Non-equilibrium magnetic fields in ab initio spin dynamics

Starting from the continuity equation for the magnetization in time-dependent spin-density functional theory, we derive an expression for the effective time-dependent magnetic fields driving the out-of-equilibrium spin dynamics in magnetic systems. We evaluate these, so called, kinetic magnetic fields in the ultrafast demagnetization response to optical pulse excitations of ferromagnetic iron-based materials, namely Fe$_6$ cluster and bulk bcc Fe. We identify spatial "hot spots" where the demagnetization is particularly enhanced as a result of the increased kinetic torque.