Abstract
The presence of a large applied magnetic field removes the degeneracy of the vacuum energy states for spin-up and spin-down neutrons. For polarized neutron reflectometry, this must be included in the reference potential energy of the Schrödinger equation that is used to calculate the expected scattering from a magnetic layered structure. For samples with magnetization that is purely parallel or antiparallel to the applied field which defines the quantization axis, there is no mixing of the spin states (no spin-flip scattering) and so this additional potential is constant throughout the scattering region. When there is non-collinear magnetization in the sample, however, there will be significant scattering from one spin state into the other, and the reference potentials will differ between the incoming and outgoing wavefunctions, changing the angle and intensities of the scattering. The theory of the scattering and recommended experimental practices for this type of measurement are presented, as well as an example measurement.
Highlights
Polarized specular neutron reflectometry measurements require at least a small magnetic field to be applied throughout the measurement apparatus, in order to maintain a well defined neutron quantization axis
In real laboratory environments the magnetic field transition is not as abrupt as what is shown in Fig. 1, and the direction is not perfectly defined, though typically the applied magnetic field is realized in a small volume centered on the sample and the field gradient experienced by the probe neutron is, to first order, radial with respect to the sample
The reflectivity measurements were undertaken at the Polarized Beam Reflectometer instrument (PBR) at the NIST Center for Neutron Research, with a supermirror spin polarizer and analyzer and current-coil Mezei-type spin flippers for the incident and reflected beams
Summary
Polarized specular neutron reflectometry measurements require at least a small magnetic field to be applied throughout the measurement apparatus, in order to maintain a well defined neutron quantization axis. The reflectivity calculation formalism including the Zeeman term was briefly described by van de Kruijs et al (2000), Fitzsimmon et al (2006) and Liu et al (2011), but to our knowledge a detailed description of the calculation is not available in the literature, nor has such a calculation been incorporated into commonly used modeling software These shifts are not a major concern in many experiments (Liu et al, 2011) because the effect is significant only when there is both a large applied field and strong spin-flip scattering. We present the changes that need to be made to an existing commonly used computer algorithm (implemented in gepore.f ; Majkrzak et al, 2006) in order to calculate the scattering correctly, and we present recommended practices for performing the measurements when both the applied magnetic field H and the magnetization M are large and not parallel to each other. Some of the kinetic energy along z^ is traded for potential energy during a spin-flip process, so the earlier definitions do not apply in this circumstance, while Q remains strictly out of plane
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