Observation of the Magneto-Thomson Effect

We report the observation of the higher-order thermoelectric conversion based on a magneto-Thomson effect. By means of thermoelectric imaging techniques, we directly observed the temperature change induced by the Thomson effect in a polycrystalline ${\mathrm{Bi}}_{88}{\mathrm{Sb}}_{12}$ alloy under a magnetic field and found that the magnetically enhanced Thomson coefficient can be comparable to or even larger than the Seebeck coefficient. Our experiments reveal the significant contribution of the higher-order magnetothermoelectric conversion, opening the door to “nonlinear spin caloritronics.”

Figure 1

Thomson and magneto-Thomson effects. (a) Schematic of the conventional Thomson effect. When a charge current ${\mathbf{J}}_c$ and a temperature gradient $\nabla T$ are applied to a conductor, the Thomson effect induces heat absorption or release depending on the scalar product of ${\mathbf{J}}_c$ and $\nabla T$. (b) Schematic of the magneto-Thomson effect. The heat production rate due to the Thomson effect can be modulated by applying a magnetic field $\mathbf{H}$ to a conductor.

Figure 2

Thermal imaging of Thomson effect at zero magnetic field. (a) Experimental configuration for the measurements of the Thomson effect in the ${\mathrm{Bi}}_{88}{\mathrm{Sb}}_{12}$ slab using the lock-in thermography method. During the measurement, a square-wave-modulated ac charge current with the amplitude $J_c$, frequency $f$, and zero dc offset was applied to the slab. The data shown in this figure were measured in the absence of an external magnetic field. (b),(c) Lock-in amplitude $A$ and phase $\varphi$ images for the ${\mathrm{Bi}}_{88}{\mathrm{Sb}}_{12}$ slab at $J_c=100.0\mathrm{mA}$ and $f=1.0\mathrm{Hz}$, measured when the heating power $P$ of the heater is 30 mW (b) or 0 mW (c). (d) $A_{\text{TE}}$ and ${\varphi }_{\text{TE}}$ images for the ${\mathrm{Bi}}_{88}{\mathrm{Sb}}_{12}$ slab, obtained by subtracting the images in (c) from those in (b). (e)–(g) Steady-state temperature $T$ (e), $A_{\text{TE}}$ (f), and ${\varphi }_{\text{TE}}$ (g) profiles along the $y$ direction for various values of $J_c$ and $P$. The profiles were obtained by averaging 16 $y$-directional raw profiles along the $x$ direction; the center of the averaged area is marked with dotted lines in (d). (h) $J_c$ dependence of $A_{\text{TE}}$ on the region $R1$ for various values of $P$. (i) $|{\nabla }_{y}T|$ dependence of $A_{\mathrm{TE}}/j_c$ on $R1$. $j_c$ and $|{\nabla }_{y}T|$ denote the square-wave amplitude of the charge current density and the temperature gradient along the $y$ direction, respectively. The data points in (h) and (i) are obtained by averaging the $A_{\text{TE}}$ values on the area defined by the square with the size of $16\times 16\mathrm{pixels}$ ($0.24\times 0.24{\mathrm{mm}}^2$) in (d). The error bars represent the standard deviation of the data in the corresponding squares, which are smaller than the size of the data points.

Figure 3

Observation of magneto-Thomson effect. (a),(b) $A_{\text{TE}}$ and ${\varphi }_{\text{TE}}$ images for the ${\mathrm{Bi}}_{88}{\mathrm{Sb}}_{12}$ slab at $J_c=100.0\mathrm{mA}$, $f=1.0\mathrm{Hz}$, and $P=30\mathrm{mW}$, measured when the magnetic field of $|{\mu }_{0}H|=0.0\text{T}$ (a) or 0.9 T (b) was applied along the $x$ direction. (c) $|{\mu }_{0}H|$ dependence of the Thomson signal ${\eta }_{\mathrm{TE}}(=|A_{\mathrm{TE}}/(j_c{\nabla }_{y}T)|)$ on $R1$ of the ${\mathrm{Bi}}_{88}{\mathrm{Sb}}_{12}$ slab. The inset to (c) shows the $|{\mu }_{0}H|$ dependence of ${\varphi }_{\text{TE}}$ on $R1$. The data points in (c) are obtained by averaging the $A_{\text{TE}}$ and ${\varphi }_{\text{TE}}$ values on the areas defined by the squares with the size of $16\times 16\mathrm{pixels}$ in (a) and (b). The error bars represent the standard deviation of the data in the corresponding squares.

Figure 4

Magnetic field and temperature dependences of Seebeck coefficient. (a) ${\mu }_{0}H$ dependence of the Seebeck coefficient $S$ of the ${\mathrm{Bi}}_{88}{\mathrm{Sb}}_{12}$ slab for various values of $T$. (b) $T$ dependence of $S$ for various values of ${\mu }_{0}H$. (c) ${\mu }_{0}H$ dependence of the Thomson coefficient $\tau$ at $T=300\mathrm{K}$, calculated from the data in (a) and (b) based on Eq. (2).