Spin‐density functional theory: Some open problems and application to inhomogeneous Heisenberg models

Abstract

Spin-density-functional theory (SDFT) is the most widely implemented and applied formulation of density-functional theory. However, it is still finding novel applications, and occasionally encounters unexpected problems. In this paper we first briefly describe a few of the latter, related to issues such as nonuniqueness, noncollinearity, and currents. In the main part we then turn to an example of the former, namely SDFT for the Heisenberg model. It is shown that time-honored concepts of Coulomb DFT, such as the local-density approximation, can be applied to this (and other) model Hamiltonians, too, once the concept of 'density' has been suitably reinterpreted. Local-density-type approximations for the inhomogeneous Heisenberg model are constructed. Numerical applications to finite-size and impurity systems demonstrate that DFT is a computationally efficient and reasonably accurate alternative to conventional methods of statistical mechanics for the Heisenberg model.

A bird's-eye view of density-functional theory

“…55 Some recent work on SDFT is described in Ref. [133]. A more detailed discussion of SDFT can be found in Refs.…”

Comparative study of magnetic properties of dilute Fe doped with transition magnetic ions and GaN, InN doped with rare-earth magnetic ions

“…Spin-density-functional theory (SDFT) [19], a realistic invention of density functional theory, is the most extensively employed technique in revealing and explaining the magnetic properties of different transition and rare-earth magnetic ions doped in magnetic and non-magnetic materials. However, it is still finding innovative solicitations and can reliably predict magnetic properties of different materials and alloys.…”

Energy of bond defects in quantum spin chains obtained from local approximations and from exact diagonalization

“…This so-called local-spin approximation [4,5] has been applied to investigate the energetics of impurities in one, two and three-dimensional Heisenberg models [4,5,6,7]. Impurities here are defined, relative to a homogeneous model in which all sites have the same spin S, as sites with a spin S I = S (see inset of Fig.…”

“…In ab initio electronic-structure calculations DFT [3] is a useful way to include correlations beyond the mean-field approximations, at very little additional computational cost. To deal with defects within DFT for spin chains, we propose a local-bond approximation (LBA), akin to the local-density approximation (LDA) of ab initio DFT and the local-spin approximation (LSA) previously proposed for spin systems with impurities [4,5,6,7]. These schemes are described in Sec.…”