignment of the precession regions. Figure 3 4 shows one of the precession scans. The scans came out to what would be expected and indicate that there was very little additional polarization rotation in the zero field chamber. Table 3 1 shows the measurements taken which show the devices ability to maintain polarization. The next set of measurements were performed by placing a solenoid in the zero field chamber to serve as a sample. T he polarization matrix components were measured, thes e results are also shown in Table 3 1 . Spallation Neutron Source, ORNL Figure 3 5 shows the full setup on HYSPEC. It is important to note that HYSPEC was used as a triple axis spectrometer and not as the time of flight instrument that it is . For this setu p HYSPEC has a polarizing mode, so the v cavity previously used at MURR was not needed and used the Heusler crystal as a polarizer [26] . Instead of the V cavity at the beginning of the beam, a Mezzei flipper was added to the upstream side to act as both a guide field and to flip the neutron polarization. Also, the analyzer used was not the analyzer that HYSPEC normally uses but the one. This analyzer is old and only had a small channel where it would function properly. The magnetic field from this analyzer was strong enough to couple to the device without any guide fields. Samples Measured As mentioned previously, use of the orange cryostat enables the testing of the device to be done with different types of samples. The first sample used was silicon.

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71 Manga nese Oxide , MnO, is the first sample to be measured with our device that has a magnetic peak. It is a paramagnetic material with a rocksalt/face centered cubic lattice that undergoes an anti ferromagnetic transition below its magnetic ordering temperature of 118K [27,28,29] . The unit cell for its magnetic structure is twice the size of the unit cell for its nuclear structure so the magnetic propagation vector is k = [½, ½, ½] [27,28,29] . In the (1,1,1) planes the spins are aligned parallel and the spin dir ection is reversed in adjacent (1,1,1) planes [27,28,29] . In our measurements for MnO we measured both a nuclear peak and a magnetic peak. The nuclear peak is in the (1,1,1) plane and the magnetic peak in the (½, ½, ½) plane. Since, the magnetic unti cell is larger than the nuclear cell, the scattering would be purely magnetic [27,28,29] . Bismuth ferrite was the next and last sample measured. This material has been widely studied and the magnetic structure is known to be G type antiferromagnetic [30,31] . It has antiferromagnetic ordering at temperatures below 643 K [30,31] . The scattering plane was the (½, ½, ½) plane. For this material a nuclear peak was not measured due to some time constraints and the desire to measure more magnetic peaks with the device. Experimental Discussion Once the device was successfully mounted, the procedure for calibration was run . However, this time during the precession scan for the downstream/measurement region, the current being applied to the coils would break superconductivity after about 6 amps. Figures 3 6 and 3 7 show the data that was measured and representative of good calibration data, with the exception that one of the precession regions could not be scanned as large as the other. Since the device was al ready cooled and time was limited, the decision to press on and to use as much data from the scan while also referencing data from the upstream/control region since the two regions are nearly identical.

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72 Data was first collected using the direct beam to understand what the initial polarization would look like. The Heusler crystals that are used on HYPSEC for polarization mode do not have the same polarizing power that the V cavity used in MURR had. These measurements are also dow n to show that the device is capable of maintaining the polarization and also guiding it into the different directions. Following the direct beam measurement was a measurement using silicon, as mentioned earlier calibration can also be done with a crystal ( like silicon ) that has a strong nuclear scattering peak. These two measurements should be comparable and equal to each other, the data shown suggests that the device is functioning as it should , despite not having a whole dataset for the downstream preces sion region. After these measurements were done the silicon sample was removed and the MnO sample was placed and rotated to measure its nuclear peak first , followed by BiFeO 3 . The polarization matrix data collected can be viewed in Table 3 2. The nuclear p eak was measured to compare with the silicon nuclear peak and the direct beam. The measured polarization for the nuclear peak is noticeably decreased compared to the silicon crystal. This could be due to the lower scattering intensity . The instrument was t hen rotated to measure the magnetic peak of MnO . It was during this measurement where the polarization measured had some significant deviations from what was expected. Specifically, each component measured was okay until the P xz component. Here the polariz ation was too high and suggests that some polarization was being maintained when it should not have. This could be due to some misalignment of the device or distortion caused by the magnetic fields through the device. In the next sample BiFeO 3, this same l evel of polarization can be measured as well as a higher than normal level at the P yx component. When looking back at the polarization data for MnO the P yx component is also quite high but

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73 acceptable. Ultimately it suggests that there is some unexpected po larization occurring and the device needs to be optimized further. Recall that the upstream precession region had an electronic failure and could only be operated within a certain range of current. The upstream precession region is responsible for adjusti ng the polarization into the X direction, or the YX plane. Since the data for the downstream region was used in its place assuming identical components, it is possible that the upstream precession region was not correctly rotating into the X direction and either over or under rotating the polarization. This would give the polarization direction some value in the Y direction or its Y vector component which leads to some polarization being maintained in the Y direction which can more properly explain the incr eased polarization for the P xy component. When considering the additional polarization for the P yx component, the upstream precession region would be turned off and would not affect this value. This could be a result of the nutator being maligned though unlikely, or the downstream precession also not rotating the polarization perfectly. Another factor to consider with the imprecision of the results is that in this setup the sample stick and holder did not have any tilt stages. The sample stick is intende d to have two ATTOCUBE® tilt stages on the end in order to adjust the sample holder. It is possible that the alignment of the sample was not perfectly aligned and could have led to some of the neutron polarization being adjusted into unintended directions as a result. After the experiment was run, both CCRs were opened up and an investigation to modes of failure was carried out. It was quickly determined there was a problem with the clamping connection for the superconducting YBCO tape. Seen in F igure 3 8, there should be two screws that are clamping the connection and there was only one in place. The clamped connection was

