Anomalous Nernst effect of ${\mathrm{Fe}}_3{\mathrm{O}}_4$ single crystal

We report a complete characterization of the anomalous Nernst effect (ANE) and its relationship with the anomalous Hall effect (AHE) in ${\mathrm{Fe}}_3{\mathrm{O}}_4$. By combining full thermoelectric and electric transport measurements as a function of temperature, we have verified that the universal scaling relation between the anomalous Hall and diagonal conductivities (${\sigma }_{zy}\propto {\sigma }_{zz}^{1.6}$), observed in materials with bad-metal-hopping type of conduction, is also applicable to the thermoelectric transport. We further show that the ANE and AHE are commonly related through the Mott relation, therefore demonstrating its validity for anomalous transport phenomena in materials with conduction in the the dirty regime.

Figure 1

(a) Schematic illustration of the measurement geometry. (b) Results obtained for different applied thermal gradients at 300 K. The inset shows the dependence of $V_y^{\mathrm{sat}}$ measured at different magnitudes of the temperature difference ($\Delta T$) across the sample. (c) Comparison of the measured anomalous Nernst voltage and the magnetization of the sample.

Figure 2

(a) Schematic illustration of the experimental geometry. (b) Dependence of $V_y$ with the direction of applied magnetic field. (c) Angular dependence of the $V_y$ voltage measured at saturation ($V_y^{\mathrm{sat}}$); the solid line corresponds to the best fit to a sinusoidal dependence.

Figure 3

(a) Temperature dependence of the observed anomalous Nernst effect measured for two ${\mathrm{Fe}}_3{\mathrm{O}}_4$ samples. (b) Seebeck effect and resistivity data. The inset shows the schematic of the Seebeck measurement. (c) Anomalous Hall effect measured at 300 K and fitting to the universal power factor $|{\sigma }_{zy}|\approx {10}^{-4}{\sigma }_{zz}^{1.6}$ (see inset).

Figure 4

Comparison of the measured anomalous Nernst signal and the joint contribution of the Seebeck component and the AHE above 110 K (inset shows full temperature range).

Figure 5

Temperature dependence of (a) $S_{zy}$ and (b) ${\alpha }_{zy}$ for the ${\mathrm{Fe}}_3{\mathrm{O}}_4$ single crystal (S1) above the Verwey transition; the solid lines are the best fits using Eqs. (4) and (5).