Small-angle neutron scattering by spatially inhomogeneous ferromagnets with a nonzero average uniaxial anisotropy

Abstract

Micromagnetic small-angle neutron scattering theory is well established for analyzing spin-misalignment scattering data of bulk ferromagnets. Here, this theory is extended to allow for a global uniaxial magnetic anisotropy (texture) of the material, in addition to the already included random zero-average local anisotropy. Macroscopic cross sections and spin-misalignment response functions are computed analytically for several practically relevant mutual anisotropy and external magnetic field orientations in both parallel and perpendicular scattering geometries for field magnitudes both above and below the rotational saturation. Some of these expressions are tested on published experimental data of magnetic-field-annealed Vitroperm and plastically deformed Ni, allowing determination of the corresponding global uniaxial anisotropy quality factors.

Magnetic neutron scattering from spherical nanoparticles with Neel surface anisotropy: Analytical treatment

“…The zero-order term ∝ j 1 (υ)/υ in (37) represents the form factor of a homogeneously magnetized sphere [2]. In the limiting case of an infinite applied magnetic field, which is equivalent to the limit κ β → ∞, the additional terms [second line in (37)] vanish [compare (25)] and the spherical form factor remains. On the other hand, if k s = 0, the additional terms also vanish because from the physical point of view, the Néel surface anisotropy cancels and from (18) we know that the coefficients a β νµ are linear in k s .…”

“…Progress in magnetic SANS theory [16][17][18][19][20][21][22][23][24][25] strongly suggests that for the analysis of experimental magnetic SANS data the spatial nanometer scale variation of the orientation and magnitude of the magnetization vector field must be taken into account, and that macrospinbased models-assuming a uniform magnetization-are not adequate. The starting point for a proper analysis of the scattering problem is a micromagnetic continuum expression for…”

“…[3][4][5][6][7][8][9][10][11][12][13][14][15] and references therein). The magnetic SANS data analysis largely relies on structural form-factor-models for the cross section, borrowed from nuclear SANS, which do not properly account for the existing spin inhomogeneity inside magnetic nanoparticles or nanomagnets (NM).Progress in magnetic SANS theory [16][17][18][19][20][21][22][23][24][25] strongly suggests that for the analysis of experimental magnetic SANS data the spatial nanometer scale variation of the orientation and magnitude of the magnetization vector field must be taken into account, and that macrospinbased models-assuming a uniform magnetization-are not adequate. The starting point for a proper analysis of the scattering problem is a micromagnetic continuum expression for…”

MuMag2022: a software tool for analyzing magnetic field dependent unpolarized small-angle neutron scattering data of bulk ferromagnets

“…This is achieved by varying H d , in addition to A, within the limits H min The micromagnetic SANS theory on which MuMag2022 is based assumes a statistically isotropic ferromagnetic material with random nanoscale variations in the magnitude and orientation of the magnetic anisotropy field as well as nanoscale spatial variations in the saturation magnetization. Recently, an extended SANS theory which takes into account a global uniaxial anisotropy (magnetic texture) has been developed (Zaporozhets et al, 2022). The corresponding Comparison between experiment and theory.…”

Magnetic neutron scattering from spherical nanoparticles with Neel surface anisotropy: Atomistic simulations

“…The magnetic SANS data analysis largely relies on structural form-factor-models for the cross section, borrowed from nuclear SANS, which do not properly account for the existing spin inhomogeneity inside a magnetic nanoparticle. Progress in magnetic SANS theory [25][26][27][28][29][30][31][32][33][34] strongly suggests that for the analysis of experimental magnetic SANS data, the spatial nanometer scale variation of the orientation and magnitude of the magnetization vector field must be taken into account, going beyond the macrospin-based models that assume a uniform magnetization.…”