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74 redesigned to be a bit larger and encompass the entire length of the protruding YBCO tape. Offline tests proved that this fix was suffic ient and the precession regions could handle upwards of 20 amps of current (this type of current would likely not be needed for SNP experiments). After making this adjustment and also making some modifications to the support structures the device was set t o finally be tested at HFIR. H igh Flux Isotope Reactor, ORNL The device was setup at HB 1 in its entirety seen in F igure 3 9. Some additional support structures were built and added to provide more stability to the design . Despite some of the preparation there were still some issues that occurred during this experimental runtime. Initially, the experiment began similarly to before and calibration started with the direct beam. These measurements were fairly straight forward and went as expected. When the sa mple stick was placed into the orange cryostat some issues came up. Samples Measured As mentioned previously, use of the orange cryostat enables the testing of the device to be done with different types of samples. The first sample used was silicon , followed by bismuth ferrite, BiFeO 3 , and lastly CYCO, . CYCO, is an interesting material since it exhibits many body effects and can have 1D ferromagnetic structures [32,33] . Like the other materia ls, CYCO has an antiferromagnetic ordering below its transition temperature. For CYCO the transition occurs at T n = 29 K [32,33] . For CYCO the magnetic peak was viewed along the (0,0,1) plane and the nuclear peak along the (0,0,2) plane. Experimental Disc ussion The calibration process began similarly to what was done previously on HYSPEC and by following the procedure that CRYOPAD uses. Measurements with the direct beam were straight forward and quick to preserve as much time to be used when measuring with samples. However,

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75 once the orange cryostat was in place and the measurements for silicon began the calibration data suggested something was highly irregular . The data should be smooth and fit to a sinusoidal curve but it can clearly be seen in F igure 3 10 there is some interference with the neutron polarization. At this point, a thorough analysis of the polarization data was done as well as an investigation on the beam setup itself. The sample stick was removed and the orange cryostat was also removed. Th e initial consideration was that a nearby experiment, on beamline HB 1A, using a high magnetic field (> 5 T) could be causing an interference. Some measurements using a flux gate were taken at several positions near the zero field chamber and within the ze ro field chamber. These measurements revealed that within the zero field chamber the magnetic field was less than 1 microTesla but near the entrance to the upstream tunnel, the magnetic field rose to about 12 microTesla. The setup was then rotated back to 0 degrees and magnetic field measurements revealed that the previous measurements were not the same. The measured magnetic field at the zero field chamber was about 2 microTesla and at the entrance it rose to about 19 microTesla. It is not exactly well kn own where the stray field was coming from or why it varied depending on the position of the scattering arm. In an effort to reduce these effects a compensation coil on the upstream mu metal tunnel was made and extra mu metal foil was added onto various com ponents of the device. The added compensation coil was able to reduce the field at the mu metal tunnel from 19 microTesla to 3 mircoTesla and the extra mu metal foil reduced the zero field chamber back to approximately 1 microTesla. Polarization measuremen ts were done to find an optimal current setting for the compensation coil in addition to the measurements taken by hand. Once the current was tuned in the compensation coil the beamline

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76 was setup again and the measuremnets began again. Unfortunately, the p olarization data was still irregular and suggested something was still wrong with the setup or the equipment. The device was then dismantled and measurements using the flux gate and a Hull probe were taken. After an exhausting search it was found that at the sample stick there was some residual magnetization from a screw that was used to hold the sample mount. Using the Hull probe it had a fie ld between 12 20 Gauss depending on the location. This screw along with the heater on the end of the sample stick, that also had some residual magnetic field associated with it, were removed. After removing these components and assembling the beam again th e device ran as expected and the data fit a sinusoidal curve seen in F igure 3 11 . Calibration data and polarization measurements from the silicon were taken and the experiment was able to progress to the other samples. The sinusoidal curves for the calibra tion can be seen in F igures 3 12 and 3 13. In this instance, examining the curves it is seen that there is some slight misalignment that had to be corrected for since the curves were not entirely centered about 0. The same sample BiFeO 3 was measured as we ll as another sample CYCO. The data from these show that the device is functioning better than it was on HYSPEC . The measured polarization matrices can be viewed in Table 3 3 . The data suggests that the corrected precession regions were now rotating the po larization to the right degree and the device is overall working to better precision. CG4B After the device was run on HFIR it was made clear that stray magnetic field can have a significant impact on the operation of the SNP device. The device was next p laced onto CG4B for some extensive calibration testing seen in F igure 3 14 . This would be the time when the calibration procedure followed that for SANPA and a sphere of polarization was measured using

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77 the device in several different configurations. Each c onfiguration had a different set of magnetic shielding around the device ranging from less shielding to more. The initial measurements were taken with no shielding around the precession region, the mu metal cradles were removed. The results are shown in F igures 3 1 5 and 3 1 6 . Where in F igure 3 1 3 the data can be represented as three circles combined to give the impression of a sphere. In this calib ration process the data should look like a sphere and the measurements taken suggest the device is working and calibrated well with some exception. It can be seen that there is some tilt in the XY plane. This tilt in the XY plane is one of the examples th at can be used to describe the usefulness from the SANPA calibration mentioned back in C hapter 2. Essentially, the CRYOPAD calibration data would show that the polarization is slightly decreased but overall would be good, since the data is still circular. However, the SANPA calibration also shows that while the polarization is good it is not optimized since there is a tilt. The device was then shielded as fully as it was when it was run on HB 1, this includes the mu metal cradles and the extra mu metal foi l that was used for the device. The measurements taken shown that the overall performance of the device decreased with the added on shielding. An explanation for why this occurs is given in the following chapter but essentially the shielding protects from stray fields but the fields from the device itself were shown to cause some issues. Following the measurements of the fully shielded device, some measurements were then taken with only half of the mu metal shielding this was guided by simulations done in COMSOL that will be spoken of in detail in the next chapter.

