Developing Spherical Neutron Polarimetry for wide-angle time-of-flight neutron source

1. Developing Spherical Neutron Polarimetry for wide-angle time-of-flight neutron source Tianhao (Radian) Wang1,3 B. Winn1, T. Wang1,3, N. Silva1, F. Li1, R. Pynn1,2 , Chenyang (Peter) Jiang1 1. Oak Ridge National Laboratory (ORNL) Neutron Technologies Division Neutron Science Division 2. Indiana University Bloomington 3. China Spallation Neutron Source (CSNS)

2. Table of content Spherical Neutron Polarimetry (SNP) concept and strategy Limitation of SNP on wide-angle time-of-flight measurement Potential theoretical solution to SNP limitation

3. Spherical Neutron Polarimetry Principle Txx Txx Pix Pfx Pfx Pix Txy Txy Txz Txz • Advantages: • Access to off-diagonal tensor component • Decouple sample training field with neutron guiding field • Requirements: • Proper zero magnetic field shielding • Full-range spin manipulation Tyx Tyx Pfy Pfy 0 0 Tyy Tyy Tyz Tyz = = · · Tzx Tzx Pfz Pfz 0 0 Tzy Tzy Tzz Tzz Geometry of Spherical Neutron Polarimetry Geometry of ordinary polarization analysis

4. Acquiring well-defined non-adiabatic transition through superconductor • Isolated region achieved by a combination of: • Meissner Shield (Niobium, YBCO) • Mu-Metal Photo of CryoCUP device Schematic of a small angle SNP device (CryoCUP)

5. Difficulty in applying SNP to time-flight beamline • Combination of adiabatic transition and precession • Adiabatic transition determine the polar angle (ɵ) • Controlled precession determine the azimuthal angle (φ) Traditional SNP neutron polarization manipulation setup Traditional SNP neutron polarization manipulation strategy • Difficulty for applying SNP on wide-angle time-of-flight neutron source • Simultaneous wide-angle measurement requires neutron polarization at different direction based on Q • Precession manipulation act differently for neutron with different wavelength

6. Use rotation matrix to measure Blume tensor and generated polarization z, z1’,z2' z Blume equation Pf = TBlume ∙ Pi + Pg Sample y Pf: final polarization Pi: initial polarization Pg: polarization generated from sample Tblume: Blume Tensor z,z1' y1' x2' x y2' x1' Q2 y z,z2' Q1 y1’ Laboratory coordinate measurement steps x1' x • 1. Measure initial and final polarization in laboratory coordinate. • 2. Determine Blume tensor and generated polarization in laboratory coordinate • 3. Calculate Tblume and Pg in the scattering coordinate based on the angle between the two coordinate systems. y x2' y2’ x y axis along incoming neutron direction z axis points vertically up x axis orthogonal to y and z axis x-y-z laboratory coordinate: x'-y’-z’ scattering coordinate: x' axis along scattering vector Q z' axis points vertically up y’ axis orthogonal to x’ and z’ axis

7. Applying SNP measurement for wide-angle time-of-flight neutron • Measurement in Laboratory coordinate remains the same direction through different scattering direction. • Allows simultaneous wide-angle measurement • Measure polarization using adiabatic transition • No precession needed for polarization manipulation, eliminated wavelength dependency of polarization manipulation z, z1’,z2' z Sample y z,z1' y1' x2' x y2' x1' Q2 y z,z2' Q1 y1’ Incoming Neutron x1' x y Meissner shield x2' y2’ Guide field B x Outgoing Neutrons General Algorithm Adiabatic transition Rθin∙Pf = Rθin∙TBlume ∙Rθout-1 ∙Rθout ∙ Pi + Rθin∙ Pg P’i T’Blume P’g P’f

8. Instrument realization of the theoretical solution • Technical realization: Measure neutron polarization along two non-parallel Meissner plain adjacent to the zero-field sample chamber • Questions to answer before realization: • Measure alongtwoorthogonal plane • Covering large scattering angle • Polarization data and tensor data extraction • measurement error propagation • Off scattering plane signal Meissner shield 1 Meissner shield 1 Zero field B=0 Zero field B=0 y y 90° 90° Zero field B=0 x x Guide field B Guide field B Meissner shield 2 Meissner shield 2 Concept of measurement along two orthogonal direction

9. Conclusion • Spherical Neutron Polarimetry technique requires neutron polarization control, achieved through superconductor Meissner screen and controlled adiabatic transition and precession • Simultaneous Wide-angle measurement and polychromatic neutron limits the application of SNP on time-of-flight neutron beamline • Using calculation based on rotation matrix between laboratory coordinate and scattering coordinate, we can decouple measurement direction and the scattering direction, which eliminate the limitation on wide-angle and time-of-flight SNP measurement. • Realizing such measurement still requires a lot instrument development work. The polarization development group and Thank you for your attention This work was supported by the U.S. Department of Energy (DOE), Office of Science (OS), Basic Energy Sciences (BES), Materials Sciences and Engineering Division (sample design, fabrication, and physical property characterization) and by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory (ORNL), managed by UT-Battelle, LLC, for the U. S. DOE (PNR). The research at ORNL’s High Flux Isotope Reactor was sponsored by the Scientific User Facilities Division, BES, U.S. DOE.