Efficient Modulation of Magnon Conductivity in ${\mathrm{Y}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$ Using Anomalous Spin Hall Effect of a Permalloy Gate Electrode

We report the control of the modulation efficiency of the magnon conductivity in yttrium iron garnet (YIG) using magnon spin injection from a ferromagnetic metal permalloy (Py) used as a modulator in a three-terminal magnon transistor geometry. The modulation efficiency is estimated by means of nonlocal spin-transport measurements between platinum injector and detector strips. A charge current is sent through the Py modulator to create a spin accumulation at the YIG-Py interface via the spin Hall effect and the anomalous spin Hall effect (ASHE). We observe an enhancement of the modulation efficiency for the electrically generated magnons from 2.5%/mA at 10 mT to 4.7%/mA for magnetic fields higher than 50 mT. That enhancement is attributed to the ASHE, which is maximized when the Py magnetization is perpendicular to the charge current. However, the modulation efficiency of the thermally generated magnons exhibits an opposite behavior, 12.0%/mA at 10 mT to 6.6%/mA at 50 mT, which disagrees with what we expect from the ASHE contribution to the modulation.

Figure 1

(a) Schematic illustration showing the electrical connections of the transistor device and the phenomena involved. The injection of magnons via SHE produced by a charge current $(I_{\mathrm{ac}})$ in the injector, transmission of magnons in YIG, the conversion of spin current into a charge current by ISHE in the detector and the applied charge current $(I_{\mathrm{dc}})$ in the modulator. (b),(c) First-harmonic-dependent voltage as a function of the relative angle $\alpha$ between $\overrightarrow{B}$ and $\hat{y}$, and magnetic field strength, respectively, for the reference sample without the modulator. The inset in (b) shows the electrical configuration of the measurements. (d),(e) Second-harmonic-dependent measurements.

Figure 2

Presence of the Py modulator produces the MGE, where the absorption of magnons is lower (a), or higher (b), due to the relative orientation between the magnetizations of the Py strip and the YIG layer. (c),(d) Enlargement of the nonlocal resistances for different modulator widths ($w$) for 1f and 2f, respectively.

Figure 3

(a),(b), [(e),(f)] Angular dependence of 1f and 2f of nonlocal resistances for a magnetic field of 10 mT [60 mT] for different modulator currents. (c),(d), [(g),(h)] Values of $A^{1\omega }$, $B^{1\omega }$, $A^{2\omega }$, and $B^{1\omega }$ at 10 mT [60 mT] as a function of the charge current in the modulator, from the best fit of Eq. (5) and (6). In our configuration, the positive modulator current produces a depletion of the magnon conductivity.

Figure 4

(a) Magnetic field dependence of the 1f nonlocal resistance for different applied charge currents in the Py modulator. The asymmetry between positive and negative current corresponds to the spin-current-controlled modulation. (b) In the 2f response, the modulation generates a vertical shift between the positive and the negative currents.

Figure 5

(a) The difference of $\left[R_{\mathrm{NL}}^{1\omega }\left(1\mathrm{ mA}\right)-R_{\mathrm{NL}}^{1\omega }\left(0\mathrm{ mA}\right)\right]$ and $\left[R_{\mathrm{NL}}^{1\omega }\left(-1\mathrm{ mA}\right)-R_{\mathrm{NL}}^{1\omega }\left(0\mathrm{ mA}\right)\right]$ is plotted as a function of the magnetic field applied for $\alpha =0^{\circ }$. (b) The magnetic field dependence of the magnon transport modulation efficiency for the 1f signal shows the enhancement of the modulation due to the ASHE contribution. (c) The 2f response shows an opposite behavior of the modulation efficiency.

Figure 6

(a) Magnetic field dependency of the nonlocal resistance using the middle Py strip as the injector. The inset shows the electrical connections used in these measurements. (b) Angular dependence of the 1f nonlocal resistances, showing the increase of the signal due to the contribution of the ASHE up to 50 mT.