Nonlocal Detection of Out-of-Plane Magnetization in a Magnetic Insulator by Thermal Spin Drag

We demonstrate a conceptually new mechanism to generate an in-plane spin current with out-of-plane polarization in a nonmagnetic metal, detected by nonlocal thermoelectric voltage measurement. We generate out-of-plane ($\nabla T_{\mathrm{OP}}$) and in-plane ($\nabla T_{\mathrm{IP}}$) temperature gradients, simultaneously, acting on a magnetic insulator-Pt bilayer. When the magnetization has a component oriented perpendicular to the plane, $\nabla T_{\mathrm{OP}}$ drives a spin current into Pt with out-of-plane polarization due to the spin Seebeck effect. $\nabla T_{\mathrm{IP}}$ then drags the resulting spin-polarized electrons in Pt parallel to the plane against the gradient direction. This finally produces an inverse spin Hall effect voltage in Pt, transverse to $\nabla T_{\mathrm{IP}}$ and proportional to the out-of-plane component of the magnetization. This simple method enables the detection of the perpendicular magnetization component in a magnetic insulator in a nonlocal geometry.

Figure 1

(a) Device schematics and electrical connections (not to scale). (b) Top and side view of a representative device and coordinate system. Shaded red color in the lower panel of (b) indicates the presumed heat distribution upon current injection through the Au heater layer.

Figure 2

(a) Second harmonic voltages recorded with a heater current of $I_{\mathrm{ac}}=50\mathrm{mA}$ during a $\phi$ rotation in a constant external field ${\mu }_{0}H=500\mathrm{mT}$ of devices with different heater-detector separation $d$. (b) In-plane field sweep measurements for different angles $\phi$, where the signal jumps are associated with the SSE. (c) Angular dependence of the SSE signal and the fit following the expected $\cos \phi$ function. Current (d) and heater-detector distance (e) dependence of the SNMR and the SSE signals and associated fits. Signals in (a) and (b) are manually offset for clarity.

Figure 3

(a) Second harmonic voltage in in-plane magnetized $\mathrm{TmIG}/\mathrm{Pt}$ upon out-of-plane field sweep for different heater currents for $d=30\mu \mathrm{m}$. A field-induced linear slope, which we associate with the ordinary Nernst effect of Pt, and a $m_z$-dependent signal (gap between the two saturated states shown by the red arrow) are observed. (b) The same measurement configuration reported in (a) performed on a separate perpendicularly magnetized $\mathrm{TmIG}/\mathrm{Pt}$ sample with $d=10\mu \mathrm{m}$. (c) The current dependence of the $m_z$-dependent signal and fit following $V_{2\omega }\propto I^2$ for both samples. Inset: Heater-detector distance dependence of the $m_z$-dependent signal for IP $\mathrm{TmIG}/\mathrm{Pt}$ sample and exponential fit. Signals in (a) and (b) are manually offset for clarity.

Figure 4

Comparison of thermally driven (a),(c) and electrically driven (b),(d) voltage measurements. (a) The SNMR signal after subtraction of the SSE contribution due to $\nabla T_{\mathrm{OP}}$, centered on zero (measurement parameters $d=30\mu \mathrm{m}$, $I_{ac}=50\mathrm{mA}$). (b) The spin Hall magnetoresistance measured in identical condition on a nearby device by injection of $I_{ac}=1.6\mathrm{mA}$. (c) The voltage recorded during an $H_z$ sweep after subtraction of the linear field-induced slope [measurement parameters are the same as in (a)]. (d) The electrically driven Hall resistance signal with the $H_z$ sweep after subtraction of linear slope due to ordinary Hall effect. In (d), at fields lower than the saturation field of $\mathbf{m}$ there is an additional signal due to the SMR becoming dominant as the $\mathbf{m}$ trajectory presumably leads to large SMR contribution in the electrical signal.

Figure 5

Illustration of the thermal spin drag mechanism. $\nabla T_{\mathrm{OP}}$ pumps thermally generated magnons into Pt (left), which creates an imbalance of spin population in favor of out-of-plane spins, and $\nabla T_{\mathrm{IP}}$ acts as an electromotive force for the spin-polarized current and drags them toward the colder side (right). Finally, an ISHE voltage builds up orthogonal to both temperature gradients, which is the thermal spin drag voltage reported in Fig. 3.