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Anomalous Nernst effect, as a thermal partner of anomalous Hall effect, isparticularly sensitive to the Berry curvature anomaly near the Fermi level, andhas been used to probe the topological nature of quantum materials. In thiswork, we report the observation of both effects in the ferromagneticWeyl-semimetal Fe$_{3-x}$GeTe$_2$ with tunable Fe vacancies. With decreasing Fevacancies, the anomalous Hall conductivity evolves as a function of thelongitudinal conductivity from the hopping region to the region where theintrinsic Berry curvature contribution dominates. Concomitant evolutions in theanomalous Nernst signal and the anomalous off-diagonal thermoelectriccoefficient are observed below the Curie temperature, displaying a unique signchange caused by the Fe vacancies. Combining these results withfirst-principles calculations, we argue that the Fe-vacancy concentration playsa unique role in simultaneously tuning the chemical potential andferromagnetism, which in turn controls the Berry curvature contribution in thisfamily of ferromagnetic topological semimetals.

Sign-reversed anomalous Nernst effect in the ferromagnetic Weyl-semimetal Fe$_{3-x}$GeTe$_2$: the role of Fe vacancies