## CMT132

##
**
Theory of Nonequilibrium Spin Transport and Spin Transfer Torque in Superconducting-Ferromagnetic
Nanostructures
**

**Author(s):**
Erhai Zhao and J. A. Sauls
- Address: Department of Physics & Astronomy, Northwestern University, Evanston, IL 60208
- Date: February 15, 2007
**Journal:**
Phys. Rev. B 78, 174511 (2008)
[DOI]
[PDF]
**Abstract:**
Spin transport currents and the spin-transfer torques in voltage-biased superconducting-ferromagnetic
nanopillars (SFNFS point contacts) are computed. We develop and implement an algorithm based on the
Ricatti formulation of the quasiclassical theory of superconductivity to solve the time-dependent
boundary conditions for the nonequilibrium Green's functions for spin transport through the
ferromagnetic interfaces. A signature of the nonequilibrium torque is a component perpendicular to
the plane spanned by the two ferromagnetic moments. The perpendicular component is absent in
normal-metal-ferromagnetic nanopillars (NFNFN) contacts, but is shown to have the same order of
magnitude as the in-plane torque for non-equilibrium SFNFS contacts. The out-of-plane torque is due
to the rotation of quasiparticle spin by the exchange fields of the ferromagnetic layers. In the
ballistic limit the equilibrium torque is related to the spectrum of spin-polarized Andreev bound
states, while the a.c. component, for small bias voltages, is determined by the nearly adiabatic
dynamics of the Andreev bound states. The nonlinear voltage dependence of the non-equilibrium torque,
including the subharmonic gap structure and the high-voltage asymptotics, is attributed to the
interplay between multiple Andreev reflections, spin filtering and spin mixing. These properties of
spin angular momentum transport may be exploited to control the state of nanomagnets.

- Comment: 15 pages with 14 figures.

**Eprint:**
[PDF]
[arXiv]