Europhys. Lett.
Volume 67, Number 4, August 2004
Page(s) 620 - 626
Section Condensed matter: electronic structure, electrical, magnetic, and optical properties
Published online 01 August 2004
Europhys. Lett., 67 (4), pp. 620-626 (2004)
DOI: 10.1209/epl/i2003-10305-x

Spin Josephson effect in ferromagnet/ferromagnet tunnel junctions

F. S. Nogueira and K.-H. Bennemann

Institut für Theoretische Physik, Freie Universität Berlin Arnimallee 14, D-14195 Berlin, Germany

(Received 16 December 2003; accepted in final form 10 June 2004)

We consider the tunnel 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 tunnel spin current $I_{\ab{J}}^{\ab{spin}}\propto
\sin(\theta_{1}-\theta_{2})$ . Here the phases are associated with the planar contribution to the magnetization, $\langle
c_{\uparrow}^{\dagger} c_{\downarrow}\rangle\sim e^{i\theta}$ . 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: $[\theta,S^{z}]=i$. This is the counterpart to the commutation relation $[\varphi,N]=i$ in superconductors, where $\varphi$ is the phase associated with the superconducting order parameter and N is the Cooper pair number operator. We briefly discuss the experimental consequences of our theoretical analysis.

72.25.-b - Spin polarized transport.
72.25.Mk - Spin transport through interfaces.
74.50.+r - Tunneling phenomena; point contacts, weak links, Josephson effects.

© EDP Sciences 2004