Absence of the Thermal Hall Effect in Anomalous Nernst and Spin Seebeck Effects

The anomalous Nernst effect (ANE) and the spin Seebeck effect (SSE) in spin caloritronics are two of the most important mechanisms to manipulate the spin-polarized current and pure spin current by thermal excitation. While the ANE in ferromagnetic metals and the SSE in magnetic insulators have been extensively studied, a recent theoretical work suggests that the signals from the thermal Hall effect (THE) have field dependences 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, we systematically study the THE in a ferromagnetic metal, Permalloy (Py), and magnetic insulator, an yttrium iron garnet (YIG), by using different Seebeck coefficients between electrodes and contact wires. Our results demonstrate that the contribution of the THE by the thermal couple effect in the Py and YIG is negligibly small if one includes the thickness dependence of the Seebeck coefficient. Thus, the spin-polarized current in the ANE and the pure spin current in the SSE remain indispensable for exploring spin caloritronics phenomena.

Figure 1

(a) TSSE configuration with a ${\nabla }_{x}T$. (b) LSSE configuration with a ${\nabla }_{z}T$. (c) The angular dependence of the thermal voltage for Py (50 nm) with the setup of ANE measurement. (d) Schematic diagram of the THE measured by the LSSE configuration. The wires and the electrode serve as a thermocouple.

Figure 2

(a) Schematic diagram of the thermocouple effect composed of a Pt (50 nm) thin film and two wires with a heat source on a top electrode. The thermal emf measured by two Cu wires in (b) and Pt wires in (c). (d) Schematic diagram of the thermocouple effect with a heat source on a bottom electrode. The thermal emf measured by two Cu wires in (e) and Pt wires in (f).

Figure 3

A series of geometries for the field-dependent thermal voltage measurement with a uniform vertical temperature gradient in the Py (50 nm) sample, which are (a) parallel connecting Cu and Pt wires in different positions, (b) connecting two wires in the same position, (c) connecting two wires in the same position with an additional short Pt wire, and (d) connecting two wires in the same position of the $\mathrm{Pt}(5\mathrm{nm})/\mathrm{Py}(50\mathrm{nm})$ bilayer sample.

Figure 4

(a) Schematic diagram of the field-dependent thermal voltage measured with a uniform vertical temperature gradient in the $\mathrm{Pt}/\mathrm{YIG}$ sample. Field dependence of the thermal voltage on (b) $\mathrm{Pt}(10\mathrm{nm})/\mathrm{YIG}$ and (c) $\mathrm{Pt}(5\mathrm{nm})/\mathrm{YIG}$ measured by connecting Cu and Pt wires in the same position.

Figure 5

Schematic diagram of using a $T$-type thermocouple (i.e., Cu wire and ${\mathrm{Cu}}_{55}{\mathrm{Ni}}_{45}$ wire) to measure the field-dependent thermal voltage with a uniform vertical temperature gradient for (a) Py (50 nm), (b) $\mathrm{Pt}(5\mathrm{nm})/\mathrm{YIG}$ (0.5 mm), (c) Py (10 nm), and (d) $\mathrm{Pt}(5\mathrm{nm})/\mathrm{YIG}(55\mathrm{nm})$.