Exchange constants for local spin Hamiltonians from tight-binding models

TL;DR

This paper develops a method to derive local spin Hamiltonians from tight-binding models, improving the accuracy of magnetic interactions for small fluctuations and out-of-equilibrium states in itinerant-electron systems.

Contribution

It introduces a linear term in the local spin Hamiltonian to better capture non-collinear magnetic states and provides a practical implementation based on constraining fields.

Findings

Accurate calculation of exchange constants for iron dimers and chains.

Enhanced modeling of magnetic fluctuations near equilibrium states.

Validation of the formalism through numerical examples.

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.