Spin-orbit torque and Nernst effect in Bi-Sb/Co heterostructures

Harmonic measurements of the longitudinal and transverse voltages in Bi-Sb/Co bilayers are presented. A large second harmonic voltage signal due to the ordinary Nernst effect is observed. In experiments where a magnetic field is rotated in the film plane, the ordinary Nernst effect shows the same angular dependence in the transverse voltage as the dampinglike spin-orbit torque and in the longitudinal voltage as the unidirectional spin-Hall magnetoresistance, respectively. Therefore, the ordinary Nernst effect can be a spurious signal in spin-orbit torque measurements, leading to an overestimation of the spin-Hall angle and spin-Hall conductivity in topological insulators or semimetals.

Figure 1

A double Hall-bar structure is used to measure transverse ($V_{xy}$) and longitudinal ($V_{xx}$) voltages on the Bi-Sb bilayer samples considered in this work. The magnetic field is applied in the film plane at an angle $\phi$ with respect to the current direction. The inset shows a micrograph of an actual double Hall-bar device. The width of the Hall bar is $6\mu \mathrm{m}$.

Figure 2

Upper panel: The planar Hall effect is only observed in the samples with magnetic layers (Bi-Sb/Co and Pt/Py). Here ${\phi }_{\text{B}}$ is the angle between the current direction and $B_{\text{ext}}$ in the film plane. Lower panel: $V_{2\omega }$ shows a $cos\left({\phi }_{\text{B}}\right)$ dependence in the samples with Bi-Sb, due to the ordinary Nernst effect. In the sample Pt/Py, spin-orbit torque and anomalous Nernst effect are present. The solid lines are fits to Eq. (3).

Figure 3

Upper panel: $V_{1\omega }^{xx}$ as a function of ${\phi }_{\text{B}}$. A constant offset was removed for easy comparison. The anisotropic magnetoresistance is observed only in the magnetic samples Bi-Sb/Co and Pt/Py. Lower panel: $V_{2\omega }^{xx}$ in Bi-Sb/Co and Bi-Sb/Al shows a $sin\left(\phi \right)$ dependence. This is expected from the ordinary Nernst effect. In the sample Pt/Py contributions from spin-orbit torque, anomalous Nernst effect and the unidirectional spin-Hall magnetoresistance are observed. The solid lines are fits to Eq. (4).

Figure 4

The magnetic field dependence of the second harmonic voltage. In Bi-Sb/Co and Bi-Sb/Al a linear increase in voltage can be observed, as expected from the ordinary Nernst effect. In Pt/Py on the other hand the harmonic voltage is decreasing as expected from dampinglike spin-orbit torque and unidirectional spin-Hall magnetoresistance, respectively. Note that the voltage in Pt/Py has been enhanced for visual clarity.