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78 Figure 3 1. Test fit and device setup on HB 1, the only missing component is the orange cryostat and associated cabl es

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79 Figure 3 2. Schematic representation of the beam setup along with the actual setup. (1) V cavity polarizer, (2) control nutator, (3) control precession region , (4) zero field chamber, (5) measurement precession region , (6) measurement nutator, (7) S bender analyzer, (8) detector X Z Neutron path 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8

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80 Figure 3 3. A ) Test solenoid created to act as a sample for experiments at MURR, it was wound with aluminum wire and encased with some Mu metal. B ) Top view showing the placement of the solenoid within the zero field ch amber, note the angle displacement which is approximately 30° Neutron Zero Field Chamber Solenoid A ) B )

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81 Figure 3 4. Precession scan showing expected sinusoidal curve

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82 Table 3 1. MURR theoretical polarization matrices vs their measured polarization matrices Theoretical Polarization Matrix Measured Polarization Matrix Direct Beam Test Solenoid

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83 Figure 3 5. Full SNP setup at HYSPEC

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84 Figure 3 6. Precession scan for the upstream/ control precession region. Due to an error the scan could not cycle through the entire range of current without losing superconductivity 0 5000 10000 15000 20000 25000 30000 -8 -6 -4 -2 0 2 4 6 8 Detector Counts Current (Amps) Upstream precession scan counts fit

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85 Figure 3 7. Precession scan for the downstream/ measurement precession region. The data was able to be fit and also used for the upstream/control precession region 0 5000 10000 15000 20000 25000 30000 -8 -6 -4 -2 0 2 4 6 8 Detector Counts Current (Amps) Downstream precession scan counts fit

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86 Figure 3 8. The clamp for the YBCO tape was incorrectly attached and led to a poor electrical and thermal contact. As a result of the weak connection, at higher applied current the YBCO would lose superconductivity

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87 Table 3 2. HYSPEC theoretical polarization matrices vs their measured polarization matrices Sample Peak Type Theoretical Polarization Matrix Measured Polarization Matrix Silicon Crystal Nuclear MnO Nuclear MnO Magnetic BiFeO 3 Magnetic

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88 Figure 3 9. Full SNP setup at HFIR beamline HB 1

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89 Figure 3 10. Nutator scan data when sample stick containing silicon sample was added to the sample environment. Note, that the data should resemble a parabola but has many features that suggest something is affecting the polarization and spin transport. -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 0 50 100 150 200 250 300 350 400 Polarization Degrees Nutator Scan

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90 Figure 3 1 1 . 360 nutator scan of the silicon sample that has been corrected -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 0 50 100 150 200 250 300 350 400 Polarization Degrees Nutator Scan

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91 Figure 3 1 2 . Upstream/ Control precession region scan 0 10000 20000 30000 40000 50000 60000 -10 -8 -6 -4 -2 0 2 4 6 8 10 Detector Counts Current (Amps) Upstream Precession Scan Measured Counts Sinusoidal Fit

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92 Figure 3 1 3 . Downstream/m easurement precession scan 0 10000 20000 30000 40000 50000 60000 -10 -8 -6 -4 -2 0 2 4 6 8 10 Detector Counts Current (Amps) Downstream Precession Scan Measured Counts Sinusoidal Fit

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93 Table 3 3. HFIR theoretical polarization matrices vs. their measured polarization matrices Sample Peak Type Theoretical Polarization Matrix Measured Polarization Matrix Silicon Nuclear Bismuth Ferrite BiFeO 3 Magnetic CYCO Nuclear CYCO Magnetic

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94 Figure 3 1 4 . Full SNP setup on CG 4B

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95 Figure 3 1 5 . Calibration data from the SNP device where all great circles are shown together to represent the sphere

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96 Figure 3 1 6 . Calibration data of each plane

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97 CHAPTER 4 ADVANCING SNP The device presented is capable of performing SNP; however, it can be improved. To improve the device we consider the generation of magnetic fields, the magnetic shielding, and then the operational limits of the device . The calibration data indicates that the magnetic fields generated from the device are suff icient for adjusting the polarization. This same data also indicates slight misalignment but the simulation s cannot replicate the details that would cause this. S imulations of the components reveal unif orm magnetic fields the simulations are more useful for understanding the magnetic shielding therefore, a ny misalignment will have to be compensated for by understanding calibration data. T he magnetic shielding can also be improved . Using the Multiphysics software COMSOL ® , the magnetic fields of each component were modeled and simulated. The model used for simulation was first generated in the software Inventor ® then imported into COMSOL ® for simulation. T he simulations done with COMSOL ® show h ow the magnetic fields interact around the device and the existing shielding. To validate the simulation results, some measurements were taken with hull probes at key spacings the center of the nutator, the center of the solenoid, and the sample position . The values from the hull probes were in agreement with the simulation results. Apart from running simulations to understand the magnetic shielding, the magnetic shielding itself is going through some redesigns. Specifically, the central ZFC chamber has been redesigned and it was simulated to determine that it is sufficient. Final ly, we consider operational limits . One operational constrain is how long it takes for the device takes measurements. Different neutron optics or improvements to the device can help

