We present a method of extracting the exchange parameters of the classical Heisenberg model from first-principles calculations of spin-spiral total energies based on density functional theory. The exchange parameters of the transition-metal monoxides
MnO and NiO are calculated and used to estimate magnetic properties such as transition temperatures and magnon energies. Furthermore we show how to relate the magnon energies directly to differences in spin-spiral total energies for systems containing an arbitrary number of magnetic sublattices. This provides a comparison between magnon energies using a finite number of exchange parameters and the infinite limit.
We explore the derivation of interatomic exchange interactions in ferromagnets within density-functional theory (DFT) and the mapping of DFT results onto a spin Hamiltonian. We delve into the problem of systems comprising atoms with strong spontaneou
s moments together with atoms with weak induced moments. All moments are considered as degrees of freedom, with the strong moments thermally fluctuating only in angle and the weak moments thermally fluctuating in angle and magnitude. We argue that a quadratic dependence of the energy on the weak local moments magnitude, which is a good approximation in many cases, allows for an elimination of the weak-moment degrees of freedom from the thermodynamic expressions in favor of a renormalization of the Heisenberg interactions among the strong moments. We show that the renormalization is valid at all temperatures accounting for the thermal fluctuations and resulting in temperature-independent renormalized interactions. These are shown to be the ones directly derived from total-energy DFT calculations by constraining the strong-moment directions, as is done e.g. in spin-spiral methods. We furthermore prove that within this framework the thermodynamics of the weak-moment subsystem, and in particular all correlation functions, can be derived as polynomials of the correlation functions of the strong-moment subsystem with coefficients that depend on the spin susceptibility and that can be calculated within DFT. These conclusions are rigorous under certain physical assumptions on the measure in the magnetic phase space. We implement the scheme in the full-potential linearized augmented plane wave method using the concept of spin-spiral states, considering applicable symmetry relations and the use of the magnetic force theorem. Our analytical results are corroborated by numerical calculations employing DFT and a Monte Carlo method.
The magnetic state of Nitrogen-doped MgO, with N substituting O at concentrations between 1% and the concentrated limit, is calculated with density-functional methods. The N atoms are found to be magnetic with a moment of 1 Bohr magneton per Nitrogen
atom and to interact ferromagnetically via the double exchange mechanism. The long-range magnetic order is established above a finite concentration of about 1.5% when the percolation threshold is reached. The Curie temperature increases linearly with the concentration, and is found to be about 30 K for 10% concentration. Besides the substitution of single Nitrogen atoms, also interstitial Nitrogen atoms, clusters of Nitrogen atoms and their structural relaxation on the magnetism are discussed. Possible scenarios of engineering a higher Curie temperature are analyzed, with the conclusion that an increase of the Curie temperature is difficult to achieve, requiring a particular attention to the choice of chemistry.
