  While the ground state of magnetic materials is in general well described on
the basis of spin density functional theory (SDFT), the theoretical description
of finite-temperature and non-equilibrium properties require an extension
beyond the standard SDFT. Time-dependent SDFT (TD-SDFT), which give for example
access to dynamical properties are computationally very demanding and can
currently be hardly applied to complex solids. Here we focus on the alternative
approach based on the combination of a parameterized phenomenological spin
Hamiltonian and SDFT-based electronic structure calculations, giving access to
the dynamical and finite-temperature properties for example via spin-dynamics
simulations using the Landau-Lifshitz-Gilbert (LLG) equation or Monte Carlo
simulations. We present an overview on the various methods to calculate the
parameters of the various phenomenological Hamiltonians with an emphasis on the
KKR Green function method as one of the most flexible band structure methods
giving access to practically all relevant parameters. Concerning these, it is
crucial to account for the spin-orbit coupling (SOC) by performing relativistic
SDFT-based calculations as it plays a key role for magnetic anisotropy and
chiral exchange interactions represented by the DMI parameters in the spin
Hamiltonian. This concerns also the Gilbert damping parameters characterizing
magnetization dissipation in the LLG equation, chiral multispin interaction
parameters of the extended Heisenberg Hamiltonian, as well as spin-lattice
interaction parameters describing the interplay of spin and lattice dynamics
processes, for which an efficient computational scheme has been developed
recently by the present authors.

Materials Science