Reciprocity in diffusive spin-current circuits*

Similarly to their purely electric counterparts, spintronic circuits may be presented as networks of lumped elements. Due to interplay between spin and charge currents, each element is described by a matrix conductance. We establish reciprocity relations between the entries of the conductance matrix of a multi-terminal linear device, comprising normal metallic and strong ferromagnetic elements with spin-inactive interfaces between them. In particular, reciprocity equates the spin transmissions through a two-terminal element in the opposite directions. When applied to ``geometric spin ratchets'', reciprocity shows that certain effects, announced for such devices, are, in fact, impossible. Finally, we discuss the relation between our work and the spintronic circuit theory formalism.