Contribution of the thermal Hall effect to the anomalous Nernst and spin Seebeck effects

   Heat dissipation has been the most formidable challenge in information technology due to the continued increase in power dissipation, and it has hampered the development of charged-based electronic devices. Unlike purely charge-based systems, information devices encoded in magnetization states in spintronics are nonvolatile, which can reduce the power requirement for maintaining the data. Therefore, within a very short period of time, we have witnessed the remarkable success of spintronics to transfer fundamental science into practical applications.
   The manipulation of the spin-dependent transport properties in terms of the spin-polarized current (JSP) or pure spin current (JS) is one key aspect in the field of spintronics. The anomalous Nernst effect (ANE) and the spin Seebeck effect (SSE) are two of the most important mechanisms that generate and detect the JSP and JS by thermal excitation, respectively. Thus, research regarding the interplay among the charge, spin, and heat in the ANE and SSE has been intensively conducted. Nevertheless, recent research suggests that the thermal Hall effect (THE) has field dependences that are indistinguishable from, and may even overwhelm, those of the ANE and SSE. Therefore, it is vital to investigate the contribution of the THE in the ANE and SSE. In this work, for the first time, we successfully separated the contribution of the THE from the ANE in the ferromagnetic metal permalloy (Py) and that from the SSE in the magnetic insulator yttrium iron garnet (YIG), by designing several special measurement geometries.
   The JSP of the ANE can be generated in the lateral direction from ferromagnetic metals by a perpendicular temperature gradient (zT). This current can be converted into a transverse electric field to be detected by electrical means. The JS of the SSE can be generated from ferromagnetic insulators by the zT and can be detected in an adjacent normal metal by the inverse spin Hall effect (ISHE). The transverse ANE voltage and the transverse ISHE voltage share the same field dependence, as shown in Fig. 1. Recent research suggests that the THE, including the magnon Hall effect and the anomalous Righi-Leduc effect, may significantly contribute to the ANE and SSE but may be overlooked. Strikingly, the THE exhibits exactly the same magnetic-field angular dependence as that of the ANE and SSE. As such, the THE alone could potentially account for the observed spin-dependent signals, including the ISHE, SSE and ANE.
   In our experiments, we demonstrate that the THE via the thermocouple effect is inevitable due to the strong thickness dependence of the Seebeck effect in the ANE and SSE configurations. However, by using different Seebeck coefficients between the devices and contact electrodes, as shown in the schematic of Fig. 2, we can separate the THEs from the ANE in Py and from the SSE in YIG. We show that the contributions of the THE by the thermal couple effect in the 50 nm Py and 0.5 mm YIG are negligibly small, as shown in Fig. 2(a) and 2 (b), respectively. The magnitude of the THE is less than 0.2% of the ANE in Py and less than 0.03% of the SSE in YIG, which indicates that the JSP in the ANE and the JS in the SSE remain indispensable elements to explore these two spin caloritronics phenomena. Our work also sheds light on a new method to investigate materials with a strong Dzyaloshinskii-Moriya interaction and inversion symmetry breaking via the THE by thermal excitation.
Figure 1. The THE in the framework of the (a) ANE and (b) SSE.
Chen, Y., and Huang, S. (2016). Absence of the thermal Hall effect in anomalous Nernst and spin Seebeck effects. Physical Review Letters, 117(24), 247201. DOI:10.1103/PhysRevLett.117.247201
Yi-Jia Chen
Department of Physics
Ssu-Yen Huang
Professor, Department of Physics