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

We consider an implementation of the adiabatic spin dynamics approach in a tight-binding description of the electronic structure. The adiabatic approximation for spin degrees of freedom assumes that the faster electronic degrees of freedom are always in a quasiequilibrium state, which significantly reduces the numerical complexity in comparison to the full electron dynamics. Noncollinear magnetic configurations are stabilized by a constraining field, which allows us to directly obtain the effective magnetic field from the negative of the constraining field. While the dynamics are shown to conserve energy, we demonstrate that adiabatic spin dynamics does not conserve the total spin angular momentum when the lengths of the magnetic moments are allowed to change, which is confirmed by numerical simulations. Furthermore, we develop a method to extract an effective two-spin exchange interaction from the energy curvature tensor of noncollinear states, which we calculate at each time step of the numerical simulations. We demonstrate the effect of noncollinearity on this effective exchange and limitations due to multispin interactions in strongly noncollinear configurations beyond the regime where the Heisenberg model is valid. The relevance of the results are discussed with respect to experimental pump-probe experiments that follow the ultrafast dynamics of magnetism.