Observation of the Anisotropic Magneto-Thomson Effect

We report the observation of the anisotropic magneto-Thomson effect (AMTE), which is one of the higher-order thermoelectric effects in a ferromagnet. Using lock-in thermography, we demonstrated that in a ferromagnetic NiPt alloy, the cooling or heating induced by the Thomson effect depends on the angle between the magnetization direction and the temperature gradient or charge current applied to the alloy. AMTE observed here is the missing ferromagnetic analog of the magneto-Thomson effect in a nonmagnetic conductor, providing the basis for nonlinear spin caloritronics and thermoelectrics.

Figure 1

Schematics of the cooling induced by the anisotropic magneto-Thomson effect in the $\nabla T\parallel \mathbf{I}\parallel \mathbf{M}$ (a) and $\nabla T\parallel \mathbf{I}\perp \mathbf{M}$ (b) configurations. When a charge current $\mathbf{I}$ and a temperature gradient $\nabla T$ are applied to a ferromagnetic conductor, the magnitude of the Thomson-effect-induced cooling or heating depends on the direction of the spontaneous magnetization $\mathbf{M}$ due to the spin-orbit interaction acting on spin-polarized conduction carriers.

Figure 2

(a) Temperature $T$ dependence of the Seebeck coefficient $S$ for the ${\mathrm{Ni}}_{95}{\mathrm{Pt}}_5$ slab under external magnetic fields of $|{\mu }_{0}H|=0$ (gray squares) and 800 mT (black circles) in the $\nabla T\perp \mathbf{H}$ configuration. $\mathbf{H}$ denotes the magnetic field with the magnitude $H$. The independent data points represent the experimental data, and the solid lines represent the fitting results obtained using 3rd-order polynomial functions. The error bars represent the standard deviations of the data during six consecutive measurements. (b) $T$ dependence of the Thomson coefficient $\tau$ estimated from Eq. (2) using the experimental data points (gray squares and black circles) and the polynomial fitted curves in (a) (gray and black curves). The blue curve represents the $T$ dependence of the anisotropy of the Thomson coefficient $\mathrm{\Delta }\tau =3({\tau }_{0\mathrm{mT}}-{\tau }_{800\mathrm{mT}})$, where ${\tau }_{0\mathrm{mT}}$ (${\tau }_{800\mathrm{mT}}$) represents the value of $\tau$ at 0 mT (800 mT) in the $\nabla T\perp \mathbf{H}$ configuration.

Figure 3

(a) Schematic of the experimental configuration for the measurements of the Thomson effect in the ${\mathrm{Ni}}_{95}{\mathrm{Pt}}_5$ slab using LIT. (b) Time ($t$) chart of the charge current applied to the sample and the resultant Thomson-effect-induced heat. During the measurement, a square-wave-modulated alternating charge current with amplitude $I$, frequency $f$, and zero offset was applied to the slab. (c) Lock-in amplitude $A$ and phase $\varphi$ images for the ${\mathrm{Ni}}_{95}{\mathrm{Pt}}_5$ slab at $I=0.8\mathrm{A}$ and $f=1.0\mathrm{Hz}$, measured with a left (right) heater power of $P_{\mathrm{L}}=2.0\mathrm{W}$ ($P_{\mathrm{R}}=0.5\mathrm{W}$). (d) $A$ and $\varphi$ images, measured with a left (right) heater power of $P_{\mathrm{L}}=1.3\mathrm{W}$ ($P_{\mathrm{R}}=1.5\mathrm{W}$). (e) $A_{\mathrm{TE}}$ and ${\varphi }_{\mathrm{TE}}$ images for the ${\mathrm{Ni}}_{95}{\mathrm{Pt}}_5$ slab, obtained by subtracting the images in (d) from those in (c). (f)–(h) The $y$-directional steady-state temperature $T$ (f), $A$ or $A_{\mathrm{TE}}$ (g), and $\varphi$ or ${\varphi }_{\mathrm{TE}}$ (h) profiles for the images shown in (c)–(e). The profiles were obtained by averaging 100 $y$-directional profiles along the $x$ direction; the averaged area is marked by white dotted lines. The Joule heating in the sample uniformly increases $T$ by $\sim 2\mathrm{K}$ but does not affect the estimation of $\nabla T$. (i) $I$ dependence of $A_{\mathrm{TE}}$ at $\nabla T\approx 9.7\times {10}^3{\mathrm{Km}}^{-1}$. (j) $|\nabla T|$ dependence of $A_{\mathrm{TE}}$ at $I=1.0\mathrm{A}$. The data points in (i) and (j) were obtained by averaging the $A_{\mathrm{TE}}$ values in the area indicated by the blue square with a size of $100\times 100\mathrm{pixels}$ ($0.3\times 0.3\mathrm{mm}$) in (e).

Figure 4

(a),(b) $A_{\mathrm{TE}}$ and ${\varphi }_{\mathrm{TE}}$ images for the ${\mathrm{Ni}}_{95}{\mathrm{Pt}}_5$ slab at $I=1.0\mathrm{A}$ and $f=1.0\mathrm{Hz}$, measured when a magnetic field of $|{\mu }_{0}H|=140\mathrm{mT}$ and $\nabla T\approx 9.2\times {10}^3{\mathrm{Km}}^{-1}$ were applied in the $\nabla T\parallel \mathbf{I}\parallel \mathbf{H}$ configuration (a) and $|{\mu }_{0}H|=500\mathrm{mT}$ and $\nabla T\approx 10.1\times {10}^3{\mathrm{Km}}^{-1}$ were applied in the $\nabla T\parallel \mathbf{I}\perp \mathbf{H}$ configuration (b). (c),(d) $|{\mu }_{0}H|$ dependence of $\mathrm{\Delta }{\eta }_{\parallel }$ and $\mathrm{\Delta }{\eta }_{\perp }$ for the ${\mathrm{Ni}}_{95}{\mathrm{Pt}}_5$ slab in the $\nabla T\parallel \mathbf{I}\parallel \mathbf{H}$ and $\nabla T\parallel \mathbf{I}\perp \mathbf{H}$ configurations. In the $\nabla T\parallel \mathbf{I}\parallel \mathbf{H}$ ($\nabla T\parallel \mathbf{I}\perp \mathbf{H}$) configuration, we define $\mathrm{\Delta }{\eta }_{\parallel (\perp )}(|H|)={\eta }_{\parallel (\perp )}(|H|)-{\eta }_{\parallel (\perp )}$ (0 mT) with ${\eta }_{\parallel (\perp )}=|A_{\text{TE}}/(j_{\mathrm{c}}\nabla T)|$ and $j_{\mathrm{c}}$ being the square-wave amplitude of the charge current density. The inset in (d) shows the $f$ dependence of $\mathrm{\Delta }{\eta }_{\perp }$. The data points in (c) and (d) were obtained by averaging the $A_{\mathrm{TE}}$ values in the areas indicated by the blue squares with sizes of $100\times 100\mathrm{pixels}$ ($0.3\times 0.3\mathrm{mm}$) in (a) and (b), respectively. The error bars represent the standard deviations of the data in the corresponding squares.