Coexistence of low-frequency spin-torque ferromagnetic resonance and unidirectional spin Hall magnetoresistance

We investigate the DC voltage under an applied microwave current for platinum(Pt)/cobalt(Co), tantalum(Ta)/Co, and tungsten(W)/Co bilayers, where the microwave-induced alternating magnetic field ($B_{\mathrm{rf}}$) is parallel to an external static magnetic field ($B_{\mathrm{ext}}$). Whereas spin torque ferromagnetic resonance (ST FMR) signals do not appear because of the parallel configuration of $B_{\mathrm{rf}}$ and the magnetization of the Co layer, we recently found a clear hysteresis signal around $B_{\mathrm{ext}}=0\mathrm{mT}$ only when the microwave frequency ($f_{\mathrm{MW}}$) is low, typically less than 10 GHz. This low-frequency ST FMR (LFST FMR) signal enables us to detect magnetization switching induced by spin-orbit torque (SOT) with high sensitivity. In this study, we found an additional background (BG) signal superimposed on the LSFT FMR signal. The additional BG signal also has hysteresis behavior and appears even at high $f_{\mathrm{MW}}$, where the LSFT FMR signal completely disappears. The sign of the BG signal is changed by changing the nonmagnetic material from Pt to Ta or W. By measuring $f_{\mathrm{MW}}$, the microwave current, the temperature, and the magnetic field angle dependences, we conclude that the BG signal is induced by spin-dependent unidirectional spin Hall magnetoresistance (SD USMR), which is generated by a spin current induced by the spin Hall effect of nonmagnetic metals and spin-dependent electron mobility in ferromagnetic metals. The SD USMR signal appears in wide ranges of $f_{\mathrm{MW}}$ and $B_{\mathrm{ext}}$ because the SD USMR originates from the nonlinearity of current-dependent resistance and is not related to magnetization dynamics. From the magnitude of the BG signal, the spin Hall angles of Pt and Ta are calculated to be 0.026 ± 0.006 and −0.042 ± 0.006, respectively. In addition, we demonstrate SOT magnetization switching using the BG signal.

Figure 1

(a) Schematic of the device structure and the electrical circuit used in this study. (b,e) $R_{\mathrm{NM}/\mathrm{FM}}$, (c,f) $-\frac{\mathrm{\Delta }{R}_{\mathrm{NM}/\mathrm{FM}}}{\mathrm{\Delta }{B}_{\mathrm{ext}}}$, and (d,g) $V_{\mathrm{DC}}$ as a function of $B_{\mathrm{ext}}$ along the $y$ axis for samples A and C, respectively. $V_{\mathrm{DC}}$ was measured under microwave irradiation with $f_{\mathrm{MW}}=0.2\mathrm{GHz}$ and microwave power $P_{\mathrm{MW}}=5\mathrm{dBm}$ ($I_{\mathrm{rf}}^0=4.5$ mA for sample A and 5.2 mA for sample C).

Figure 2

(a) $V_{\mathrm{DC}}$ as a function of $B_{\mathrm{ext}}$ under various microwave frequencies, $f_{\mathrm{MW}}$, and (b) enlarged $V_{\mathrm{DC}}\text{−}{B}_{\mathrm{ext}}$ curves from −40 to +40 mT (meshed area) for sample C. $P_{\mathrm{MW}}$ was 5 dBm with $I_{\mathrm{rf}}^0$ ranging from 4.3 mA at $f_{\mathrm{MW}}=13\mathrm{GHz}$ to 5.2 mA at $f_{\mathrm{MW}}=0.2\mathrm{GHz}$. (c) $V_{\mathrm{DC}}$ as a function of $B_{\mathrm{ext}}$ at various $f_{\mathrm{MW}}$ values, and (d) enlarged plot for sample D. $P_{\mathrm{MW}}$ was 10 dBm, with $I_{\mathrm{rf}}^0$ ranging from 8 mA at $f_{\mathrm{MW}}=13\mathrm{GHz}$ to 10 mA at $f_{\mathrm{MW}}=0.2\mathrm{GHz}$.

Figure 3

(a) $V_{\mathrm{BG}}/I_{\mathrm{rf}}^{0^2}$ as a function of $f_{\mathrm{MW}}$ at $P_{\mathrm{MW}}=5\mathrm{dBm}$ with $I_{\mathrm{rf}}^0$ ranging from 4.3 mA at $f_{\mathrm{MW}}=13\mathrm{GHz}$ to 5.2 mA at $f_{\mathrm{MW}}=0.2\mathrm{GHz}$, and (b) $V_{\mathrm{BG}}$ as a function of $I_{\mathrm{rf}}^0$ at $f_{\mathrm{MW}}=0.2\mathrm{GHz}$ for sample C. (c) $V_{\mathrm{BG}}$ as a function of temperature for sample E. Under the applied voltage for microwave generation, $V_{\mathrm{MW}}$ and $f_{\mathrm{MW}}$ were 2 V ($I_{\mathrm{rf}}^0=13$ mA) and 0.1 GHz, respectively. Temperature dependence of DC voltage due to the SF USMR, where the voltage at 300 K is normalized to the same value of $V_{\mathrm{BG}}$ at 300 K for sample E.

Figure 4

(a−c) Schematics of the measurement for the magnetic field angle dependence of $V_{\mathrm{BG}}$. (d) $V_{\mathrm{BG}}$ as a function of α, β, and γ for sample E. $V_{\mathrm{MW}}$ and $f_{\mathrm{MW}}$ were 2 V ($I_{\mathrm{rf}}^0=13$ mA) and 0.1 GHz, respectively.

Figure 5

Numerically calculated $B_{\mathrm{ext}}$ dependence of $V_{\mathrm{DC}}$ generated by the SD USMR for (a) sample A and (b) sample C. The $y$ component of the magnetization was estimated from the anisotropic magnetoresistance (AMR) signal in the $R_{\mathrm{NM}/\mathrm{FM}}\text{−}{B}_{\mathrm{ext}}$ curve shown in Figs. 1 and 1. Difference between experimentally obtained $V_{\mathrm{DC}}\text{−}{B}_{\mathrm{ext}}$ curves [Figs. 1 and 1] and the calculated $V_{\mathrm{DC}}\text{−}{B}_{\mathrm{ext}}$ curves due to the SD USMR [Figs. 5 and 5] for (c) sample A and (d) sample C.

Figure 6

(a) $V_{\mathrm{DC}}$ as a function of $B_{\mathrm{ext}}$ under microwave with various frequencies for $\mathrm{W}/\mathrm{Co}/\mathrm{Si}{\mathrm{O}}_2$ device with $P_{\mathrm{MW}}=5\mathrm{dBm}$ with $I_{\mathrm{rf}}^0$ ranging from 1.7 mA at $f_{\mathrm{MW}}=13\mathrm{GHz}$ to 2.1 mA at $f_{\mathrm{MW}}=0.2\mathrm{GHz}$. (b) A schematic of the electrical circuit for demonstration of the magnetization switching. (c,d) Enlarged $V_{\mathrm{DC}}\text{−}{B}_{\mathrm{ext}}$ curves between −3 and +3 mT (left panels) and $\mathrm{\Delta }{V}_{\mathrm{PLS}}$ as a function of pulse current density $J_{\mathrm{PLS}}$ (right panels) for (c) $f_{\mathrm{MW}}=0.2\mathrm{GHz}$ and (d) 13 GHz.