Abstract
Using analytical expressions for the magnetization textures of thin submicron-sized magnetic cylinders in vortex state, we derive closed-form algebraic expressions for the ensuing small-angle neutron scattering (SANS) cross sections. Specifically, for the perpendicular and parallel scattering geometries, we have computed the cross sections for the case of small vortex-center displacements without formation of magnetic charges on the side faces of the cylinder. The results represent a significant qualitative and quantitative step forward in SANS-data analysis on isolated magnetic nanoparticle systems, which are commonly assumed to be homogeneously or stepwise-homogeneously magnetized. We suggest a way to extract the fine details of the magnetic vortex structure during the magnetization process from the SANS measurements in order to help resolving the long-standing question of the magnetic vortex displacement mode.
Highlights
We suggest a way to extract the fine details of the magnetic vortex structure during the magnetization process from the small-angle neutron scattering (SANS) measurements in order to help resolving the long-standing question of the magnetic vortex displacement mode
We have assumed a linear relationship between the vortex-center displacement and the applied magnetic field, which is valid in almost the entire range of the external field magnitudes, where the vortex state exists
The vortex is a low-field configuration, which implies that the subtraction of the saturated neutron scattering cross section significantly distorts the cross-section images
Summary
Magnetic SANS experiments are performed by subjecting the sample to a stream of neutrons (characterized by a wave vector k0) in the presence of an applied magnetic field H. The expressions for the unpolarized SANS cross sections of ferromagnetic media are summarized elsewhere[8] They are related to the Fourier transforms of the Cartesian components of the magnetization vector field M = {M X, M Y, M Z}; in particular, the total unpolarized nuclear and magnetic SANS cross section reads[33]: dΣ⊥ dΩ. The above SANS cross sections are functions of the scattering vector q, which is q⊥ in the perpendicular geometry and q|| in the parallel geometry. In order to study the magnetic effects only, one must eliminate the nuclear scattering contribution (∝ N 2) For this purpose, it is customary to consider the so-called spin-misalignment SANS cross section, dΣM = dΣ − dΣ. The saturation magnetization of the magnetic material itself is assumed to be constant, which is denoted by the symbol MS without tilde and without the argument q
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