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98 make the measurements quicker. Another constraint pertains to the portability of the device and its overall size and associated hardware. The device itself has also shown to be highly portable and able to be mounted onto several beamlines, but can thi s further be improved to fit on more beamlines? Magnetic Shielding SNP simulations reveal how the magnetic fields interact with the Mu metal. I n the previous design it was found that the ZFC had some limitations. During operation the window that covered th e gap would have to be removed and replaced . The tunnel on the measurement or downstream side would have a collision issue with this window as different scattering angles were measured. Designs for a new chamber were developed and shown in F igure 4 1 . In t his design the scattering tunnel rotates without needing the window to be removed and replaced because t he window itself can rotate. To be sure the newly designed chamber would still work as intended , a simulation in COMSOL was don e by placing the chamber in a static magnetic field. The results of the simulation can be seen in F igure 4 2 . O utside of the chamber the field ranges from 10 20 G and within the chamber the field is much less than 1 mG. More detailed s imulations including the remaining components of the device were also done but will be shown later in the chapter. SNP S imulations . The entire device was simulated , with several of the magnetic fields turned on and oriented in different directions. From experimental testing we know the magnetic fields are strong enough to adjust the neutron polarization as needed. These simulations verify that the field strength is sufficient to maintain polarization and adjust the polarization direction , which was expected; but, m ore importantly it allows one to visualize the fields and how they connect and pass through the device . The results can be seen in F igure 4 3, showing excl usively the field lines as they pass through the device. Some points to consider about the data shown, is

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99 that the software begins iterating at a specific point and moves from there so the line density may appear asymmetric. Also, the field lines shown do not represent the magnitude of the field lines, merely the direction . This is particularly useful to see how the magnetic fields interact with the magnetic shielding, i.e. mu metal, of the SNP device. Since it is also crucial for SNP to have a zero field region for the neutron path, the simulations can determine how effective the shielding is or if the mu metal has become saturated. Recall, that the magnetic shielding for the device was created primarily with mu metal and then also with Meissner screens. W ithin COMSOL ® the material properties for mu metal are accounted for and the properties can be adjusted to reflect the behavior of mu metal, most notably the magnetic permeability. Mu metal has a magnetic permeability within the range of 100,000 to 150,000 depending on the vendor and exposure to magnetic field . This value can be set in COMSO L ® and is necessary for calculating and running the study. The Meissner screens can be set via the magnetic insulation boundary in COMSOL ®. The simulation data revealed how the magnetic fields interact with the shielding material. Looking at F igure 4 4 a , the field lines from the nutator enter the first mu metal region at the precession region, go over the first Meissner screen , pass over the top and bottom of the precessi on region , and extend into the zero field chamber for a distance. These field lines do not represent the magnitude of the field which is shown in F igure 4 4b. From F igure 4 4b the field at the surface of the Meissner screen drops off to about 2 G and on th e opposite end is 0.02 mG. In this case the field at the surface of the Meissner screen becomes a littler lower than would be preferred. Addit io nal simulations were done by adjusting the mu metal shielding , f irst, using only half of the mu metal around the precession region and then without using any mu metal shielding around the precession region. Looking at F igure 4 5 a , where the design removes half of

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100 the mu metal entrance , t he field lines no longer bunch up or collect at the entrance to the precession region. From 4 5b the field at the surface of the Meissner screen is 10 G and the field on the opposite end is 0.2 mG. An additional advantage for this configuration is that the nutator could be placed closer to the vacuum assembly, this helps the field lines extend to the surface of the YBCO film. Also, t he field lines do extend over the Meissner screen still but to a lesser extent. Figure 4 6 a shows the case where the entire mu metal cradle is removed. In this case the field lines look similarly to the field lines with only the half mu metal cradle assembled. The issue in this design however is the field strength at the opposite end of the precession region or the entrance of th e zero field tunnel. From 4 6b the field at the surface is also 10 G but the field on the opposite end is about 1 G. This is a feature that is undesirable, because the magnetic field protruding into the zero field chamber will affect the overall polarizati on state of the neutrons. It may account for some of the inaccuracies that were measured during the experiments. Operational Limitations After considering the magnetic fields and magnetic shielding, there are other factors that can be optimized for the dev ice. As an example nutator reorientation speed was improved overtime by changing the motor parameters and then replacing the motors altogether. Initially, the motors on the goniometers were set to a speed that would complete a full rotation in about 15 min utes reducing the time the device can be measuring . When first testing the device speed of streamlined and understood, it became an important factor to consider. With in SPICE the motor configuration parameters were adjusted to push the motors and the rotation time was reduced to about 5 minutes for a full rotation, a significant improvement Then the motors were replaced and the rotation time was reduced to about 50 sec onds.

