A Solid State Paramagnetic Maser Device Driven by Electron Spin Injection

In response to an external, microwave-frequency magnetic field, a paramagnetic medium will absorb energy from the field that drives the magnetization dynamics. Here we describe a new process by which an external spin-injection source, when combined with the microwave field spin pumping, can drive the paramagnetic medium from one that absorbs microwave energy to one that emits microwave energy. We derive a simple condition for the crossover from absorptive to emissive behavior. Based on this process, we propose a solid-state, paramagnetic device in which microwave amplification by stimulated emission of radiation is driven by spin injection.

Figure 1

Power flow in and out of a paramagnetic medium to illustrate the principle behind the spin-injection maser. (a) Part of the input rf power is absorbed to produce precessing spin accumulation in the medium; power is lost to internal dissipation due to spin relaxation processes, and to a spin sink. (b) When additional spins are provided by an externally powered spin-injection source, it is possible for the system to exhibit gain, resulting in net emission of rf power.

Figure 2

Schematic of an electrical spin-injection source for the paramagnetic medium. An electrical current is driven across the interface between a ferromagnetic layer and the paramagnetic layer (separated by an oxide tunnel barrier), which causes a spin current $I_s$ to flow into the paramagnet. It is assumed that the static field $B_z$ is sufficiently strong to saturate the magnetization $M$ of the ferromagnetic layer normal to the film plane.

Figure 3

A vector diagram in the rotating reference frame showing the field (white arrow) and the in-plane spin accumulation (black arrow), for (a) ${\mu }_s=0$, (b) ${\mu }_s=-\hslash \omega$, and (c) ${\mu }_s=-2\hslash \omega$. The ${\mu }_{\parallel }$ axis is the spin accumulation in phase with the field, while the ${\mu }_{\perp }$ axis is the spin accumulation out of phase with the field. The half-plane ${\mu }_{\perp }<0$ represents in-plane $\mu$ that lags the field (absorption), the half-plane ${\mu }_{\perp }>0$ represents in-plane $\mu$ that leads the field (emission).

Figure 4

(a) Resonant RLC circuit for the spin-injection maser connected to a rf voltage source. The paramagnetic medium is enclosed within the inductor coil (the bare coil has inductance $L_0$). The modification of the inductance by the complex magnetic susceptibility of the paramagnet results in the equivalent circuit (b), with an additional resistance $R^{\prime }$ and inductance $L^{\prime }$.