Larmor Phase Correction of MIEZE

Abstract

Modulation of Intensity Emerging from Zero Effort (MIEZE) is a neutron resonant spin echo technique which allows one to measure the time correlation functions in materials by modulating the neutron beam using radio-frequency (RF) neutron spin flippers [1]. This technique avoids neutron spin manipulation between the sample and the detector, and thus could find applications in cases where the sample depolarizes the neutron beam. However, the finite sample size creates a variance in the neutron path length between the locations where scattering and detection happens, which causes the aberrations in Larmor phase. Such aberrations greatly limit the contrast in the intensity modulation towards long correlation times or large scattering angles. We propose two approaches to correct for such aberrations, which will enable us to extend those detection limits to longer times and larger angles. The first approach involves two additional magnetic Wollaston prisms (MWPs) in addition to the two RF flippers [2] and the second approach requires the physical tilting of the RF flippers in the primary spectrometer with respect to the beam direction [3]. Both approaches can shape the wave front of the intensity modulation at the sample position to compensate for the path variance from the sample and the detector. Therefore, the resolution function of MIEZE can be modified such that the contrast of the intensity modulation can be maximized at any scattering angle of interest. To correct for the phase aberration of MIEZE, both approaches involve the generation of a Larmor phase gradient along the transverse direction in the space domain. With such a phase gradient, it is possible to keep the wave front perpendicular to the scattering direction of interest. Therefore, the intensity modulation could propagate towards the detector with its wave front parallel to the detector surface, with which the aberration from the transverse size of the sample could be minimized, as shown in Figure 1. The employment of MWPs to steer the wave front of the intensity-modulated neutron beam is very similar to a phased array radar, which can create a beam of radio waves that can be electronically steered to point in different directions without moving the antennas. In this case, in additional to the traditional time focusing condition in MIEZE, i.e. (ω 2 (L 2 +L s ) = ω 1 (L 1 +L s )), the magnetic field required for the MWPs is determined by