Interplay of Peltier and Seebeck Effects in Nanoscale Nonlocal Spin Valves

We have experimentally studied the role of thermoelectric effects in nanoscale nonlocal spin valve devices. A finite element thermoelectric model is developed to calculate the generated Seebeck voltages due to Peltier and Joule heating in the devices. By measuring the first, second, and third harmonic voltage response nonlocally, the model is experimentally examined. The results indicate that the combination of Peltier and Seebeck effects contributes significantly to the nonlocal baseline resistance. Moreover, we found that the second and third harmonic response signals can be attributed to Joule heating and temperature dependencies of both the Seebeck coefficient and resistivity.

Figure 1

(a) Schematic drawing of a typical spin valve experiment. Current is sent through the first $\mathrm{Cu}/\mathrm{Py}$ interface, while the voltage drop is measured at the second interface. (b) Because of the difference in the Peltier coefficients for Cu and Py, the heat current $Q$ carried by the electrons changes across the interface. Hence, interface 1 is locally heated or cooled depending on the direction of the current. (c) The second interface acts as a thermocouple and detects the local electron temperature via the Seebeck effect.

Figure 2

Scanning electron microscope (SEM) image of the device layout. (a) Standard nonlocal spin valve geometry. Current is sent from contact 1 to 3, while the voltage is measured between 5 and 4. Contact 2 is not used. (b) Similar device geometry with an electrically isolated detector circuit.

Figure 3

(a) $R_{1b}$ measured as a function of the spacing $L$ between the two ferromagnets, as indicated by the measurement geometry in the inset. The triangles reflect measurements taken for two different samples, whereas the blue dots correspond to the FEM calculations. (b) Nonlocal spin valve measurement with the magnetic field swept back and forth, being indicated by the arrows. $R_{1s}$ is defined as the resistance due to the presence of a spin accumulation and $R_{1b}$ is the baseline resistance. (c) $R_{1s}$ as a function of the separation $L$ between both ferromagnets.

Figure 4

(a) $R_2$ as a function of magnetic field. The baseline resistance is mainly caused by the Seebeck voltage induced by Joule heating. (b) $R_3$ plotted versus magnetic field. The baseline reflects the modification in Seebeck coefficient and resistance due to temperature changes. Likewise, the spin signal indicates how the spin valve signal is altered by temperature. (c) Baseline resistance $R_{2b}$ as a function of $L$. Triangles represent data for two different samples, blue dots are simulation results. (d) $R_{3b}$ measured versus $L$. The shape of $R_{3b}$ is similar to $R_{1b}$ because it describes the temperature dependence of the effects that generate $R_{1b}$.