Statistical and analytical approaches to finite-temperature magnetic properties of the compound SmFe12

Abstract

To investigate the magnetic properties of $\mathrm{Sm}{\mathrm{Fe}}_{12}$, we construct an effective spin model, where magnetic moments, crystal-field (CF) parameters, and exchange fields at 0 K are determined by first-principles calculations. Finite-temperature magnetic properties are investigated by using this model. We further develop an analytical method with strong mixing of states with a different quantum number of angular momentum $J$ ($J$-mixing), which is caused by a strong exchange field acting on the spin component of $4f$ electrons. Comparing our analytical results with those calculated by Boltzmann statistics, we clarify that the previous analytical studies for Sm transition-metal compounds overestimate the $J$-mixing effects. The present method enables us to perform a quantitative analysis of the temperature dependence of magnetic anisotropy (MA) with high reliability. The analytical method with model approximations reveals that the $J$-mixing caused by the exchange field increases the spin angular momentum, which enhances the absolute value of the orbital angular momentum and MA constants via spin-orbit interaction. It is also clarified that these $J$-mixing effects remain even above room temperature. Magnetization of $\mathrm{Sm}{\mathrm{Fe}}_{12}$ shows a peculiar field dependence known as the first-order magnetization process (FOMP), where the magnetization shows an abrupt change at a certain magnetic field. The result of the analysis shows that the origin of FOMP is attributed to competitive MA constants between positive ${K}_{1}$ and negative ${K}_{2}$. The sign of ${K}_{1(2)}$ appears due to an increase in the CF potential denoted by the parameter ${A}_{2}^{0}\ensuremath{\langle}{r}^{2}\ensuremath{\rangle}$ (${A}_{4}^{0}\ensuremath{\langle}{r}^{4}\ensuremath{\rangle}$) caused by hybridization between $3d$-electrons of Fe on the $8i$ ($8j$) site and $5d$ and $6p$ valence electrons on the Sm site. It is verified that the requirement for the appearance of FOMP is given as $\ensuremath{-}{K}_{2}<{K}_{1}<\ensuremath{-}6{K}_{2}$.