We experimentally investigate second-harmonic transverse voltage response to ac electrical current for a magnetic nodal-line semimetal Fe$_3$GeTe$_2$. For zero magnetic field, the observed second-harmonic voltage depends as a square of the longitudinal current, as it should be expected for non-linear Hall effect. The magnetic field behavior is found to be sophisticated:while the first-harmonic response shows the known anomalous Hall hysteresis in FGT, the second-harmonic Hall voltage is characterized by the pronounced high-field hysteresis and flat ($B$-independent) region with curves touching at low fields. The high-field hysteresis strongly depends on the magnetic field sweep rate, so it reflects some slow relaxation process. For the lowest rates, it is also accomplished by multiple crossing points. Similar shape of the second-harmonic hysteresis is known for skyrmion spin textures in non-linear optics. Since skyrmions have been demonstrated for FGT by direct visualization techniques, we can connect the observed high-field relaxation with deformation of the skyrmion lattice. Thus, the second-harmonic Hall voltage response can be regarded as a tool to detect spin textures in transport experiments.

We study magnetization reversal and first order reversal curves for two different magnetic topological semimetals, Co3Sn2S2 and Fe3GeTe2, in a wide temperature range between 80 K and 180 K. For the magnetization hysteresis loops, we observe strong temperature dependence of the initial (low-temperature) step-like magnetization switchings, so asymmetric regions of slanted magnetization appears above 140 K. Usually, similar behavior is ascribed to appearance of the second, temperature-induced magnetic phase. However, first order reversal curve analysis shows two-phase behavior even at lowest temperatures of our experiment. While the bulk ferromagnetic phase is of high temperature dependence, the second magnetic phase demonstrates perfect temperature stability below the Curie temperature. We connect the robust second phase with the surface spin textures, which are inherent for magnetic topological semimetals, so the excellent temperature stability is due to the topological protection of the semimetal surface states. This conclusion is also supported by the characteristic bow-tie magnetic hysteresis loops.

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