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101 From here, a design was proposed to further improve on this rotation time. The device only needs to rotate 90° if the current power supplies are bipolar. By using a combination of the 90° rotations and adjusting which current, (+/ ), is sent to the electromagnets, the device can fully function and record all necessary data. A design is proposed to further improve the rotation speed by adding an additional discrete 90° rotation , which can already be achieved in about 15 seconds. The design, seen in F i gure 4 7 , will operate by having two concentric cylinders where one is free to rotate by 90° within the outer cylinder. The outer cylinder will attach onto the goniometer and can be used to function as normal. The inner cylinder will have a mounting arm, w here it can be connected to a cam and pneumatic drive so that the 90° rotation can be much quicker than 15 seconds. This can increase the reconfiguration speed and further optimize the device. A high speed alternative to rotating the nutator and in collabo ration with Tosado, a different approach is proposed . Replacing nutation with a double precession system to guide the neutron polarization in every direction. Recall, that CRYOCUP has two precession regions separated by a zero field tunnel. By modifying th e orientation of the precession regions so that one is perpendicular to the other rather than parallel, the double precession system could theoretically guide the polarization in every direction. So that as the neutrons pass through CRYOCUP, they would see a horizontal field, a zero field region, and then a vertical field. The idea for a double precession region can also be seen in MUPAD and their sets of precession coils. In an approach similar to how MUPAD operates, using two sets of precession coils, the neutron polarization can also be guided into every direction. A design was developed, fabricated, and ready to be tested. This decouples the counting time from nutator rotation time by using this

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102 r and precession region that the SNP device currently uses. The design can be seen in F igure 4 8 where it can be seen two precession regions from the initial device are used and placed orthogonal to each other with a short zero field tunnel in between them. T he magnetic fields they generate are perpendicular to each other , with one field along the ve rtical direction and the other field is in the horizontal/ transverse direction. By using each precessor in tandem, the neutron polarization can theoretically be guided into every direction. Since this can all be done simply by adjusting the electrical curr ents the response time would be much quicker than the rotation time of the nutator and further optimize the SNP device. Another operational constraint is the overall size of the device. The overall length of the device is approximately 105 cm long without any additional coupling guide fields, apertures, or neutron optics. When in use, a dditional components are needed , so the overall length is a factor to consider when installing onto a beam. These other components include a neutron monitor, an aperture on e ach end of the device (to columnize/characterize the beam), and magnetic guide fields on both ends of the device. The design proposed moving forward aims to reduce the overall length by reducing the length of the tunnels on the zero field chamber. By doin g so, the length was reduced from 105 cm long to approximately 86 cm long. However, this came with its own challenges . B y reducing the length of the tunnels this meant that the precession regoin and nutator would move closer to the center of the device and they interfered with the orange cryostat and its associated support structure. So the structure and shape of the vacuum chamber was also redesigned to remove the interference .

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103 Figure 4 9 shows what the proposed redesign looks like. The vacuum chamber and associated mu metal shielding h ave a more box like structure. The precession region will be in the narrow region of the vacuum chamber whereas the CCR has been moved off to the side to avoid any collision issues. The precession region will be connected to the CCR with copper braiding and the frame itself will be mounted onto an insulating frame made from G10 to avoid cooling the alumnium from the outer vacuum chamber . The vacuum chamber and associated mu metal shielding can be seen in an exploded view in F igure 4 10 . The mu metal shielding has panels that overlap at the connections with the exception of the top and bottom edges. Additionally, since previous simulations proved that the nutator field can penetrate quite far into the zero field region an extra mu metal shield was added in the vacuum chamber to surround the precession region. Since the device was shortened and the mu metal shielding had changed shaped a couple of questions arose: How do the magnetic fields look around the device? H ow far does th e nutator field penetrate into the zero field region? Simulations were run using COMSOL for several different cases. The first case used a small mu metal window similar to the size of the zero field tunnel (about 5 cm diamater), the second case a larger mu metal window about the size of the pole piece spacing (about 11 cm diameter), and the last case without the inner mu metal shield. The results of these simulations provide unambiguous bias for the last case . In the first case , seen in F igure 4 11 , the simulation showed that by having such a small window , the magnetic field has a difficult time entering the zero field region at all. At the surface of the YBCO film the magnetic field was less than 1 G, compared to the current design where it is anywh ere from 5 10 G. This type of shielding may have an undesirable effect on the spin transport since the field is quite curved along the entrance of the window. The second case, seen

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104 in F igure 4 12 , the larger window does allow for the magnetic field to more easily enter the zero field region, however; the inner mu metal layer prevents the field from getting to the surface of the YBCO. The field strength at the YBCO surface is still less than 1 G but the field itself has a more uniform and vertical structure. The final case , F igure 4 13 demonstrates a preferred scenario. The field can penetrate to the surface of the YBCO film and not beyond that. At the surface of the YBCO film the field strength is about 8 G and on the other side of the precession region and the zero field chamber center it is much less than 1 m G. From these simulations an ideal mu metal structure can be designed and it can also demonstrate that, at least theoretically, a smaller SNP device will function. Moving from being able to fit the device onto multiple beamlines, a proposed design to shor ten the overall length of the device to fit on yet, even more beamlines, is it possible to fit the an SNP device onto a different instrument altogether? Some preliminary work on developing an SNP device onto HYSPEC has been done. Concept Design for HYSPEC The SNP device has proven to work and fits on a variety of beamlines/beam ports. While this SNP device was mounted onto HYSPEC, HYSPEC was not used as a wide angle time of flight instrument, and instead operated more as a diffractometer . To date, no SNP de vice has ever been develop for a wide angle time of flight instrument. The existing device is being modified to be able to mount onto HYSPEC and function in the time of flight mode. A concept design has been proposed and is waiting to be manufactured and t ested. The upstream portion of the device does not need to be changed but the downstream side and the zero field chamber would need to be heavily modified to function on HYSPEC. One of the biggest difficulties with operating on HYSPEC as a time of flight i nstrument is handling the different neutron wavelengths. On HYSPEC, the incident beam is monochromatic but the

