Exchange interactions and local-moment fluctuation corrections in ferromagnets at finite temperatures based on noncollinear density-functional calculations

Abstract

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 spontaneous 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 (FLAPW) 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.

Extended spin model in atomistic simulations of alloys

“…A large number of works have later been focused on the effect of longitudinal fluctuations in the description of the half metallic properties of the Heusler alloys [12][13][14][15] . Common to these works is the proposal of a model Hamiltonian that considers a separate treatment of the strongmoment components and the induced moment, such that it can effectively take into account the fluctuations on the induced moments by renormalization of the exchange interactions.…”

Higher-dimensional Wannier functions of multiparameter Hamiltonians

“…It thus follows that HΨ kλn = E kλn Ψ kλn in line with Eq. (8). Therefore, the product states satisfy the Schrödinger equation…”

“…In magnetic systems with non-collinear spin-spiral texture, the additional parameter λ can be identified with the spin-spiral vector q. The related energy E(q) serves to determine Heisenberg exchange constants [8]. Frequently, the ferromagnetic magnetization directionm plays the role of λ.…”

The antiphase boundary in half-metallic Heusler alloy Co2Fe(Al,Si): atomic structure, spin polarization reversal, and domain wall effects

“…First-principles calculations of exchange constants is not a trivial problem, however, it has been done for simplistic systems, including the bulk CMS. 33 By using the bulk values reported in Ref. 33 and performing DFT calculations for the energy differences between the AFM and FM states in the presence of APB, we have calculated the average strength of the exchange interactions across the APB defect.…”