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On the anomalous low-resistance state and exceptional Hall component in hard-magnetic Weyl nanoflakes

Magnetic topological materials, which combine magnetism and topology, are expected to host emerging topological states and exotic quantum phenomena. In this study, with the aid of greatly enhanced coercive fields in high-quality nanoflakes of the magnetic Weyl semimetal Co3Sn2S2, we investigate anomalous electronic transport properties that are difficult to reveal in bulk Co3Sn2S2 or other magnetic materials. When the magnetization is antiparallel to the applied magnetic field, the low longitudinal resistance state occurs, which is in sharp contrast to the high resistance state for the parallel case. Meanwhile, an exceptional Hall component that can be up to three times larger than conventional anomalous Hall resistivity is also observed for transverse transport. These anomalous transport behaviors can be further understood by considering nonlinear magnetic textures and the chiral magnetic field associated with Weyl fermions, extending the longitudinal and transverse transport physics and providing novel degrees of freedom in the spintronic applications of emerging topological magnets.


Introduction
Recently, the first magnetic Weyl semimetal Co3Sn2S2 was discovered [1][2][3][4][5][6], which has significantly improved the understanding of the interplay of magnetic order and topological physics after the experimental realization of the quantum anomalous Hall effect (QAHE) [7]. Co3Sn2S2 is a Shandite compound with Weyl nodes at ~60 meV above the Fermi level and shows semi-metallicity with small Fermi surfaces and low carrier concentration. Transport properties are dominated by the electrons near Fermi energy. As the topological features in this system are sufficient close to the Fermi energy and there are few trivial bands, it is promising to observe the transport behavior dominated by topological band structures. In Co3Sn2S2 bulk single crystals, large intrinsic anomalous Hall conductivity and anomalous Hall angle have been detected [1,2]. In the two-dimensional (2D) limit, theoretical studies have predicted that the desired high-temperature QAHE could be realized [8][9][10], which has been indicated experimentally by the observation of chiral edge states in a recent STM measurement [11]. In addition, regardless of the specific types of magnetic domain walls, there may exist a large magnetoresistance (MR) that can be retained against the finite strength of the disorder in Co3Sn2S2 [10].
The application prospects of Co3Sn2S2 make it a promising candidate for practical applications of topological materials in spintronic or advanced electronic devices. For topology-related spintronic applications and the realization of QAHE, the growth and physical study of Co3Sn2S2 films are highly desired. Epitaxial polycrystalline Co3Sn2S2 films can be grown via molecular beam epitaxy and co-sputtering deposition methods [12,13]. Moreover, reports on Co3Sn2S2 nanoflakes grown via the chemical vapor transport (CVT) method exist [14,15]. Out-of-plane ferromagnetic order and large anomalous Hall effects were observed. These studies offer important indications for further studies of low-dimensional magnetic Weyl semimetals. In addition to studies on possible QAHE and its practical applications, the unexplored properties of this magnetic Weyl low-dimensional system are important.
Anomalous transport properties in Co3Sn2S2 nanoflakes have been observed in our previous work [14]. However, these intriguing behaviors still need to be studied and 4 analyzed in detail.
In this work, anomalous transport properties are studied in high-quality Co3Sn2S2 single-crystalline nanoflakes with 30-100-nm thickness. The system clearly enters a lower electrical resistance state once the external magnetic field is antiparallel to the magnetization. Furthermore, an exceptional Hall component besides the normal and anomalous Hall effects is observed concurrently. Possible magnetic textures induced by an antiparallel magnetic field are possibly responsible for the anomalous transport behaviors, as the interaction between Weyl electrons and magnetic textures can result in local states and conductive modes [16][17][18][19][20]. This study will attract interest in the interplay of magnetic order and topological transport behavior and offer a platform for magnetic topological material-based applications.

Materials and methods
Single-crystalline Co3Sn2S2 nanoflakes were grown via CVT using Co3Sn2S2 polycrystalline powder as the precursor. The morphology and thickness were investigated using atomic force microscopy. Hall bar pattern with a long edge along the a axis of Co3Sn2S2 for out-of-plane transport measurement was fabricated using microfabrication technology (Supplementary Note 1). Transport data were measured using a Janis system and collected by employing lock-in amplifier technology.
Symmetric and antisymmetric processes were performed on the longitudinal and transverse resistivity, respectively (details in Supplementary Note 3).

