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

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 Neel 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 alpha phase of iron. Initial testing of our MSD model is done using a 0 K parametrization of the Neel interaction model. After this, we examine how individual Neel parameters impact the B1 and B2 magnetostrictive coefficients using a moment-independent delta sensitivity analysis. The results from this study are then used to initialize a genetic algorithm optimization which explores the Neel 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 B1 and B2 , only the genetic algorithm optimized results can capture the second peak in the B1 magnetostrictive coefficient which occurs near approximately 800 K.