First harmonic measurements of the spin Seebeck effect.

We present measurements of the spin Seebeck effect (SSE) by a technique that combines alternating currents (AC) and direct currents (DC). The method is applied to a ferrimagnetic insulator/heavy metal bilayer, Y$_3$Fe$_5$O$_{12}$(YIG)/Pt. Typically, SSE measurements use an AC current to produce an alternating temperature gradient and measure the voltage generated by the inverse spin-Hall effect in the heavy metal at twice the AC frequency. Here we show that when Joule heating is associated with AC and DC bias currents, the SSE response occurs at the frequency of the AC current drive and can be larger than the second harmonic SSE response. We compare the first and second harmonic responses and show that they are consistent with the SSE. The field dependence of the voltage response is used to characterize the damping-like and field-like torques. This method can be used to explore nonlinear thermoelectric effects and spin dynamics induced by temperature gradients.