Temperature dependence of magnetic anisotropy and magnetoelasticity from classical spin-lattice calculations

Here we present a classical molecular-spin dynamics (MSD) methodology that enables accurate computations of the temperature dependence of the magnetocrystalline anisotropy as well as magnetoelastic properties of magnetic materials. The nonmagnetic interactions are accounted for by a spectral neighbor analysis potential (SNAP) machine-learned interatomic potential, whereas the magnetoelastic contributions are accounted for using a combination of an extended Heisenberg Hamiltonian and a Néel pair interaction model, representing both the exchange interaction and spin-orbit-coupling effects, respectively. All magnetoelastic potential components are parameterized using a combination of first-principles and experimental data. Our framework is applied to the α phase of iron. Initial testing of our MSD model is done using a 0 K parametrization of the Néel interaction model. After this, we examine how individual Néel parameters impact the $B$₁ and $B$₂ magnetostrictive coefficients using a moment-independent δ sensitivity analysis. The results from this study are then used to initialize a genetic algorithm optimization which explores the Néel parameter phase space and tries to minimize the error in the B₁ and B₂ magnetostrictive coefficients in the range of 0–1200 K. Our results show that while both the 0 K and genetic algorithm optimized parametrization provide good experimental agreement for $B$₁ and $B$₂, only the genetic algorithm optimized results can capture the second peak in the $B$₁ magnetostrictive coefficient which occurs near approximately 800 K.