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We consider an implementation of the adiabatic spin dynamics approach in atight-binding description of the electronic structure. The adiabaticapproximation for spin-degrees of freedom assumes that the faster electronicdegrees of freedom are always in a quasi-equilibrium state, which significantlyreduces the numerical complexity in comparison to the full electron dynamics.Non-collinear magnetic configurations are stabilized by a constraining field,which allows to directly obtain the effective magnetic field from the negativeof the constraining field. While the dynamics are shown to conserve energy, wedemonstrate that adiabatic spin dynamics does not conserve the total spinangular momentum when the lengths of the magnetic moments are allowed tochange, which is confirmed by numerical simulations. Furthermore, we develop amethod to extract an effective two-spin exchange interaction from the energycurvature tensor of non-collinear states, which we calculate at each time stepof the numerical simulations. We demonstrate the effect of non-collinearity onthis effective exchange and limitations due to multi-spin interactions instrongly non-collinear configurations beyond the regime where the Heisenbergmodel is valid. The relevance of the results are discussed with respect toexperimental pump-probe experiments that follow the ultra-fast dynamics ofmagnetism.

Adiabatic spin dynamics and effective exchange interactions from constrained tight-binding electronic structure theory: Beyond the Heisenberg regime