Bridging the atomistic picture of magnetism to larger length scales is an important challenge for the design and discovery of technologically relevant magnetic materials. We present a multiscale computational approach for obtaining magnetic exchange constants and their derived continuum properties from density functional theory, DFT+U+J. The Heisenberg exchange constants are highly sensitive to two important prerequisites: the magnetic ground-state, as well as Hubbard U and Hund J values. The on-site U/J corrections are calculated using a custom linear response workflow that we’ve built within the atomate code framework. Additionally, we have implemented and benchmarked a “source-free” exchange-correlation magnetic field in VASP, which is implemented using a fully parallelized fast Poisson solver.
This source-free functional, paired with a custom particle swarm optimization strategy, SpinPSO, has resulted in improved agreement with a variety of magnetic ground-states that were measured using neutron diffraction. The custom U and J values and optimized spin moment ground-state are used as inputs to the calculation of exchange constants using VASP+Wannier90 and TB2J via the single-particle Green’s function approach. Equipped with calculated exchange constants, we study the finite temperature behavior using a custom Monte Carlo code, which is MPI and OpenMP parallelized and written in Cython. Additionally, we present a general approach for obtaining the continuum Ginzburg Landau (GL) free energy functional from the microscopic Hamiltonian. Starting from this functional, we probe how microstructure influences hysteresis using a custom Python-based micromagnetic code, which is also parallelized using MPI. This ground-up computational approach will allow for the discovery of magnetic materials with technological applications ranging from spintronics to cost-effective magnetocaloric materials for magnetic refrigeration.
