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Anomalous transverse response of Co$_2$MnGa and universality of the room-temperature $α^A_{ij}/σ^A_{ij}$ ratio across topological magnets

The off-diagonal (electric, thermal and thermoelectric) transport coefficients of a solid can acquire an anomalous component due to the non-trivial topology of the Bloch waves. We present a study of the anomalous Hall (AHE), Nernst (ANE) and thermal Hall effects (ATHE) in the Heusler Weyl ferromagnet Co$_2$MnGa. The Anomalous Wiedemann-Franz law, linking electric and thermal responses, was found to be valid over the whole temperature window. This indicates that the AHE has an intrinsic origin and the Berry spectrum is smooth in the immediate vicinity of the Fermi level. From the ANE data, we extract the magnitude and temperature dependence of $α^A_{ij}$ and put under scrutiny the $α^A_{ij}/σ^A_{ij}$ ratio, which approaches k$_B$/e at room temperature. We show that in various topological magnets the room-temperature magnitude of this ratio is a sizeable fraction of k$_B$/e and argue that the two anomalous transverse coefficients depend on universal constants, the Berry curvature averaged over a window set by either the Fermi wavelength (for Hall) or the de Broglie thermal length (for Nernst). Since the ratio of the latter two is close to unity at room temperature, such a universal scaling finds a natural explanation in the intrinsic picture of anomalous transverse coefficients.