Anomalous Nernst and anisotropic magnetoresistive heating in a lateral spin valve

We measured the anomalous Nernst effect and anisotropic magnetoresistive heating in a lateral multiterminal permalloy/copper spin valve using all-electrical lock-in measurements. To interpret the results, a three-dimensional thermoelectric finite-element model is developed. Using this model, we extract the heat profile which we use to determine the anomalous Nernst coefficient of permalloy $R_N=0.13$ and also determine the maximum angle $\theta =8^{\circ }$ of the magnetization prior to the switching process when an opposing noncollinear 10${}^{\circ }$ magnetic field is applied.

Figure 1

Colored scanning electron microscope images of the fabricated device. (a) Top view of the device. The two ferromagnets are connected to each other by a copper strip. FM${}_1$ is connected by three thick gold heat sinks (1–3) through which we can send a charge current to heat it. FM${}_2$ is also connected by two gold heat sinks (5,7), but have two additional NiChrome contacts (4,6). The magnetizations ${\vec{M}}_1$ and ${\vec{M}}_2$ are selectively switched by applying an opposing magnetic field $\vec{B}$. (b) Three-dimensional image of the device illustrating the thick gold contact used as thermal heat sinks.

Figure 2

Illustration of the anomalous Nernst effect and magnetoresistive heating. (a) The Joule heating of FM${}_1$ induces a heat flow $Q$ through FM${}_2$ and the four contacts connecting it. The anomalous Nernst effect induces voltage gradients in the ferromagnet perpendicular to the heat flow and magnetization $M_2$. (b) Three contacts are present on FM${}_1$ to send the current parallel or under a $\pm$45${}^{\circ }$ angle with respect to the magnetization of FM${}_1$. (c) When the opposing magnetic field has a small angle with respect to the antiparallel direction of the magnetization, the magnetization first rotates prior to switching at its switching field, increasing or decreasing the Joule heating depending on the orientation of the current.

Figure 3

Measured voltage from the Py-NiCr thermocouple by selectively switching the magnetizations by an antiparallel magnetic field in a lateral spin valve. The right-hand thermocouple is measured when the Joule heating current is sent (a) parallel to the magnetization $M_1$, (b) under a 45${}^{\circ }$ angle and (c) under a $-{45}^{\circ }$ angle. The results were calculated by sending a rms charge current of 1.5 mA. The other thermocouple was also measured and shows similar results.

Figure 4

Measured voltage from the Py-NiCr thermocouple by selectively switching the magnetizations by an opposing magnetic field at 0${}^{\circ }$ and $\pm$10${}^{\circ }$. The left-hand thermocouple is measured when (a) sending the current under a 45${}^{\circ }$ angle and (b) under a $-{45}^{\circ }$ angle with respect to the easy magnetization axis. (c) The measured configuration and (d) the magnetic field configuration and current direction for the measurements of (a) and (b). The other thermocouple was also measured and shows similar results.

Figure 5

Simulated results of the three-dimensional thermoelectric model. (a) The temperature distribution of the device with a current of 1 mA sent parallel ($I_{2-3}$) to the alignment of the magnetization. (b) Input parameters used for the model. The electrical conductivities $\sigma$ are measured while the others are taken from literature (Refs. 10 and 11). (c) The simulated anomalous Nernst voltage from the thermocouples 4–5 and 6–7 as a function of the magnetization angles $\theta$ on the $x$-$y$ axis and $\phi$ between the $x$-$y$ plane and the $z$ axis of FM${}_2$. (d) The simulated AMR heating as a function of the magnetization direction of FM${}_1$.