Einstein–de Haas Nanorotor

We propose a nanoscale rotor embedded between two ferromagnetic electrodes that is driven by spin injection. The spin-rotation coupling allows this nanorotor to continuously receive angular momentum from an injected spin under steady current flow between ferromagnetic electrodes in an antiparallel magnetization configuration. We develop a quantum theory of this angular-momentum transfer and show that a relaxation process from a precession state into a sleeping top state is crucial for the efficient driving of the nanorotor by solving the master equation. Our work clarifies a general strategy for efficient driving of a nanorotor.

Figure 1

(a) Schematic diagram of proposed structure of nanorotor driven by spin injection. A voltage is applied to two half-metallic ferromagnetic electrodes with magnetizations respectively in the $z$ and $-z$ directions. An electron with a spin $s_z=\hslash /2$ from the left electrode cannot enter the right electrode because there is no electronic state for a spin $s_z=\hslash /2$. Continuous current flow is allowed via spin flipping at a rotor induced by the spin-rotation coupling that describes angular-momentum transfer from a spin to the rotor. (b) Three possible electronic states of the rotor. The number of additional electrons injected into the rotor is restricted to 0 or 1 because of the Coulomb blockade. The spin-rotation coupling is described by the $\mathrm{Hamiltonian}-\mathit{s}·\mathbf{\Omega }$, and ${\mathrm{\Gamma }}_{L\uparrow }({\mathrm{\Gamma }}_{R\downarrow })$ is an electron transfer rate between the rotor and the left (right) electrode.

Figure 2

Eigenenergies of rotational motion as a function of $k$. The upper and lower branches correspond to the precession state ($M=k\pm 1$) and the sleeping top state ($M=k$), respectively. The insets are schematic diagrams of the corresponding rotor motions.

Figure 3

Time evolutions of rotational motion for (a) $g=0$, (b) $g={10}^{-9}$, and (c) $g={10}^{-7}$. The chemical potentials of the left and right electrodes are chosen to be ${\mu }_L=-{\mu }_R=0.1\mathrm{meV}$. (d) Density plot of torque in the source and drain chemical potentials, ${\mu }_L-{\mu }_R$, plane.

Figure 4

Two channels that are relevant to electron transfer.