Results and discussion
The morphology and thickness of a single-crystalline nanoflake are shown in Figure 1(a) (more details are given in Supplementary Note 1). Samples of thicknesses 30, 41, 71, and 94 nm were studied in this work. Figure 1(b) shows one of the Hall bar patterns for transport measurements. The Curie temperatures of the two selected samples were determined as 181 K through the kink temperature in the temperature-dependent resistivity curve ( Figure S3). The single-crystalline Co3Sn2S2 nanoflakes being studied show consistent basic physical properties with bulk single crystals [1,21] (Supplementary Note 4). Furthermore, the nanoflakes show high quality with a residual resistivity ratio of ~20, an anomalous Hall conductivity of ~1000 Ω −1 m −1 , and a large coercive field as high as 5.5 T.  We further analyzed the emerging additional MR when magnetization was antiparallel to the applied magnetic field. In a widely accepted case, a system will be more magnetically ordered when the magnetic field is much higher than μ0Hc.
Between zero and coercive fields, the magnetic field gradually turns the antiparallel moments into parallel moments. Thus, the antiparallel moments become more disordered as the field increases before the magnetization reversal. Hence, the spin-dependent scattering [7,24,25] would be strong, increasing the longitudinal resistivity. Therefore, positive xx   , like the behavior in Figure 2(a), is normally observed in magnetic systems [7,26]. The difference from the common case is that the positive xx   in the studied sample appears immediately when the antiparallel magnetic field starts increasing. More widely observed positive MR peaks appear only near the coercive field [27][28][29]. The linear magnetic field dependence is also a unique and unexplained phenomenon.
Interestingly, a contrary situation emerges when the system goes to low temperatures. The longitudinal resistivity in the case when the applied field is antiparallel to the magnetization (antiparallel configuration) is even lower than that of the parallel case ( Figure 2(b)), i.e., xx   is negative. This behavior has been previously observed in our 180-nm-thick Co3Sn2S2 single-crystalline nanoflakes [14] and can also be recognized in polycrystalline films (although the spin-related positive MR is mixed in) [13]. Evidently, the trend is a universal behavior in this low-dimensional Weyl system. Nevertheless, negative xx   has scarcely been observed among common magnetic materials or magnetic functional films in the past.
A distinct mechanism resulting in a low-resistance state against the antiparallel external field may emerge in this magnetic topological system.
In magnetic information storage technology, the giant MR effect can be produced by switching the parallel and antiparallel directions of ferromagnetic and 8 antiferromagnetic layers in magnetic tunnel junctions, which use different electrical resistance states between parallel and antiparallel cases [30][31][32]. The anomalous negative MR effect observed in this magnetic nanoflake may provide a novel degree of freedom for spintronic applications.  . The other part is the high-temperature part (high-T part), which is fitted using the data just above 100 K. By adopting the form of y = A e −x/B + y0, the experimental data (dark blue dots) can be well fitted (green square symbols) above 80 K (see Figure S6 for details). The low-T part is then extracted by subtracting the high-T part from the experimental results, denoted by orange triangle symbols in Figure 2(d). The current straightforward but effective fitting indicates that the high-T part contributes to longitudinal resistivity continuously below the Curie temperature.
By contrast, the low-T part appears only below 70 K. Here, we stress that the low-resistance state can be observed directly from the original MR data without separation (Figures 1(e) and 1(f)). Thus, the current separation will not affect the main results.
We next analyze the transverse transport behavior in Co3Sn2S2 single-crystalline nanoflakes. Conventional magnetic materials usually show both normal and anomalous Hall effects. For a hard-magnetic material with coercivity and sharp magnetization reversal, the typical Hall curve is shown in the upper panel of Figure   3(a). We denote the Hall resistivity curve from +9 T to −9 T as  Figure 3(a)). For Co3Sn2S2 nanoflakes, the difference between the Hall data with different directions of the magnetic field variation is shown in Figure 3(b).
In sharp contrast, an increasing yx yx  −+ − effect exists with increasing applied fields up to the coercive field, which is quite different from the conventional case.
The corresponding Hall loop, subtracting the normal Hall component, is depicted in Figure 3(c). In a conventional hard-magnetic material, the normal Hall-subtracted Hall curve should be a square loop [7], indicated by the red-dashed lines in Figure 3    antiparallel magnetic field at low temperatures. It has been reported that nontrivial topological magnetic textures may emerge in a magnetic Weyl system [19,[33][34][35].
Once the magnetic textures (even without topological property) are formed, they will interact with the Weyl conduction electrons and affect the transport behavior in a system through an emergent chiral magnetic field [16][17][18][19][20]. The fictitious magnetic field may be reminiscent of the real-space Berry curvature in conventional materials with trivial band structures. However, the chiral magnetic field shows a richer degree of freedom as the related chiral gauge potential is closely linked to the Weyl nature and depends on the direction of the background magnetization itself [19,20].
Theoretical calculations show that there could be bound states and potential current, which are highly localized around a magnetic domain wall or texture [16,17,20]. In experiments, Co3Sn2S2 bulk samples indeed showed other possible magnetic interactions besides the out-of-plane ferromagnetic interaction, and thus, nonuniform magnetization behavior below the Curie temperature [1,21,36,37]. A round-shaped 13 domain structure has also been observed in the Co3Sn2S2 system [38]. Based on the above theoretical and experimental reports, a promising possibility responsible for the anomalous negative MR and exceptional Hall effect in Co3Sn2S2 nanoflakes is the noncollinear magnetic structure. Based on our experiment results, we consider it the magnetic texture induced by the antiparallel magnetic field.  Once the abovementioned potential magnetic textures are induced by the antiparallel magnetic field, a Weyl-fermion-correlated chiral gauge field [16][17][18][19][20] (where ex J is the exchange interaction strength between localized magnetic moments and Weyl electrons, and F v is the Fermi velocity) emerges around the magnetic textures. Furthermore, this localized chiral gauge field may lead to bound states near the textures [16,17,20]. When an electric field is applied to the sample, potential bound states can also offer emergent conductive modes in this system. As anomalous transport behaviors exist in both longitudinal and transverse channels in Co3Sn2S2 nanoflakes, a varying () Mr with a complicated order (not varied within parallel planes, schematic sketched in Figure 4(d)) may occur, leading to jm with both longitudinal (corresponding to low-resistance state) and transverse (corresponding to exceptional Hall effect) components. The specific structure of the possible magnetic textures in Co3Sn2S2 single-crystalline nanoflakes and the confirmation of its influence on the transport behaviors require further study.

Conclusions
Herein, an anomalous low electrical resistance state and exceptional Hall component are reported in high-quality single-crystalline nanoflakes of magnetic Weyl semimetal Co3Sn2S2 once the magnetization is antiparallel to external magnetic fields. Possible antiparallel field-induced magnetic textures and Weyl-fermion-associated chiral magnetic fields are expected to account for the decrease and increase in the longitudinal and transverse resistivities, respectively, through the possible additional conductive modes. Our report will draw more interest on the interplay of magnetism and topological transport phenomena, offering new elementary states for the applications of magnetic topological materials.

Supplemental material
Supplemental material is available online or from the author.