Spin and charge pumping in magnetic tunnel junctions with precessing magnetization: A nonequilibrium Green function approach

Abstract

We study spin and charge currents pumped by precessing magnetization of a single ferromagnetic layer within $F|I|N$ or $F|I|F$ ($F$-ferromagnet; $I$-insulator; $N$-normal metal) multilayers of nanoscale thickness attached to two normal-metal electrodes with no applied bias voltage between them. Both simple one-dimensional model, consisting of a single precessing spin and a potential barrier as the ``sample,'' and realistic three-dimensional devices are investigated. In the rotating reference frame, where the magnetization appears to be static, these junctions are mapped onto a four-terminal dc circuit whose effectively half-metallic ferromagnetic electrodes are biased by the frequency $\ensuremath{\hbar}\ensuremath{\omega}/e$ of microwave radiation driving magnetization precession at the ferromagnetic resonance (FMR) conditions. We show that pumped spin current in $F|I|F$ junctions, diminished behind the tunnel barrier and increased in the opposite direction, is filtered into charge current by the second $F$ layer to generate dc pumping voltage of the order of $\ensuremath{\sim}1\text{ }\ensuremath{\mu}\text{V}$ (at FMR frequency $\ensuremath{\sim}10\text{ }\text{GHz}$) in an open circuit. In $F|I|N$ devices, several orders of magnitude smaller charge current and the corresponding dc voltage appear concomitantly with the pumped spin current due to barrier induced asymmetry in the transmission coefficients connecting the four electrodes in the rotating-frame picture of pumping.