Voltage-dependent electron distribution in a small spin valve: Emission of nonequilibrium magnons and magnetization evolution

Abstract

We describe spin transfer in a ferromagnet/normal metal/ferromagnet spin-valve point contact. Spin is transferred from the spin-polarized current to the magnetization of the free layer by the mechanism of incoherent magnon emission. Our approach is based on the rate equation for the magnon occupation, using Fermi’s golden rule for magnon emission and absorption and the nonequilibrium electron distribution for a voltagebiased spin valve. The magnon emission reduces the magnetization of the free layer. Depending on the sign of the applied voltage for parallel or antiparallel magnetizations, a magnon avalanche, characterized by a diverging effective magnon temperature, sets in at a critical voltage. This critical behavior can result in magnetization reversal and consequently to suppression of magnon emission. However, magnon-magnon scattering can lead to saturation of the magnon concentration at a high but finite value. The further behavior depends on the parameters of the system. In particular, gradual evolution of the magnon concentration followed by magnetization reversal is possible. Another scenario is the steplike increase of the magnon concentration followed by a slow decrease. In this scenario a spike in the differential resistance is expected due electron-magnon scattering. Then, a random telegraph noise in the magnetoresistance can exist, even at zero temperature. A comparison of the obtained results to existing theoretical approaches and experimental data is given. We demonstrate that our approach for magnetization configurations close to collinear corresponds to the voltagecontrolled regime. Namely, the magnetization evolution is related to nonequilibrium spin-dependent electron distribution controlled by the total voltage applied to the device. In this regime the evolution has an exponential character. In contrast, the existing spin-torque approach corresponds to a current-controlled regime, and the evolution rate is restricted by value of the total spin current through the “analyzing” ferromagnetic layer. It is shown that our scenario dominates at mutual magnetization orientation close to the parallel or antiparallel.