Tensor description of X-ray magnetic dichroism at the Fe L _2,3-edges of Fe₃O₄

Abstract

A procedure to build the optical conductivity tensor that describes the full magneto-optical response of the system from experimental measurements is presented. Applied to the Fe L 2,3-edge of a 38.85 nm Fe3O4/SrTiO3 (001) thin-film, it is shown that the computed polarization dependence using the conductivity tensor is in excellent agreement with that experimentally measured. Furthermore, the magnetic field angular dependence is discussed using a set of fundamental spectra expanded on spherical harmonics. It is shown that the convergence of this expansion depends on the details of the ground state of the system in question and in particular on the valence-state spin–orbit coupling. While a cubic expansion up to the third order explains the angular-dependent X-ray magnetic linear dichroism of Fe3+ well, higher-order terms are required for Fe2+ when the orbital moment is not quenched.

Origin of Perpendicular Magnetic Anisotropy in Co$_x$Fe$_{3-x}$O$_{4+δ}$ Thin Films Studied by X-ray Magnetic Circular and Linear Dichroisms

“…In comparison with the previous first-principles calculations of CFO, the values of U = 5 eV are also plausible from the viewpoints of LFM calculations [53][54][55][56]. The multiplet parameter values are almost similar to the previous report [57]. For the Co 2+ 3d 7 case, the t 2g states are split into two levels by the tetragonal distortion, and the lowest xy states are occupied by one of the down spin electrons.…”

Magnetic excitations beyond the single- and double-magnons

“…In symmetries lower than spherical, this expansion on spherical harmonics does not truncate at finite and the angular momentum of the electrons only is not a conserved quantum number in the crystals. We have shown in our previous work that including terms up to is sufficient to describe Fe 3+ ions in octahedral crystal field 26 . The expression is given in Eq.…”

Novel magnetic excitations beyond the single- and double-magnons

“…In symmetries lower than spherical, this expansion on spherical harmonics does not truncate at finite 𝑘 and the angular momentum of the electrons only is not a conserved quantum number in the crystals. We have shown in our previous work that including terms up to 𝑘 = 3 is sufficient to describe Fe 3+ ions in octahedral crystal field (23). The expression is given in equation ( 5) and involves terms up to the 3 rd order in spin leading to single, double and triple spin flip processes.…”