Exchange Constants For Local Spin Hamiltonians From Tight-Binding Models

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 the linear response near a given magnetic state and, in general, are 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 noncollinear 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.