Towards Thermal Reading of Magnetic States in Hall Crosses

The 3ω method is a standard way to measure the thermal conductivity of thin films. In this study, we apply the method to read the magnetic state of a perpendicularly magnetized CoTb ferrimagnetic Hall cross using a thermal excitation. In order to generate the thermal excitation, an oscillating current at an ω frequency is applied to the Hall cross using different geometries. The magnetic signals oscillating at ω, 2ω, and 3ω are probed using a lock-in technique. From the analysis of the power dependence, we can attribute the 3ω response to the temperature oscillation and the 2ω to the temperature-gradient oscillation. Finally, the frequency dependence of the magnetic signals can be understood by considering the heat diffusion in a two-dimensional model