Abstract
We consider the mapping of tight-binding electronic structure theory to a local spin Hamiltonian, based on the adiabatic approximation for spin degrees of freedom in itinerant-electron systems. Local spin Hamiltonians are introduced in order to describe the energy landscape of small magnetic fluctuations, locally around a given spin configuration. They are designed for linear response near a given magnetic state and in general insufficient to capture arbitrarily strong deviations of spin configurations from the equilibrium. In order to achieve this mapping, we include a linear term in the local spin Hamiltonian that, together with the usual bilinear exchange tensor, produces an improved accuracy of effective magnetic Weiss fields for non-collinear states. We also provide examples from tight-binding electronic structure theory, where our implementation of the calculation of exchange constants is based on constraining fields that stabilize an out-of-equilibrium spin configuration. We check our formalism by means of numerical calculations for iron dimers and chains.
Highlights
The Heisenberg model and generalizations thereof are among the most important paradigms of condensed matter physics and have been very successful in describing the magnetic behavior of both magnetic insulators, for which it was suggested initially, and, with some reservations, metallic magnets
From recent results that the effective field in density functional theory (DFT) contains an additional term besides the constraining field [28], we recover the formula previously derived by Bruno for the isotropic Heisenberg exchange [23], which we extend to the full bilinear exchange tensor
We have derived the mapping of tight-binding electronic structure theory to local spin Hamiltonians
Summary
The Heisenberg model and generalizations thereof are among the most important paradigms of condensed matter physics and have been very successful in describing the magnetic behavior of both magnetic insulators, for which it was suggested initially, and, with some reservations, metallic magnets. Liechtenstein et al emphasized that for metals, the Heisenberg Hamiltonian “is applicable only for small spin deviations from the ground state” [11], which implies that terms beyond the bilinear Heisenberg exchange interactions may be required to describe the magnetic behavior for strong deviations from the ground state This was further confirmed by explicit calculations for the cases of Fe, Ni, and Fe-based magnetic alloys [12]. III, we derive expressions based on the constraining field for the exchange parameters in terms of Green’s functions and self-energies In Appendix C, we discuss the symmetry of exchange constants within the different approaches that we consider in this manuscript
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