Spin transfer and current-induced switching in a ferromagnetic single-electron transistor

Abstract

We propose a theoretical model of current-induced magnetization (CIMS) switching in a ferromagnetic single electron tunneling (FM-SET) transistor. The CIMS effect arises from the transfer of spin angular momentum from the net spin accumulation $\ensuremath{\Delta}S$ on the island electrode to the local magnetic moments via $s\text{\ensuremath{-}}d$ exchange coupling. Based on the single-domain model, we derive an analytical expression for the critical spin accumulation $\ensuremath{\Delta}{S}_{\mathrm{sw}}$ on the island for CIMS, and calculate the $M\text{\ensuremath{-}}\ensuremath{\Delta}S$ hysteresis curves which represent the effect of $\ensuremath{\Delta}S$ on the island moments. This magnetization response is then related to the charge and spin transport model in the SET transistor. We extend the Korotkov scheme spin-dependent ``orthodox'' theory of single charge tunneling, by linking the transport $I\text{\ensuremath{-}}V$ and $\ensuremath{\Delta}S\text{\ensuremath{-}}V$ characteristics to the $M\text{\ensuremath{-}}\ensuremath{\Delta}S$ hysteresis. We thus determine $\ensuremath{\Delta}S$ as a function of external bias or current and hence obtain the switching current density ${j}_{\mathit{sw}}$ for CIMS. For a typical spin polarization $P=60%$ of the source electrode, ${j}_{\mathit{sw}}$ is calculated to be of the order of ${10}^{5}\phantom{\rule{0.3em}{0ex}}\mathrm{A}∕{\mathrm{cm}}^{2}$, and this falls to just $\ensuremath{\sim}3\ifmmode\times\else\texttimes\fi{}{10}^{4}\phantom{\rule{0.3em}{0ex}}\mathrm{A}∕{\mathrm{cm}}^{2}$ when a near half-metal $(P=90%)$ is used. This value is several orders of magnitude smaller than ${j}_{\mathit{sw}}$ observed in multilayer and magnetic tunnel junction structures. The SET transistor is an ideal device for the CIMS effect since (i) a small amount of moments (on the island) need to be switched to generate a large change in conduction and (ii) the island electrode being isolated from the rest of the circuit by spin-dependent tunnel barriers effectively confines the spin accumulation $\ensuremath{\Delta}S$ in the vicinity of these moments.