Thickness dependence of the anomalous Nernst effect and the Mott relation of Weyl semimetal ${\mathrm{Co}}_2\mathrm{MnGa}$ thin films

We report a robust anomalous Nernst effect in ${\mathrm{Co}}_2\mathrm{MnGa}$ thin films in the thickness regime between 20 and 50 nm. The anomalous Nernst coefficient varied in the range of −2.0 to −3.0 $\mu \mathrm{V}/\mathrm{K}$ at 300 K. We demonstrate that the anomalous Hall and Nernst coefficients exhibit similar behavior and fulfill the Mott relation. We simultaneously measure all four transport coefficients of the longitudinal resistivity, transversal resistivity, Seebeck coefficient, and anomalous Nernst coefficient. We connect the values of the measured and calculated Nernst conductivity by using the remaining three magnetothermal transport coefficients, where the Mott relation is still valid. The intrinsic Berry curvature dominates the transport due to the relation between the longitudinal and transversal transport. Therefore, we conclude that the Mott relationship is applicable to describe the magnetothermoelectric transport in Weyl semimetal ${\mathrm{Co}}_2\mathrm{MnGa}$ as a function of film thickness.

Figure 1

(a) In-plane magnetization of ${\mathrm{Co}}_2\mathrm{MnGa}$ thin films with thicknesses between 20 and 50 nm. All thicknesses exhibit saturated magnetization of approximately 720 kA/m. (b) Comparison of in-plane and out-of-plane magnetization hysteresis loops of the 40-nm ${\mathrm{Co}}_2\mathrm{MnGa}$ film measured at 300 K.

Figure 2

Optical microscopy and thermal gradient evaluation. (a) False color optical microscopy image of our measurement platform. (b) The calibration curves of Th1 and Th2 measured at the corresponding pairs during homogeneous heating of the sample. (c) Voltages measured at the two thermometers at different heater power at two specific base temperatures of 150 and 250 K. (d) Homogeneity of the thermal gradient measured at two pairs of contacts.

Figure 3

Anomalous Nernst measurement. (a) Temperature dependence of $S_{xy}$ evaluated for each sample thickness. (b) Magnetic field dependence of the $S_{xy,\mathrm{Field}}$ at 300 K.

Figure 4

(a) Temperature dependence of ${\sigma }_{xy}$ evaluated for each sample thickness. (b) Magnetic field dependence of the ${\sigma }_{xy,\mathrm{Field}}$ at 300 K. (c) Longitudinal conductivity ${\sigma }_{xx}$ of each thickness as a function of temperature. (d) Thickness dependence of Seebeck coefficient $S_{xx}$ and longitudinal resistivity ${\rho }_{xx}$ measured at 300 K.

Figure 5

Summary of the absolute values of ${\sigma }_{xy}$ as a function of ${\sigma }_{xx}$ (determined experimentally) in various thin-film materials. The data are taken from Chuang et al. [25] for Fe, Gd, Co, and Ni thin film; from Markou et al. [20] for ${\mathrm{Co}}_2\mathrm{MnGa}$; from Lu et al. [27] for FePt; from Edmonds et al. [28] for ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$; and from Oiwa et al. [29] for ${\mathrm{In}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$.

Figure 6

(a) Thickness dependence of the anomalous Nernst effect and anomalous Hall effect measured at 300 K. Measured and calculated thickness dependence of Nernst coefficient ($|S_{xy}|$ and $|S_{xy}^c|$) (b), and conductivity ($|a_{xy}|$ and $|a_{xy}^c|$) (c) for all samples at 300 K. The insets show the temperature dependence of $|S_{xy}|$ and $|{\alpha }_{xy}|$ in (b) and (c), respectively. Both insets depict the values for the 40-nm sample of ${\mathrm{Co}}_2\mathrm{MnGa}$. The calculated red circled symbols are the best fits using Eqs. (1) and (2) with $n=1.82\pm 0.08$ for $S_{xy}^c$ and $n=1.86\pm 0.05$ for $a_{xy}^c$, respectively. (d) Comparison of the $|S_{xy}|$ values of various ferromagnetic thin films and the current study at 300 K. The data are taken from Reichlova, Wells, and Tu et al. [19, 32, 33] for ${\mathrm{Co}}_2\mathrm{MnGa}$ thin film; from Chuang et al. [25] for Py, Co, Fe, and Ni thin film; from Ramos et al. [30] for ${\mathrm{FeO}}_x$ thin film; and from Hasegawa et al. [34] for FePt, FePd, MnGa, ${\mathrm{Mn}}_2\mathrm{Ga}$, and Co/Ni thin film.