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 adiabatic approximation for degrees freedom in itinerant-electron systems. Local Hamiltonians are introduced order describe energy landscape small magnetic fluctuations, locally around given configuration. They designed linear response near state and general insufficient capture arbitrarily strong deviations configurations from equilibrium. In achieve this mapping, we include term Hamiltonian that, together with usual bilinear exchange tensor, produces an improved accuracy effective Weiss fields non-collinear states. also provide examples theory, where our implementation calculation constants is constraining that stabilize out-of-equilibrium check formalism by means numerical calculations iron dimers chains.