Statistical and analytical approaches to finite-temperature magnetic properties of the compound Sm Fe12

To investigate the magnetic properties of Sm Fe₁₂ , 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 4 f 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 Sm Fe₁₂ 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 K_{1 (2 )} appears due to an increase in the CF potential denoted by the parameter A₂⁰«r²» (A₄⁰«r⁴» ) caused by hybridization between 3 d -electrons of Fe on the 8 i (8 j ) site and 5 d and 6 p valence electrons on the Sm site. It is verified that the requirement for the appearance of FOMP is given as -K₂<K₁<-6 K₂ .