Measurement of third harmonic voltage in ferromagnet-heavy metal heterostructures

The second harmonic voltage has been widely used to measure electrically driven spin torques in ferromagnet- heavy metal heterostructures. Based on the macrospin model, the third harmonic voltage is proposed for studying thermally driven spin torques. Our experiments clearly show that two distinct physical mechanisms dominate such thermal spin torques. The first refers to thermal expansion or contraction, which generates an effective field through the magnetoelastic effect. The second comes from the thermally reduced magnetization of the ferromagnetic layer, which modulates the magnetoresistance of the heterostructure. Our study illustrates the versatile applicability of the third harmonic voltage in investigating the nonlinear effects in ferromagnet-heavy metal heterostructures.