Voltage-Controlled Magnon Transistor via Tuning Interfacial Exchange Coupling

Magnon transistors that can effectively regulate magnon transport by an electric field are desired for magnonics, which aims to provide a Joule-heating free alternative to the conventional electronics owing to the electric neutrality of magnons (the key carriers of spin-angular momenta in the magnonics). However, also due to their electric neutrality, magnons have no access to directly interact with an electric field and it is thus difficult to manipulate magnon transport by voltages straightforwardly. Here, we demonstrated a gate voltage ($V_{\mathrm{g}}$) applied on a nonmagnetic metal and magnetic insulator (MI) interface that bent the energy band of the MI and then modulated the probability for conduction electrons in the nonmagnetic metal to tunnel into the MI, which can consequently enhance or weaken the spin-magnon conversion efficiency at the interface. A voltage-controlled magnon transistor based on the magnon-mediated electric current drag (MECD) effect in a $\mathrm{Pt}\text{−}{\mathrm{Y}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}\text{−}\mathrm{Pt}$ sandwich was then experimentally realized with $V_{\mathrm{g}}$ modulating the magnitude of the MECD signal. The obtained efficiency (the change ratio between the MECD voltage at $\pm V_{\mathrm{g}}$) reached $10\%/(\mathrm{MV}/\mathrm{cm})$ at 300 K. This prototype of magnon transistor offers an effective scheme to control magnon transport by a gate voltage.

Figure 1

Mechanism of voltage-gated magnon transistor. (a) Schematics of the voltage-gated magnon transistor. A spin current is generated by the spin Hall effect in the bottom NM, which induces imbalanced spin accumulation (${\mu }_{\mathrm{s}}$) at the bottom NM-MI interface. Because of the $s\text{−}d$ exchange coupling at the interface, ${\mu }_{\mathrm{s}}$ relaxes by annihilating (generating) magnons in MI as ${\mu }_{\mathrm{s}}$ has parallel (antiparallel) polarization to the magnetization of MI. The excited magnon current was thus manipulated by $V_{\mathrm{g}}$: positive (negative) $V_{\mathrm{g}}$ increases (decreases) its magnitude. (b) Schematics of potential profile near the bottom NM-MI interface under positive $V_{\mathrm{g}}$. (c) Schematics of probability $|\psi {|}^2$ at the bottom NM-MI interface under positive and negative $V_{\mathrm{g}}$. (d) The predicted $V_0$ and $E$ dependence of $G_{\mathrm{r}}$ (the color scale bar in units of $e^2/\hslash a^2$). (e) The $E$ dependence of $G_{\mathrm{r}}$ under $V_0=5.625$, 5.675, and 5.725 eV extracted from Fig. 1.

Figure 2

Voltage-controlled MECD effect. (a) The $\gamma$ dependence of $\mathrm{\Delta }V$ with $\mathbf{H}$ rotated in the $yoz$ plane and $I_{\mathrm{in}}=5\mathrm{mA}$ under $V_{\mathrm{g}}=-5$, 0, and $+5\mathrm{V}$. The open circles (solid lines) are the experimental data (fitted curves by $\mathrm{\Delta }V=V_{\mathrm{drag}}\cos 2\gamma$). (b) The $I_{\mathrm{in}}$ dependencies of $V_{\mathrm{drag}}$ under different $V_{\mathrm{g}}$ and their linear fittings. (c) The $V_{\mathrm{g}}$ dependence of magnon drag parameter $\alpha$. Error bars for Devices 1 and 2 are from the standard deviations of the linear fittings of the $V_{\mathrm{drag}}\text{−}{I}_{\mathrm{in}}$ relation and the $\mathrm{\Delta }V=V_{\mathrm{drag}}\cos 2\gamma$ fittings, respectively. The red line is the hyperbolic tangent fitting of the $\alpha \text{−}{V}_{\mathrm{g}}$ curve. (d) The $\gamma$ dependence of the difference in $\mathrm{\Delta }V$ between $V_{\mathrm{g}}=\pm 5\mathrm{V}$.

Figure 3

Schematics setups for (a) spin pumping measurement where the spin pumping voltage ($V_{\mathrm{SP}}$) was picked up along the B-Pt stripe with $\mathbf{H}$ perpendicular to the stripe and $V_{\mathrm{g}}$ applied across the sandwich and for (e) SMR measurement where the resistance change $\mathrm{\Delta }{R}_{\mathrm{B}\text{−}\mathrm{Pt}}$ of the B-Pt stripe was measured with $\mathbf{H}$ rotated in the $yoz$ plane. (b) The $H$ dependence of the normalized $V_{\mathrm{SP}}(H)/V_{\mathrm{SP}}^{\max }$ under different rf frequencies ($f$) and $V_{\mathrm{g}}=-3.9$, 0, and $+3.9\mathrm{V}$. (c) The $H$ dependence of $V_{\mathrm{SP}}$ at $f=5\mathrm{GHz}$ and $V_{\mathrm{g}}=-3.9$, 0, and $+3.9\mathrm{V}$. (d) The $\gamma$ dependencies of the $\mathrm{\Delta }{R}_{\mathrm{B}\text{−}\mathrm{Pt}}$ (open circles) and their $\mathrm{\Delta }{R}_{\mathrm{B}\text{−}\mathrm{Pt}}=\mathrm{\Delta }{R}_{\mathrm{SMR}}\cos 2\gamma$ fittings. (f) The resonance field ($H_{\mathrm{r}}$) dependence of $f$ under $V_{\mathrm{g}}=-3.9$, 0, and $+3.9\mathrm{V}$ (open circles) and their Kittle fittings. The $V_{\mathrm{g}}$ dependence of (g) the peak value of $V_{\mathrm{SP}}\text{−}H$ curve ($V_{\mathrm{SP}}^{\mathrm{peak}}$) under $f=5\mathrm{GHz}$ and (h) the SMR ratio. (Error bars from standard deviation of the $\mathrm{\Delta }{R}_{\mathrm{B}\text{−}\mathrm{Pt}}=\mathrm{\Delta }{R}_{\mathrm{SMR}}\cos 2\gamma$ fittings.) Red lines in Figs. 3 and 3 are the hyperbolic tangent fitting of the $V_{\mathrm{SP}}^{\mathrm{peak}}\text{−}{V}_{\mathrm{g}}$ and SMR ratio-$V_{\mathrm{g}}$ curves, respectively.

Figure 4

(a) The $\gamma$ dependence of $\mathrm{\Delta }V(Vg=5V)-\mathrm{\Delta }V(Vg=-5V)$ under different $T$. (b) The $T$ dependence of the difference in the magnon drag parameter $\mathrm{\Delta }\alpha =\alpha (V_{\mathrm{g}}=+5\mathrm{V})-\alpha (V_{\mathrm{g}}=-5\mathrm{V})$ between $V_{\mathrm{g}}=\pm 5\mathrm{V}$. The solid lines are obtained by fitting data using $\mathrm{\Delta }\alpha =A{e}^{-\mathrm{\Delta }E/k_{\mathrm{B}}T}$. (c) The calculated $V_{\mathrm{g}}$ dependence of $G_{\mathrm{r}}$ by taking redistributed voltage on the contact resistance ($R_{\text{contact}}$) into consideration. The red line is the hyperbolic tangent fitting result.