Voltage Control of Rare-Earth Magnetic Moments at the Magnetic-Insulator–Metal Interface

The large spin-orbit interaction in the lanthanides implies a strong coupling between their internal charge and spin degrees of freedom. We formulate the coupling between the voltage and the local magnetic moments of rare-earth atoms with a partially filled $4f$ shell at the interface between an insulator and a metal. The rare-earth-mediated torques allow the power-efficient control of spintronic devices by electric-field-induced ferromagnetic resonance and magnetization switching.

Figure 1

Spin-charge coupling for an interface local magnetic moment. (a) Electric field at an interface between an insulator (constant electric field) and a metal (vanishing electric field). The magnetic dipole and charge quadrupole at the interface are coupled. (b) Ground state magnetization directions $\mathbf{m}=(m_x,m_y,m_z)$ as a function of the interface electric field with coupling parameter $\mathrm{\Gamma }$ [Eq. (9)] and a magnetic field tilted from the $z$ axis by an angle $\phi \sim 6°$. The system switches from a perpendicular easy-axis to an easy-plane configuration at $\mathrm{\Gamma }<0.018$.

Figure 2

(a) Magnetization dynamics induced by time-varying voltages. Comparison between analytic (solid line) and (b) numeric (dot) precessional (FMR) solutions, obtained for $\mathrm{\Gamma }={\mathrm{\Gamma }}_0\cos (\mathrm{\Omega }t)$, ${\mathrm{\Gamma }}_0=0.01$, ${\beta }_x={\beta }_z=0$, $\mathrm{\Omega }=0.08$, $h=0.1$, $\phi =45°$, and $\alpha =0.005$.

Figure 3

Precessional switching for an easy-axis perpendicular magnet (${\beta }_z=-0.03$) induced by a voltage box train. The upper panel shows the magnetization components, while the lower panel shows the box consisting of a negative voltage with $\mathrm{\Gamma }=-0.03$ for $\mathrm{\Delta }t=4000\gamma M_s$ ($\sim 1\mathrm{ns}$) followed by $\mathrm{\Gamma }=0$. This signal is repeated all $2\times {10}^5\gamma M_s$ ($\sim 25\mathrm{ns}$). Other parameters are ${\beta }_x=0$, $h=0.01$, $\phi =5.72°$, and $\alpha =0.005$.