Reciprocity in diffusive spin-current circuits

Similarly to their purely electric counterparts, spintronic circuits are made of lumped elements connected into a network. Spin and charge currents flowing into each element are described by its matrix conductance. We establish a reciprocity relation between the entries of the conductance matrix of a diffusive multi-terminal linear element. In particular, reciprocity equates the spin transmission through a two-terminal element in the forward and backwards directions. Its application to “geometric spin ratchets” shows that their directional shape does not result in preferential transmission of spin in a certain direction.