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105 scattered beam is polychromatic. The magnetic fields used in the precession field and the nutator are tuned to specific neutron wavelengths in or der to control the neutron polarization. For the case of a non adiabatic transition with precession coils there are many difficulties. For non adiabatic transitions, if the field remains constant neutrons of varying wavelength will all precess at different rates around the magnetic field, so that rotation becomes a function of final energy and time of flight . Instead, the first prototype for HYSPEC will not incorporate a non adiabatic region on the scattered beam side. Rather, the idea is to rely more heavi ly on an adiabatic transition with a YBCO film separating the zero field region and the magnetic guide fields after it. As a result, the analysis for this design will also require a careful approach. The incident polarization will have a lab frame with car tesian coordinates where x is along the beam path, z is in the vertical direction and y perpendicular to both completing the coordinate system. Similarly the scattered beam will also have a lab frame with cartesian coordinates, where x i is normal to the YB CO film, z i again in the vertical direction, and y i completing the coordinate system. By measuring the polarization of the scattered beam with the polarization aligned in x s , y s , z s then, theoretically, all 9 components of the polarizatoin matrix can be ob tained: ( 4 1 ) Or also expressed as: ( 4 2 ) The neutron wavelengths in the scattered beam can be determined from the time of flight data and each neutron wavelength will correspond to a unique scattering angle that can also be

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106 determined from the detector position . With this information , it is possi ble to determine the scattering vector Q , which can then be defined into the traditional SNP frame . From here, the incident polarization and scattered polarization can be defined into this frame through the use of rotation matrices. ( 4 3 ) (4 4) With and defined as the rotation matrices to rotate the initial polarization and the scattered polarization into the traditional SNP frame. Where and are: (4 4) (4 5) Where is the angle between x and x in and the angle between x and x s . Combining equations 4 3 and 4 4 with 4 2 one arrive s at equation 4 6: (4 6) From this equation and comparing it to equation 4 7: (4 6)

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107 Where equation 4 7 represents the polarization changes in the tradition SNP frame, it can then be seen that the polarization matrix in the traditional SNP frame can be calculated. Moreover, by doing the rotation operation to each scattered direction, the p olarization matrix for each neutron wavelength can also be calculated. However, there is some difficulty in measuring all these components. The scattered beam side will incorporate a large and flat Meissner screen to cover the wide angle region of the sc attered beam, it will be approximately 30 cm long. In order to create this Meissner screen three YBCO films will be used since they cannot be manufacted at that size. They will be approximately 10x15 cm with the same thickness as the previous YBCO films. T wo of them will be placed side by side with the 3 rd YBCO film behind it to ensure direct mechanical contact of YBCO films . In previous studies done by Wang, this was shown to still be effective as a Meissner screen. This screen will separate the scattered beam within the zero field region and the magnetic fields on the scattered beam side. Guide fields will be oriented in order to adiabatically guide the polarization into the desired direction. Due to the Meissner effect the only measureably magnetic compon ents at the YBCO surface will be parallel to the film surface. A schematic of how the setup will look can be seen in F igure 4 14. The x s and z s directions on the scattered coordinated frame are both parallel to the YBCO film so that if any field was direct ion along the x s and z s directions then the field on the YBCO film will also be in that direction. Therefore, the measurement of the and the components become more straightforward. The issue arises when trying to measure the due to its perpendicular orientation to the YBCO surface. The solution for this involves rotating the YBCO film around the z axis for a total for ± 30 ° , this can be seen in F igure 4 14 . The choice of 30° comes from a physical limitation of the components that would fit on the beamline and be

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108 capapble of such a rotation. When the YBCO film is rotated 30° or 30° , a new lab frame will be developed for each rotation. This rotation along wi th the adjusting lab frame would lead to the equations: (4 8) (4 9) By rearranging the equatoins it can be seen that to solve for is now a possibility. This would then allow for all components in the scattered polarization to be measured. This type of analysis and modification to the device can provide the pathway for SNP to be actualized on HYSPEC. The design still needs more time and thought before it is manufactured but the overall plan is being set. A rough concept can be seen in F igure 4 1 5 .

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109 Figure 4 1. A) Redesign of the zero field chamber, B) an exploded view of the zero field chamber. It can be seen that the rotating window comes in two different parts that each attach and connect into each other B ) A)

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110 Figure 4 2 . COMSOL simulation results showing the redesigned zero field chamber. The mu metal chamber was placed in a static magnetic field

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111 Figure 4 3 . COMSOL simulation results of the entire device. Important to recall that the field lines impl y only direction and not magnitude. The field in the zero field chamber is below 1 mG.

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112 Figure 4 4 . COMSOL simulation results showing the nutator and mu metal cradle. A) Notice how some of the field lines from the nutator protrude over the precession region and into the zero field chamber B) The strength o f the fields generated from the solenoid and pole pieces, notice the shielding effect from the mu metal entrance A) B)

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113 Figure 4 5 . COMSOL simulation results showing the nutator and o nly half of the mu metal cradle . A) Important to note the difference in how the field lines approach the surface of the YBCO film, not as bunched, and also do not extend as much over the precession region. B) The field strength from the nutator now extends to the surface of the YBCO film at a more reliable level A) B)

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114 Figure 4 6. COMSOL simulation results showing the nutator and none of the mu metal cradle. A) The difference here is that the field lines have a stronger intrusion into the zero field tunnel compared to the half mu meta l configuration. B) Field strength shown reaches Meissner screen but also starts to extend past the second Meissner screen A) B)

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115 Figure 4 7. A) 3 D CAD model of the modified nutator, B) An exploded view of the modified nutator setup. The block extending from the second cylinder is where the cam and pneumatic drive will attach to quickly rotate th e pole pieces along the groove by 90° A) B)

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116 Figure 4 8. A) 3 D CAD model of the double precession region, B) An exploded view of the precession region. It can be more clearly seen h ow one of the precessors is simply rotated and the additional components that connect the two precessors, alongside with the mu metal tunnel A) B)

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117 Figure 4 9 . 3 D CAD model of the redesigned SNP device. It can be seen that the device length has been decreased and that the vacuum chamber has been redesigned so that the CCR does not collide with the center structure.

