Spin Josephson effect in ferromagnet/ferromagnet tunnel junctions

Original · EN

We consider the tunnel spin current between two ferromagnetic metals from a perspective similar to the one used in superconductor/superconductor tunnel junctions. We use fundamental arguments to derive a Josephson-like spin tunnel current Iⱼ spin∝(θ₁-θ₂). Here the phases are associated with the planar contribution to the magnetization, <c† c> eⁱθ. The crucial step in our analysis is the fact that the z-component of the spin is canonically conjugate to the phase of the planar contribution: [θ,Sᶻ]=i. This is analogous to the commutation relation [ϕ,N]=i in superconductors, where ϕ is the phase associated to the superconducting order parameter and N is the Cooper pair number operator. We briefly discuss the experimental consequences of our theoretical analysis.