Anisotropic magnetothermal transport in ${\mathrm{Co}}_2\mathrm{Mn}\mathrm{Ga}$ thin films

Ferromagnetic ${\mathrm{Co}}_2\mathrm{MnGa}$ has recently attracted significant attention due to effects related to the nontrivial topology of its band structure. However, a systematic study of canonical magnetogalvanic transport effects is missing. Focusing on high quality thin films, here we systematically measure anisotropic magnetoresistance (AMR) and its thermoelectric counterpart anisotropic magnetothermopower (AMTP). We model the AMR data by free energy minimization within the Stoner-Wohlfarth formalism and conclude that both crystalline and noncrystalline components of this magnetotransport phenomenon are present in ${\mathrm{Co}}_2\mathrm{MnGa}$. The AMTP is, in comparison to the AMR, large in relative terms, since the Seebeck coefficient ${\mathrm{\Sigma }}_0$ is small, which is discussed in the context of the Mott rule and of phonon drag. A further analysis of AMTP components is presented.

Figure 1

Sample characterization. (a) Schematic image of the sample. The white areas are ${\mathrm{Co}}_2\mathrm{MnGa}$. $V_{yy}$ (AMR) are the contacts used for measuring voltage in the AMR experiment, while the current $I$ was applied between $V_{yy}$ (AMTP). In the AMTP experiment, the voltage was measured at $V_{yy}$ (AMTP). The width of the conducting channel is $45\mu \mathrm{m}$. The length is $970\mu \mathrm{m}$ between the contacts of $V_{yy}$ (AMR) and $1335\mu \mathrm{m}$ between $V_{yy}$ (AMTP). The red and green colored areas are Pt wires which are used in the AMTP experiments as on-chip heaters (red) and thermometers (green). (b) Superconducting quantum interference device measurement of magnetization $M$: hard (out-of-plane) and easy-direction $M\left(H\right)$ at $T=100$ and 300 K. The inset shows $M\left(T\right)$ at saturation, with saturated magnetic moment approaching $4{\mu }_{\mathrm{B}}$ per formula unit. (c) X-ray diffraction radial scans of ${\mathrm{Co}}_2\mathrm{MnGa}$ films with 40- and 50-nm thickness. Bragg peaks labeled by an asterisk (*) originate from the $00L$ series of the MgO substrate, while Bragg peaks of ${\mathrm{Co}}_2\mathrm{MnGa}$ are labeled by their Miller indices. (d) X-ray reflectivity pattern of the 40- and 50-nm-thick ${\mathrm{Co}}_2\mathrm{MnGa}$ films. Experimental data are shown as data points, while the solid line represents a model fit based on the extended Parratt formalism and both x-ray plots have the 50-nm sample data shifted in vertical direction for clarity.

Figure 2

Results of the AMR and AMTP measurement (crosses) and fitting (continuous lines) in the 50-nm sample at 300 K (AMR) and 250 K (AMTP). [(a),(c),(e)] Schematic sketch of the magnetic field rotation in the $\mathit{XY}, \mathit{ZY}$, and $\mathit{ZX}$ plane with respect to the coordinate system and the sample. [(b),(d),(f)] AMR (blue, left $y$ axes) and AMTP (orange, right $y$ axes) results.

Figure 3

(a), (c), (e) Data from Fig. 2 where AMR (AMTP) is fitted by Eq. (4) [Eq. (5), respectively] with second-order terms only; a lower quality, compared to Fig. 2, of the AMR fit in the bottom panel is clearly apparent but systematic deviations can also be observed for the $\mathit{XY}$ and $\mathit{ZY}$ rotations. (b), (d), (f) The difference of the experimental data and fits on the left (fit residuals); see text for a detailed discussion.

Figure 4

Temperature evolution of the parameters obtained by the phenomenological fit to AMR data. (a) Uniaxial magnetic anisotropy and (b–f) parameters for AMR defined in Eq. (4).

Figure 5

(a) Longitudinal Seebeck coefficient ${\mathrm{\Sigma }}_0$ and resistivity ${\rho }_0$ as a function of the temperature. The different samples are distinguished by the shape of symbols. The absolute value of the Seebeck coefficient of the 50-nm sample is monotonously increasing with temperature. There is a sign change at low temperatures. The Seebeck coefficients at $T=300$ K for the 50- and 40-nm sample (green square) are of comparable magnitude. (b) Comparison of the AMTP and the corresponding AMR parameters in the 50-nm sample as a function of temperature. AMR and AMTP are distinguished by line style. The $m_y^2$ contributions are in shades of orange; the $m_z^2$ contributions are in shades of green. They do not seem to follow any common trend. Error bars of AMTP and AMR parameters in (b) (implied by the fitting procedure) are too small to be visually resolved.