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118 Figure 4 10 . 3 D exploded view of the redesign vacuum assembly and the associated mu metal paneling to act as s hielding. The precession will attach to the top of the vacuum assembly and be thermally isolated with an insulator like G10, it will connect to the CCR with copper braiding. Also note the inner mu metal shielding within the vacuum assembly surrounding the precession region.

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119 Figure 4 11 . COMSOL simulation results for the shorter SNP redesign. Here it can be seen that the window size acts as a barrier for the field lines to enter the cradle so that at the YBCO film surface the field is within the mG range.

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120 Figure 4 12 . COMSOL simulation results for the shorte r SNP redesign. Here the window size was enlarged and it can be seen that magnetic flux does enter the cradle but the inner chamber also acts to prevent magnetic flux from entering. The magnetic flux at the YBCO film surface is less than 1 G.

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121 Figure 4 1 3 . COMSOL simulation results for the shorter SNP redesign. Here the inner mu metal shielding was removed and it can be seen that there is magnetic flux at the YBCO film surface of about 12 G. Additionally, the field on the opposite end of the YBCO film is a little more noticeable at 0.2 G.

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122 Figure 4 14. Top view schematic of the setup for SNP on HYSPEC. As mentioned previously the initial components of nutator and precession region will remain the same but more importantly the YBCO film downstream will be able to rotate. Also note the positions of the different lab frames, and that a new lab frame will be made when the YBCO film rotates. x in Nutator Precession Region

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123 Figure 4 1 5 . 3 D CAD model of the mock up for setting the SNP device onto HYSPEC. Note the vacuum assembly also has the CCR off to the side so that the Meissner screen inside can be as close to the sample position as possible

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124 CHAPTER 5 CONCLUSION Based off the ex perimental testing of the SNP device it was shown that it can perform and measure the polarization tensor of a sample to deduce its magnetic structure. The degrees of inaccuracy have been investigated and the device continues to be thoroughly examined and improved as well as developing better neutron optics to run and include within the device. The components within the device have been shown to have full control over the neutron polarization and the capability to adjust the polarization direction into any direction. Further improvements on the device for use on a time of flight instrument have not been tested and will be simulated to guide the overall design. Since the simulations have proven to have agreement with the measured results, it is expected that simulations of the device on a time of flight instrument can help realize the design and lead to fabrication. The inaccuracy of the SNP device is thought to have arisen from the magnetic field reaching over the Meissner shield and into the zero field cham ber. Removal of the magnetic shield to allow the field lines to move differently has shown to improve some of the accuracy within the calibration testing that was done on beamline CG4B.

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125 LIST OF REFERENCES 1. Press release. NobelPrize.org. Nobel Prize Outreach AB 2023. Thu. 11 May 2023. https://www.nobelprize.org/prizes/physics/1994/press release/ 2. Pynn, Roger. "Neutron scattering." Los Alamos Science 19 (1990). 3. Chatterji, T. Neutron Scattering from Magnetic Material (Elsevier, 2005). 4. Ressouche, E., 2014. Polarized neutron diffraction. École thématique de la Société Française de la Neutronique 13, 02002.. doi:10.1051/sfn/20141302002 5. Blume, M. (1963). Polarization effects in the magnetic elastic scattering of slow neutrons. Physical Review , 130 (5), 1670 6. Lelievre Berna, E., et al. "Precision manipulation of the neutron polarisation vector." Phys ica B: Condensed Matter 397.1 2 (2007): 120 124. 7. . Scattering, 7 Sept. 2017, www.oxfordneutronschool.org/2017/Lectures/Nilsen%20 %20Polarized%20Neutron%20Scattering.pdf. 8. Maldonado V elázquez, M., Barrón Palos, L., Crawford, C., Snow, W.M., 2017. Magnetic field devices for neutron spin transport and manipulation in precise neutron spin rotation measurements. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, S pectrometers, Detectors and Associated Equipment 854, 127 133.. doi:10.1016/j.nima.2017.02.0 9. Schärpf, O., and H. Capellmann. "The XYZ difference method with polarized neutrons and the separation of coherent, spin incoherent, and magnetic scattering cross s ections in a multidetector." Physica Status Solidi A (Applied Research);(Germany) 135.2 (1993). 10. Schweika, Werner. "XYZ polarisation analysis of diffuse magnetic neutron scattering from single crystals." Journal of Physics: Conference Series. Vol. 211. No. 1. IOP Publishing, 2010. 11. Moon, R.M., Riste, T., Koehler, W.C., 1969. Polarization Analysis of Thermal Neutron Scattering. Physical Review 181, 920 931.. https://doi.org/10.1103/physrev.181.920 12. Tasset, F. "Zero field neutron polarimetry." Physica B: Condens ed Matter 156 (1989): 627 630. 13. Takeda, Masayasu, et al. "CRYOPAD on the triple axis spectrometer TAS 1 at JAERI." Physica B: Condensed Matter 356.1 4 (2005): 136 140. 14. ML The Review of scientific instruments 87 10 (2016): 105108 .

