Theory of the spin-torque-driven ferromagnetic resonance in a ferromagnet/normal-metal/ferromagnet structure

We present a theoretical analysis of current-driven ferromagnetic resonance in a ferromagnet/normal-metal/ferromagnet trilayer. This method of driving ferromagnetic resonance was recently realized experimentally by Tulapurkar et al. [Nature 438, 339 (2005)] and Sankey et al. [Phys. Rev. Lett. 96, 227601 (2006)]. The precessing magnetization rectifies the alternating current applied to drive the ferromagnetic resonance and leads to the generation of a dc voltage. Our analysis shows that a second mechanism to generate a dc voltage, rectification of spin currents emitted by the precessing magnetization, has a contribution to the dc voltage that is of approximately equal size for the thin ferromagnetic films used in the experiment.

Figure 1

Schematic drawing of the ferromagnet/normal-metal/ferromagnet trilayer considered here. The left ferromagnet, with magnetization direction $\mathit{n}$, acts as the source reservoir. The right ferromagnet is the free layer. Its magnetization direction $\mathit{m}$ can change in response to the applied current. The currents $J(+)$ and $J(-)$ in the text are evaluated at the right and left sides of the free ferromagnetic layer, respectively.