Microscopic theory of an atomic spin diode

We present a microscopic theory of an atomic spin diode. Our proposed system consists of two magnetic adatoms deposited on the surface of a two-dimensional electron gas with Rashba spin-orbit coupling. A local type coupling between the local spins and the spins of the electrons induces a nonlocal Ruderman-Kittel-Kasuya-Yosida type interaction and a Dzyaloshinskii-Moriya interaction, in addition to dissipative interactions, between the spins. We derive the effective action for the spins using the Keldysh formalism. From the effective action, we also derive equations of motion for the spins which are shown to be of Landau-Lifshitz-Gilbert type, and give expressions for the effective field and Gilbert damping which appear in this equation. From our microscopic theory, we find that for an in-plane magnetic field perpendicular to the vector connecting the two atoms, the magnitude of the field and the distance between the atoms can always be tuned to engender perfectly diodic coupling. Our findings may pave the way for experimental realization of atomic spin diodes.