Third harmonic resistance in ferromagnet/heavy-metal bilayers

The emergence of nonlinear spin transport phenomena in magnetic heterostructures encourages a careful examination on different origins of the harmonic signals. Here, we report sizable third harmonic nonlinear resistances in permalloy (Py)/Pt bilayers, accounting for approximately 14% of the linear counterparts at low magnetic field of 5 Oe and current density of $7.9\ifmmode\times\else\texttimes\fi{}{10}^{6}\phantom{\rule{4pt}{0ex}}\mathrm{A}\phantom{\rule{4pt}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}2}$. Both the transverse and longitudinal components increase quadratically with the applied current, exhibiting a twofold symmetry on the magnetization direction. By considering the magnetization and resistance modulations due to current-induced spin-orbit torque (SOT) and Joule heating, we performed a comprehensive analysis on spin current-related transport behaviors up to the third-order terms in the bilayer systems. Through a self-consistent fitting process, it is revealed that the low-field signals are dominated by SOT-induced magnetization oscillation, while the high-field ones primarily result from thermally induced resistance changes. We also find that the possible nonlinear spin current generation is negligibly small in the present material system. Our results could contribute to the understanding of nonlinear magnetotransport phenomena in ferromagnetic/heavy-metal bilayers.