MARMOT: magnetism, anisotropy, and more, using the relativistic disordered local moment picture at finite temperature

Abstract

We present MARMOT, a hybrid Python/FORTRAN implementation of the disordered local moment picture within multiple scattering density-functional theory. MARMOT takes atom-centred, scalar-relativistic potentials and constructs an effective medium (within the coherent potential approximation) to describe the disordered magnetic moment orientations at finite temperature. By solving the single-site scattering problem fully relativistically, spin–orbit effects are included, allowing the magnetocrystalline anisotropy to be calculated. Magnetic transition temperatures, spin and orbital moments, the density-of-states, and analytical parameterizations of the magnetic potential energy surface can also be calculated. Here, we describe the theory and practical implementation of MARMOT, and demonstrate its use by calculating Curie temperatures, magnetizations and anisotropies of bcc Fe, GdFe2 and YCo5.

Quantifying temperature-induced magnetic disorder effects on the anisotropy of MnBi

“…The methodology employed to calculate the MCA at finite temperature [9,34,38] has been comprehensively reviewed in a recent article [35], so only the key points will be presented here. The first step is to perform a self-consistent, scalar-relativistic DFT calculation of the fully-ordered (ferromagnetic) state.…”

“…The second step is to use these atom-centred potentials as inputs to DFT-DLM calculations. The MARMOT code [35] is used to perform these calculations as a postprocessing step. Here, the single-site scattering problem is solved fully relativistically [34] and magnetic disorder is treated at the level of the coherent potential approximation (CPA) [36].…”

“…Numerically the approach carries a significant advantage, since it focuses on calculating one small number directly (the torque) rather than relying on the difference between two large numbers (the free energy) [41]. Reciprocal space was sampled using an adaptive algorithm [43] and the parameters controlling the complex energy integral [35] were carefully checked to ensure numerical convergence of the MCA and Weiss fields. The electronic temperature appearing in the Fermi-Dirac function was fixed to 300 K, as discussed in Appendix B.…”

“…The DFT-DLM calculations also provide access to the spin and orbital magnetic moments, calculated as integrals of the Green's function [35]. However, these moments are not then used to update the atom-centred potentials, i.e.…”

“…Treating magnetic disorder within the relativistic densityfunctional theory implementation of the disordered local moment picture (DFT-DLM) [9,34], the temperature evolution of the magnetic order parameters and the angular dependence of the free energy have been calculated from first principles, allowing the extraction of the MCA as a function of T . In particular, the study takes advantage of recent methodological developments [35] which enable access to the individual anisotropy constants K 1 , K 2 and K 3 , thus going beyond previous studies which obtained the unresolved quantity K tot . Zero-T calculations have also been performed to show the influence of hole doping on the anisotropy constants, and also to compare different implementations of DFT, either in Korringa-Kohn-Rostocker (KKR) multiple-scattering theory [36] or in the plane wave and pseudopotential formalism [37].…”