Electric field control of spin dynamics in a magnetically active tunnel junction

The dynamics of a single spin embedded in a tunnelling junction is studied. Within a nonequilibrium Keldysh Green's function technique, we derive a quantum Langevin equation describing the spin dynamics. In the high temperature limit, it reduces to a Bloch equation, for which the spin relaxation rate, as determined by the temporal fluctuation, is linearly proportional to the temperature. In the opposite limit, the relaxation rate depends on the applied voltage, in contrast to the case of a spin in an equilibrium environment. We also show that spin–flip transition processes during electron tunnelling convert the applied electric field (i.e. voltage bias) into an effective magnetic field. Consequently, the dynamics of the spin, otherwise precessing along the static magnetic field, will have either a frequency shift proportional to the dc bias or a magnetic resonance driven indirectly by an ac electric field at the Larmor frequency ω L . An experiment to measure this effect is also proposed.