Magnetoelectric torque in polar magnetic bilayers

Abstract

Energy-efficient fast switching of spin orientations or textures is a core issue of spintronics, which is highly demanded but remains challenging. Different from the mainstream routes based on spin-transfer torque or spin-orbit torque, here we propose another mechanism coined as magnetoelectric torque to switch the magnetization in polar magnetic bilayers via pure electric field. In some magnetic van der Waals bilayers, when the electrostatic energy of polarization can compensate the interlayer magnetic coupling, a magnetoelectric torque is generated to fastly flip spins within a few picoseconds, which is demonstrated by combining the first-principles calculations, analytic model, as well as atomistic simulations. Such a magnetoelectric torque doesn't rely on the spin-orbit coupling and is generally active in polar magnetic homostructures and heterostructures. Our work provides an alternative route to switch magnetization in nanoscale, which may benefit the energy-saving and fast-response spintronic devices.

Figures (5)

• Figure 1: (a) The sliding polarization of CrISe bilayer as a function of the angle ($\varphi$) between $\textbf{S}_A$ and $\textbf{S}_B$. Dots (stars): obtained from DFT calculations with (without) SOC, which are almost identical. Curve: analytical fitting using Eq. \ref{['eq1']}. Insets: side view of CrISe bilayer, schematics of Heisenberg-type exchanges ($J$'s), Dzyaloshinskii-Moriya interaction (DMI) vectors ($\textbf{D}$'s), and spin angle ($\varphi$) between layers. (b) Schematic diagram of the MET (small blue arrows) on spins (large arrows) in the $xy$-plane, generated by $E$ along the $z$ axis.
• Figure 2: The atomistic simulations and an analytic description of the magnetization ($M$) switching. (a) Evolutions of the normalized magnetization over time in the atomistic simulations at $0$ K and $10$ K. $M_s$: the saturation magnetization, i.e., $3$$\mu_{\rm B}$/Cr. Green curve: $E$ along the $z$ axis. (b) Corresponding spin textures at points A, B, C in (a). (c-d) The analytic (curves) and simulated (circles) energy ($\varepsilon$) as a function of $\varphi$ with (c) $E = 0.2$ V/Å and (d) $E = -0.2$ V/Å. In (b-d), spins in different layers are distinguished by colors.
• Figure 3: Role of MET in the magnetization switching. (a) $\textbf{S}_A$ ($\textbf{S}_B$) is confined in the easy plane. $\textbf{f}_{AA}$ and $\textbf{f}_{AB}$ ($\textbf{f}_{BB}$ and $\textbf{f}_{BA}$) are the effective fields acting on $\textbf{S}_A$ ($\textbf{S}_B$) from intra- and interlayer interactions. $\textbf{T}_A$ ($\textbf{T}_B$) is the MET acting on $\textbf{S}_A$ ($\textbf{S}_B$). (b) Evolution of magnetization and $T_A$ in the atomistic simulation. Inset: $T_A$ as a funtion of $\varphi$. (c) Evolution of three components of $\textbf{T}_A$ and $\textbf{T}_B$. The corresponding orientations of spins and torques are also illustrated. The electric field in (b-c) is the same as that in Fig. \ref{['fig2']}(a). (d) Magnetization switching simulated with different $\alpha$'s under $E = -0.2$ V/Å. Inset: the $M$-switching frequency ($1/\tau$) as a function of $1/\alpha$.
• Figure 4: The analytic energy ($\varepsilon$) surface of an easy-axis magnet (a) without and (b) with an electric field of 0.3 V/Å. $\theta_A$ ($\theta_B$) is the polar angle of $\textbf{S}_A$ ($\textbf{S}_B$). The value of $\varepsilon$ is represented by the color map. The magnetization switching paths are shown by the dashed grey arrows.
• Figure 5: A schematic illustration of the key distinctions between our MET (middle) and those of previous ones Sousa2021PRRZheng2017CPBXing2013SaAAPXing2011JoAP.