We report a comprehensive experimental and theoretical study of the anomalous Hall and Nernst effects in (001)-oriented epitaxial MnAlGe thin films. First-principles calculations of intrinsic anomalous Hall conductivity originating from Berry curvature $\left({\sigma }_{xy}^{int}\right)$ predict a large value, $\sim 856{\mathrm{S}\mathrm{cm}}^{-1}$, at 0 K and gradual reduction with temperature. Experimentally measured anomalous Hall conductivity is also large value, $\sim 670{\mathrm{S}\mathrm{cm}}^{-1}$, at 10 K but exhibits almost three times stronger reduction with temperature than the theoretical prediction. Large positive and negative values of anomalous Nernst conductivity $\left({\alpha }_{xy}^{int}\right)$ near the Fermi level were predicted at 300 K: $+3.8{\mathrm{A}\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ at 78 meV and $-3.0{\mathrm{A}\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ at $-34$ meV, respectively. Experimentally evaluated anomalous Nernst conductivity ${\alpha }_{xy}^A$ shows a significant reduction in magnitude and a sign reversal with increasing temperature, $1.09\pm 0.01$ ${\mathrm{A}\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ at 75 K to $-0.12\pm 0.01$ ${\mathrm{A}\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ at 300 K, which cannot be explained by giving any chemical potential shift based on present theoretical calculations. These discrepancies suggest that the conventional theoretical approach to calculate ${\sigma }_{xy}^{int}$ and ${\alpha }_{xy}^{int}$, commonly employed in previous studies, is insufficient to explain the anomalous Hall effect and anomalous Nernst effect observed in MnAlGe. Through examination of various possible origins, our analysis points to thermally induced spin fluctuations, likely amplified by the quasi-two-dimensional structure of MnAlGe, as the most plausible source of unique temperature dependence of ${\sigma }_{xy}^A$ and ${\alpha }_{xy}^A$ through their influence on either intrinsic or extrinsic contributions. This interpretation is supported by the observation of a pronounced magnon-induced magnetoresistance effect, which directly reveals a much stronger spin-fluctuation impact on transport in MnAlGe compared to conventional three-dimensional ferromagnets.

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• Magnetic anisotropy
• Magnetotransport
• Spintronics
• Thermoelectrics
• Density functional theory
• High-resolution transmission electron microscopy