  We show how the interference between superfluid spin currents can endow spin
circuits with coherent logic functionality. While the hydrodynamic aspects of
the linear-response collective spin transport obviate interference features, we
focus on the nonlinear regime, where the critical supercurrent is sensitive to
the phase accumulated by the condensate in a loop geometry. We propose to
control this phase by electrical gating, tuning the spin-condensate coherence
length. The nonlinear aspects of the spin superfluidity thus naturally lend
themselves to the construction of logic gates, uniquely exploiting the
coherence of collective spin currents. Vice versa, this functionality can be
used to reveal the fundamental properties of spin superfluids.

Mesoscale and Nanoscale Physics