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126 15. Bourgeat Lami, E & Fouilloux, P & Geffray, B & Gibert, Y & Kakurai, Kazuhisa & Kernavanois, N & Longuet, B & Mantegezza, F & Nakamura, Misuzu & Pujol, S & Regnault , Louis Pierre & Tasset, Francis & Takeda, M & Thomas, M & Tonon, X & Lelièvre Berna, Eddy. (2005). Advances in spherical neutron polarimetry with Cryopad. Physica B Condensed Matter. 356. 131 135. 10.1016/j.physb.2004.10.063. 16. Janoschek, Marc, et al. "Sphe rical neutron polarimetry with MuPAD." Physica B: Condensed Matter 397.1 2 (2007): 125 130. 17. Hutanu, V., et al. "MuPAD: Test at the hot single crystal diffractometer HEiDi at FRM II." Nuclear Instruments and Methods in Physics Research Section A: Accelerato rs, Spectrometers, Detectors and Associated Equipment 612.1 (2009): 155 160. 18. Tosado, J., Chen, W.C., Gnewuch, S., Hasaan, T., Dax, T., Rodriguez, E.E., 2019. Small angle neutron polarimetry apparatus (SANPA): Development at the NIST Center for Neutron Rese arch. Review of Scientific Instruments 90, 063303.. doi:10.1063/1.5091110 19. Tosado, J., Chen, W., & Rodriguez, E. E. (2019, October). A strategy for handling aberration in Spherical Neutron Polarimetry. In Journal of Physics: Conference Series (Vol. 1316, No . 1, p. 012015). IOP Publishing. 20. Wang, T., Parnell, S.R., Hamilton, W.A., Li, F., Washington, A.L., Baxter, D.V., Pynn, R., 2016. Compact spherical neutron polarimeter using high Tc YBCO films. Review of Scientific Instruments 87, 033901.. doi:10.1063/1.49 43254 21. Wang, T., Silva, N., Jiang, C.Y., Agrawal, H.K., Li, F., Debeer Schmitt, L., Masaaki, M., Ruff, J., Pynn, R., Tong, X., Winn, B., 2019. Developing Wide Angle Spherical Neutron Polarimetry at Oak Ridge National Laboratory. Journal of Physics: Conferen ce Series 1316, 012014.. doi:10.1088/1742 6596/1316/1/012014 22. Pappas, C., et al. "Chiral paramagnetic skyrmion like phase in MnSi." Physical review letters 102.19 (2009): 197202. 23. Janoschek 24. Brown, P. J., et al. "Antiferromagnetism in CuO studied by neutron polarimetry." Journal of Physics: Condensed Matter 3.23 (1991): 4281. 25. Regnault, L. P., Boullie r, C., & Lorenzo, J. E. Polarized neutron investigation of magnetic ordering and spin dynamics in BaCo 2 (AsO 4 ) 2 frustrated honeycomb lattice magnet. Heliyon , 4 (1), e00507(2018).. https://doi.org/10.1016/j.heliyon.2018.e00507 26. Zaliznyak, Igor A., et al. "Pola rized neutron scattering on HYSPEC: the HYbrid SPECtrometer at SNS." Journal of Physics: Conference Series. Vol. 862. No. 1. IOP Publishing, 2017.

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127 27. Shaked, H., Faber, J., Hitterman, R.L., 1988. ow temperature magnetic structure of mno: a high resolution n eutron diffraction study. Physical Review B 38, 11901 11903.. https://doi.org/10.1103/physrevb.38.11901 28. Paddison , J.A.M., Gutmann, M.J., Stewart, J.R., Tucker, M.G., Dove, M.T., Keen, D.A., Goodwin, A.L., 2018. Magnetic structure of paramagnetic MnO. Physical Review B 97.. https://doi.org/10.1103/physrevb.97.014429 29. Roth, W.L., 1958. Magnetic Structures of MnO, FeO, CoO, and NiO. Physical Review 110, 1333 1341.. https://doi.org/10.1103/physrev.110.1333 30. Béa, H., Bibes, M., Petit, S., Kreisel, J., Barthélémy, A., 2007. Structural distortion and magnetism of BiFeO3epitaxial thin films: A Raman spectroscopy and neutron di ffraction study. Philosophical Magazine Letters 87, 165 174.. https://doi.org/10.1080/09500830701235802 31. Sosnowska, Izabela, T. Peterlin Neumaier, and E. Steichele. "Spiral magnetic ordering in bismuth ferrite." Journal of Physics C: Solid State Physics 15.23 (1982): 4835. 32. Matsuda, M., Ma, J., Garlea, V.O., Ito, T., Yamaguchi, H., Oka, K., Drechsler, S. L., Yadav, R., Hozoi, L., Rosner, H., Schumann, R., Kuzian, R.O., Nishimoto, S., 2019. Highly dispersive magnons with spin gap like features in the frustrated ferromagneticS=12. Physical Review B 100.. https://doi.org/10.1103/physrevb.100.104415 33. Kuzian, R. O., et al. "Ca 2 Y 2 Cu 5 O 10: The first frustrated quasi 1d ferromagnet close to criticality." Physical Review Letters 109.11 (2012): 117207.

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128 BIOGRAPHICAL SKETCH Nicolas Silva attended the University of Florida for h is Bachelor of S cience degree and from here became acquainted with Dr. Yong Yang. After some discussion with Dr. Yang, Silva pursued a PhD program and began research into the degradation mechanisms of spent nuclear fuel. However, Silva had to take some tim e away from the program and in that time was offered a position at Oak Ridge National Laboratory. At ORNL , Silva would become acquainted with several staff members who would later encourage him to incorporate his new work into this doctoral dissertation.