Origin of perpendicular magnetic anisotropy in amorphous rare-earth–transition-metal alloys

Determine the dominant microscopic mechanism(s) responsible for perpendicular magnetic anisotropy in amorphous rare-earth–transition-metal ferrimagnetic alloys (e.g., Tb–Co and Gd–Co), distinguishing among single-ion anisotropy, magnetostrictive (stress-induced) anisotropy, shape anisotropy arising from macroscopic structural inhomogeneities, and pair-ordering-driven dipolar anisotropy, and ascertain the relative contributions of the transition-metal and rare-earth sublattices to the observed anisotropy.

Background

The paper models ferrimagnets as two antiferromagnetically coupled layers and discusses the sources of perpendicular magnetic anisotropy (PMA) in amorphous rare-earth–transition-metal alloys. While Tb-containing alloys often attribute PMA to single-ion anisotropy, Gd-based systems—despite Gd’s spherical 4f orbital—also exhibit PMA, suggesting that additional mechanisms may contribute and that both sublattices could play roles.

Given this uncertainty, the authors assume equal anisotropy energy in both sublattices for simulations, noting that equivalent results can be achieved even if anisotropy is present only in the rare-earth layer. Clarifying the microscopic origin(s) of PMA and the sublattice contributions remains essential for accurate modeling and interpretation of experimental results.

References

The origin of perpendicular magnetic anisotropy in amorphous alloys remains not fully understood, but several mechanisms have been proposed [40] [41] [42] [43]: single-ion anisotropy, stress-induced (magnetostrictive) anisotropy, shape anisotropy arising from macroscopic structural inhomogeneities (e.g., columnar growth), and pair ordering due to non-uniform atomic distributions, where dipole- dipole interactions define a preferred axis.

— Modeling Ferrimagnets in MuMax3: Temperature-Dependent Skyrmion Dynamics  (2509.21289 - Antonov et al., 25 Sep 2025) in Section 2, Description of the equivalent model