Dynamical exchange interaction between localized spins out of equilibrium

The electron mediated exchange interaction between local spins adsorbed on two-dimensional surface is studied under non-equilibrium conditions. The effective spin-spin interaction is found to depend both on the spin-polarization of the substrate and the excitation spectrum of the local spins. For spatially anisotropic spin-polarization of the substrate, the spatial dependence of the interaction comprise components decaying as sin(2k_FR)/(2k_FR) and sin(2k_FR)/(2k_FR)^2.