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

To investigate the magnetic properties of SmFe12, 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 SmFe12 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 K1 and negative K2. The sign of K1(2) appears due to an increase in the CF potential denoted by the parameter A20(r2) (A40(r4)) 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 -K2<K1<-6K2.