Relation of planar Hall and planar Nernst effects in thin film permalloy

We present measurements of the planar Nernst effect (PNE) and the planar Hall effect (PHE) of nickel-iron (Ni-Ee) alloy thin films. We suspend the thin-film samples, measurement leads, and lithographically-defmed heaters and thermometers on silicon-nitride membranes to greatly simplify control and measurement of thermal gradients essential to quantitative determination of magnetothermoelectric effects. Since these thermal isolation structures allow measurements of longitudinal thermopower, or the Seebeck coefficient, and four-wire electrical resistivity of the same thin film, we can quantitatively demonstrate the link between the longitudinal and transverse effects as a function of applied in-plane field and angle. Finite element thermal analysis of this essentially 2D structure allows more confident determination of the thermal gradient, which is reduced from the simplest assumptions due to the particular geometry of the membranes, which are more than 350 mu m wide in order to maximize sensitivity to transverse thermoelectric effects. The resulting maximum values of the PNE and PHE coefficients for the Ni-Fe film with 80% Ni we study here are alpha PNE,max = 30 nV K-1 and rho PHE,max = 2 n Omega m, respectively. All signals are exclusively sin 2 theta symmetry with applied field, ruling out longdistance spin transport effects. We also consider a Mott-like relation between the PNE and PHE, and use both this and the standard Mott relation to determine the energy-derivative of the resistivity at the Fermi energy to be (partial derivative)rho/(partial derivative)E = 4.7 x 10(-7) Omega m eV(-1), which is very similar to values for films we previously measured using similar thermal platforms. Finally, using an estimated value for the lead contribution to the longitudinal thermopower, we show that the anisotropic magnetoresistance (AMR) ratio in this Ni-Fe film is two times larger than the magnetothermopower ratio, which is the first evidence of a deviation from strict adherence to the Mott relation between Seebeck coefficient and resistivity.