  Describing the (a) electronic and magnetic properties (EMP) of
antiferromagnetic or paramagnetic phases of compounds generally requires the
knowledge of (b) the spin configurations and lattice structure (SCLS) of such
phases at a given temperature. Indeed, studying the coupling between (a) and
(b) has been an outstanding challenge in the theory of magnetism. The
traditional approach to electronic phases of matter has generally focused on
solving the problem of EMP regarding the SCLS as a spectator degree of freedom
(DOF). Yet, it has been recognized that EMP of a compound generally respond
self-consistently to changes in SCLS and vice versa. We construct here a
practical, density functional theory (DFT)-based approach that provides the
SCLS as a function of temperature, involving the description of spin, lattice,
and spin-lattice dynamics of different magnetic phases. We distinguish three
Levels of dynamics: (I) dynamics of the spin DOF treated via noncollinear
Heisenberg Monte-Carlo with exchange energies from DFT, (II) dynamics of the
lattice DOF treated by ab initio molecular dynamics (AIMD) employing a fixed
spin configuration from Level I at the simulated temperature, and (III)
coupling of spin and lattice dynamics via Landau-Lifshitz-Gilbert spin dynamics
combined with AIMD. Such SCLS at each of the three levels are used as inputs to
DFT supercell calculations, providing the EMP at each temperature. The results
of this sequence include electronic band structures, band gaps, density of
states, as well as the statistical distribution of local moments and the
short-range order parameters, each as a function of temperature. Using NiO as a
test case, we address the separability of the DOF in magnetic insulators for a
minimal description of electronic and magnetic properties, demonstrating that
inclusion of spin dynamics and, to some level, lattice dynamics is enough to
explain the EMP.
