Thickness dependence of anomalous Nernst effect in ferromagnetic metals

The connection between thermoelectricity and spintronics has recently attracted much attention because of its potential application for the high-efficiency electric devices and the iste heat recycling. In particular, anomalous Nernst effect (ANE), the conversion of thermal energy into the spin-dependent electric signal in ferromagnetic metals(FMs), is one of the most important mechanism to study the coupling between charge, spin, and heat. Although, the spintronic devices based on the ANE, including the multilayer structure and ferromagnetic thermal thermopile, have been extensively investigate, the issue for the thickness dependence of ANE has never been addressed. In this work, by using a vertical temperature gradient, we systematically study the thickness dependence of the ANE in several ferromagnetic metals (FMs), including permalloy (Py), iron (Fe), and cobalt (Co) at room temperature. The sign of the ANE can immediately tell that the sign of the Nernst angle in Fe is opposite to that of Py and Co. In the thickness-dependent measurement, we report that the ANE signal in all FMs samples are constant in thick films region while the signal decreases with decreasing thicknesses (less than 10 nm, except for ultra-thin Fe). Importantly, there is no measurable ANE signal when thickness is less than 2 nm, even the ferromagnetic ordering with Curie temperatures still above room temperature. After taking the thickness dependence of the resistivity and magnetization into account, we are able to determine the intrinsic ANE coefficient in ferromagnetic metals for the first time. More surprisingly, we observed the sign change of ANE signal between thick and thin Fe samples. In addition, unlike other FMs, the ANE voltage showed increased instead of decreased signal, when the thickness of Fe sample is less than 6 nm. We suggest this enhancement signal is origin from the intrinsic property of ultra-thin Fe film. Our results provide an important insight on how the role of thickness effect has a strong influence on the development of multilayer structure or ferromagnetic thermal thermopile devices.