DFT-based description of spin dynamics, lattice dynamics, and spin-lattice dynamics of antiferromagnetic and paramagnetic phases at finite temperature

An outstanding issue in electronic structure of antiferromagnets (AFM) and paramagnets (PM) is obtaining a theoretical description of the finite temperature configurations of spins and ionic positions, to be used in (supercell) DFT calculations of the electronic and magnetic properties vs temperature. We demonstrate this for the respective phases in NiO thus introducing temperature into DFT through statistical mechanics for magnetic insulators. We define three Levels of dynamics for the investigation: (I) dynamics of the spin degrees of freedom via noncollinear Heisenberg Monte Carlo solved with exchange energies obtained from DFT Cluster Expansion (II) Using the foregoing spin configurations while allowing for a vibrating lattice using ab initio molecular dynamics (III) Coupling spin and lattice dynamics via Landau-Lifshitz-Gilbert spin dynamics plus ab initio molecular dynamics. Such spin-lattice configurations at each of the 3 levels vs temperature are used as input to DFT supercell calculations, from which we illustrate the distribution of magnetic moment, density of states, electronic band structure, band gaps, and short-range order parameters vs T. This opens the door for ab initio description of the coupling between different local degrees of freedom at all temperatures.