A. Vernes, B.L. Gyorffy, P. Weinberger:

"Spin currents, spin-transfer torque, and spin-Hall effects in relativistic quantum mechanics\";

Physical Review B,76(2007), 0124081 - 0124084.

It is shown that a useful relativistic generalization of the conventional spin density s!!r! , t" for the case of

moving electrons is the expectation value (T(r,t)T4(r,t))of the four-component Bargmann-Wigner polarization

operator T =(T,T4) Proc. Natl. Acad. Sci. U.S.A. 34, 211 (1948)) with respect to the four components

of the wave function. An exact equation of motion for this quantity is derived using the one-particle Dirac

equation, and the relativistic analogs of the nonrelativistic concepts of spin currents and spin-transfer torques

are identified. Using this theoretical framework, in the classical limit the Bargmann-Michel-Telegdi equation

(Phys. Rev. Lett. 2, 435 !(1959)) for a relativistic wave packet crossing a nonmagnetic/ferromagnetic interface

is derived, to lowest order in the spin-orbit coupling it is shown that a contribution to the polarization current

occurs with spin-Hall symmetry, and the spin-transfer torque for the simple "perfect spin filter" model is

calculated and discussed.\

Created from the Publication Database of the Vienna University of Technology.