Magnetization oscillations induced by spin current in a paramagnetic disc

When electron spins are injected uniformly into a paramagnetic disk, they can precess along the demagnetizing field induced by the resulting magnetic moment. Normally this precession damps out by virtue of the spin relaxation, which is present in paramagnetic materials. We propose a mechanism to excite a steady-state form of this dynamics by injecting a constant spin current into this paramagnetic disk. We show that the rotating magnetic field generated by the eddy currents provide a torque that makes this possible. Unlike the ferromagnetic equivalent, the spin-torque oscillator, the oscillation frequency is fixed and determined by the dimensions and intrinsic parameters of the paramagnet. The system possesses an intrinsic threshold for spin injection, which needs to be overcome before steady-state precession is possible. The additional application of a magnetic field lowers this threshold. We discuss the feasibility of this effect in modern materials. Transient analysis using pump-probe techniques should give insight in the physical processes which accompany this effect.

Figure 1

Conceptual diagram. (a) An out-of-plane spin current ${\vec{I}}_s$ is injected into a paramagnetic disk. (b) The injected out-of-plane spin accumulation ${\vec{\mu }}_z$ creates a demagnetization field ${\vec{B}}_d$ along which any naturally present ${\vec{\mu }}_{\left|\right|}$ precesses. This precession creates a magnetic field ${\vec{B}}_e$ owing to the eddy currents, which can tilt the spin accumulation ${\vec{\mu }}_z$ in plane. The effect is enhanced by the application of a static magnetic field $B_a$. (c) Sketch of the eddy current density in the (spheroid) disk when a changing uniform spin accumulation is present.

Figure 2

Axis definition eddy fields. (a) The disk is approximated by a spheroid with diameter $d$ and thickness $t$. (b) The in-plane spin accumulation ${\mu }_{\left|\right|}$ initially points in the $x$ (or $\left|\right|$) direction while (c) $\partial {\mu }_{\left|\right|}/\partial t$ points in the $-y$ (or $\perp$) direction. The eddy currents arising in the $xz$ plane are also illustrated.

Figure 3

Possible realization schemes. (a) An out-of-plane spin current can be injected by sending a current from ferromagnet FM${}_1$ into a paramagnetic metallic disk. The paramagnet is electrically separated by a tunnel barrier. The in-plane spin accumulation can be measured using a second ferromagnet with its magnetization in plane. (b) The effect can be studied by optical spin injection in which a circular polarization for the pump can induce out-of-plane spin polarized carriers. The in-plane component can, for example, be measured using Kerr rotation of a linearly polarized pulse under a small angle.