Towards the theory of ferrimagnetism

TL;DR

This paper develops a theoretical framework for ferrimagnetism involving two sublattices, explaining phase transitions and magnon effects, and successfully reproduces experimental magnetization curves including compensation points.

Contribution

A modified spin-wave theory is introduced to describe two phases in ferrimagnetism, capturing complex magnon interactions and matching experimental data.

Findings

Identifies two magnetic phases separated by a transition at temperature T*

Reproduces known magnetization curves, including compensation points

Provides a theoretical basis for understanding magnon suppression effects

Abstract

Two-sublattice ferrimagnet, with spin-$s_1$ operators $\bf{S_{1i}}$ at the sublattice $A$ site and spin-$s_2$ operators $\bf{S_{2i}}$ at the sublattice $B$ site, is considered. The magnon of the system, the transversal fluctuation of the total magnetization, is a complicate mixture of the transversal fluctuations of the sublattice $A$ and $B$ spins. As a result, the magnons' fluctuations suppress in a different way the magnetic orders of the $A$ and $B$ sublattices and one obtains two phases. At low temperature $(0,T^*)$ the magnetic orders of the $A$ and $B$ spins contribute to the magnetization of the system, while at the high temperature $(T^*,T_N)$, the magnetic order of the spins with a weaker intra-sublattice exchange is suppressed by magnon fluctuations, and only the spins with stronger intra-sublattice exchange has non-zero spontaneous magnetization. The $T^*$ transition is a transition between two spin-ordered phases in contrast to the transition from spin-ordered state to disordered state ($T_N$-transition). There is no additional symmetry breaking, and the Goldstone boson has a ferromagnetic dispersion in both phases. A modified spin-wave theory is developed to describe the two phases. All known Neel's anomalous $M(T)$ curves are reproduced, in particular that with "compensation point". The theoretical curves are compared with experimental ones for sulpho-spinel $MnCr2S_{4-x}Se_{x}$ and rare earth iron garnets.