Spin-Current-Controlled Modulation of the Magnon Spin Conductance in a Three-Terminal Magnon Transistor

Efficient manipulation of magnon spin transport is crucial for developing magnon-based spintronic devices. In this Letter, we provide proof of principle of a method for modulating the diffusive transport of thermal magnons in an yttrium iron garnet channel between injector and detector contacts. The magnon spin conductance of the channel is altered by increasing or decreasing the magnon chemical potential via spin Hall injection of magnons by a third modulator electrode. We obtain a modulation efficiency of $1.6\%/\mathrm{mA}$ at $T=250\mathrm{K}$. Finite element modeling shows that this could be increased to well above $10\%/\mathrm{mA}$ by reducing the thickness of the channel, providing interesting prospects for the development of thermal-magnon-based logic circuits.

Figure 1

(a) Colorized SEM image of device $G1$; electrical connections indicated schematically. Arrows mark charge current flow in the circuit. (b) A sketch of the device with schematic side views of the $\mathrm{modulator}|\mathrm{YIG}$ interface for positive (negative) dc currents. When the magnetic moment of the spin accumulation ${\mu }_s$ in the modulator is antiparallel (parallel) to the YIG magnetization $M_{\mathrm{YIG}}$, ${\mu }_m$, and, hence, $n_m$ in the channel is increased (decreased). Consequently, the magnon spin conductance from injector to detector is increased (decreased).

Figure 2

(a),(b),(e),(f) [(c),(d),(g),(h)] First and second harmonic voltage for a positive (negative) dc modulator current as a function of $\alpha$. Raw data are presented in (a) and (c) for the first harmonic; solid lines are ${\sin }^2(\alpha +{\varphi }^{1\omega })$ fits to the data. For the second harmonic, (e) and (g) show the raw data fitted by a $\sin (\alpha +{\varphi }^{2\omega })$ dependence. Panels (b),(d) [(f),(h)] show the residues (i.e., the data minus the fit) of the first (second) harmonic signal for positive and negative dc current, respectively. Residues are fitted by a ${\sin }^3(\alpha +{\varphi }^{1\omega })$ and ${\sin }^2(\alpha +{\varphi }^{2\omega })$ angular dependence for the first and second harmonic (solid lines). Residues for $I_{\mathrm{dc}}=0$ have been subtracted from the data to exclude effects not induced by the dc current. In (a) and (c), a constant offset was subtracted (see the Supplemental Material [31], Sec. S6). Data obtained for $I_{\mathrm{ac}}=100\mu \mathrm{A}$.

Figure 3

(a) [(c)] Amplitude of the ${\sin }^2\alpha$ oscillation ($\sin \alpha$) as a function of dc current. Solid lines are quadratic fits to the data. (b),(d) The amplitudes of the ${\sin }^3\alpha$ and ${\sin }^2\alpha$ component in the first and second harmonic voltage, respectively. Solid lines are linear fits to the data. Data obtained at $T=250\mathrm{K}$. Error bars represent one standard error obtained from the least squares fits to Eqs. (6) and (7).

Figure 4

(a) Magnon chemical potential profile due to the SHE injection of magnons by the dc modulator current. (b) Average magnon chemical potential in the channel as a function of $I_{\mathrm{dc}}$. (c) Low-energy part of the magnon spectral density $N_m=D(\epsilon )f(\mu ,T,\epsilon )$ for zero dc current (dashed line) and maximum current (solid line). (d) Magnon chemical potential profile due to the ac injector current. (e) Modulation efficiency as a function of the temperature for a film with $t_{\mathrm{YIG}}=210\mathrm{nm}$. Solid line shows the simulation results; symbols show the experimental results for the first harmonic obtained from sample $G1$. (f) Relative modulation as a function of $I_{\mathrm{dc}}$ for various YIG thicknesses.