Domain wall magneto-Seebeck effect

The interplay between charge, spin, and heat currents in magnetic nanostructures subjected to a temperature gradient has led to a variety of novel effects and promising applications studied in the fast-growing field of spin caloritronics. Here, we explore the magnetothermoelectrical properties of an individual magnetic domain wall in a permalloy nanowire. In thermal gradients of the order of few $\mathrm{K}/\mu \mathrm{m}$ along the long wire axis, we find a clear magneto-Seebeck signature due to the presence of a single domain wall. The observed domain wall magneto-Seebeck effect can be explained by the magnetization-dependent Seebeck coefficient of permalloy in combination with the local spin configuration of the domain wall.

Figure 1

Sample geometry and temperature distribution. (a) Micrograph of the $\mathsf{L}$-shaped permalloy nanostructure with Pt contact probes for voltage and resistance measurements. The inset below shows the notch with higher magnification. The coordinate system and the direction of the external magnetic field are indicated by the white arrows. (b) The temperature increase for three heater powers $P=17$, 22, and $27\mathrm{mW}$ as a function of the distance to the heater. Experimental results are shown by blue bullets; numerical results (gray lines) show a good agreement.

Figure 2

Magnetoresistance and magnetothermopower measurement. (a) The resistance $R$ of the wire vs applied field ${\mu }_{0}H$ measured in transversal geometry ($\varphi ={90}^{\circ }$). (b) Domain wall magnetoresistance measured at $\varphi =0^{\circ }$. The pinning fields of the corner and the notch are indicated by $H_1$ and $H_2$, respectively. (c) A set of domain wall magnetoresistance measurements for angles $\left|\varphi \right|<{80}^{\circ }$. The resistance is indicated by the color scale. (d) The thermopower of the wire measured in transversal geometry ($\varphi ={90}^{\circ }$). (e) Domain wall magnetothermopower measured at $\varphi =0^{\circ }$. (f) A set of domain wall magnetothermopower measurements for all angles $\left|\varphi \right|<{80}^{\circ }$. The thermopower is indicated by the color scale.

Figure 3

(a) Domain wall magnetothermopower measured at $\varphi ={-30}^{\circ }$ (upsweep, thick line; downsweep, thin line). The graph shows the thermopower change with respect to the remanent state $V_{\mathrm{T}\parallel }$. (b) The calculated AMS contribution (blue) and the calculated contribution due to AMS and ANE acting together (gray). (c) Calculated contribution due to PNE (green) and ANE (brown). (d) Example of a simulated magnetization distribution showing a vortex DW. The local magnetization direction is indicated by the color scale. (e)–(g) The calculated temperature gradient in the $x, y$, and $z$ directions.