Determining the planar Nernst effect from magnetic-field-dependent thermopower and resistance in nickel and permalloy thin films

We present magnetic-field-dependent measurements of thermopower, $\alpha$(H), and resistance, $R\left(H\right)$, for ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$ and Ni thin films. We conducted these experiments in fields oriented parallel and perpendicular to the applied thermal gradient, $\vec{\nabla }T$, for $\alpha$(H) and applied current for $R\left(H\right)$. We deposited the 20-nm-thick films on 500-nm-thick suspended Si-N thermal isolation platforms that enable in-plane measurements of thermal and electrical properties of thin films. Both $\alpha \left(H\right)$ and $R\left(H\right)$ in Ni-Fe and Ni films exhibit evidence of spin-dependent scattering through an even field dependence and a linear proportionality between $\alpha \left(H\right)$ and $1/R\left(H\right)$. Finally, we use $\alpha \left({\mathrm{H}}_{\parallel }\right)$ and $\alpha \left({\mathrm{H}}_{\perp }\right)$ to determine the planar Nernst coefficient in Ni-Fe and Ni thin films and use this coefficient to predict the size of the planar Nernst effect (PNE) in the micromachined platform. The measured field dependence of the PNE is well matched by the prediction obtained from our $\alpha$(H) results.

Figure 1

(a) Scanning electron micrograph of a thermal isolation platform with the $\alpha$ circuit shown schematically. (b) SEM micrograph zoom of one island with leads and film highlighted in false color.

Figure 2

$▵$$T$ dependence of the voltage generated in response to an applied thermal gradient for Ni-Fe and Ni films with linear fits displayed as solid lines. The slope from the linear fit to the data gives $\alpha$.

Figure 3

Temperature dependence of $\alpha$ for a 20-nm-thick Ni (top panel) and a Ni-Fe (bottom panel) film (circles) compared to previously measured films[16] (dotted lines) and bulk literature values (solid lines) for Ni[17] and Ni-Fe.[18]

Figure 4

Magnetic field dependence of R and $\alpha$ for a 20 nm thick Ni film. (a) $\mathrm{R}\left({\mathrm{H}}_{\parallel }\right)$, (b) $\alpha \left({\mathrm{H}}_{\parallel }\right)$, (c) $\mathrm{R}\left({\mathrm{H}}_{\perp }\right)$, and (d) $\alpha \left({\mathrm{H}}_{\perp }\right)$. Solid lines in (b) and (d) represent $\alpha \left(\mathrm{H}\right)$ values predicted using linear fits to the $\alpha$ vs 1/R plot for Ni. All measurements are made at a base temperature of 276 K.

Figure 5

Magnetic field dependence of R and $\alpha$ for a 20 nm thick Ni-Fe film. (a) $\mathrm{R}\left({\mathrm{H}}_{\parallel }\right)$, (b) $\alpha \left({\mathrm{H}}_{\parallel }\right)$, (c) $\mathrm{R}\left({\mathrm{H}}_{\perp }\right)$, and (d) $\alpha \left({\mathrm{H}}_{\perp }\right)$. Solid lines in (b) and (d) represent $\alpha \left(\mathrm{H}\right)$ values predicted using linear fits to the $\alpha$ vs 1/R plot for Ni-Fe. All measurements are made at a base temperature of 276 K.

Figure 6

Inverse $R$ dependence of $\alpha$ for (a) Ni and (b) Ni-fe films measured in $H$${}_{\parallel }$ and $H$${}_{\perp }$. Solid lines represent linear fits to the data.

Figure 7

(a) Angular dependence of the calculated PNE coefficients (${\alpha }_{\mathrm{PNE}}$) for Ni-Fe and Ni generated using Eq. (4). (b) Angular dependence of the expected voltage from Ni (solid line) compared with the voltage generated by the PNE from Avery et al.[8] for a 20-nm Ni film deposited at the same time as the Ni sample from this experiment.

Figure 8

Magnetic field dependence of the ${\mathrm{V}}_{\mathrm{T}}$ generated by the transverse thermopower (or planar Nernst effect) for a 20-nm-thick Ni film[16] at $\theta$ = 45${}^{\mathrm{o}}$, 135${}^{\mathrm{o}}$, 225${}^{\mathrm{o}}$, 315${}^{\mathrm{o}}$. The solid lines represent the voltage predicted using ${\alpha (H}_{\parallel })$ and $\alpha \left(H_{\perp }\right)$, where the film is saturated. Dotted lines represent the prediction where $\vec{M}$ is not well-defined.