Large topological Hall effect in an easy-cone ferromagnet (Cr0.9B0.1)Te

The Berry phase understanding of electronic properties has attracted special interest in condensed matter physics, leading to phenomena such as the anomalous Hall effect and the topological Hall effect. A non-vanishing Berry phase, induced in momentum space by the band structure or in real space by a non-coplanar spin structure, is the origin of both effects. Here, we report a sign conversion of the anomalous Hall effect and a large topological Hall effect in (Cr0.9B0.1)Te single crystals. The spin reorientation from an easy-axis structure at high temperature to an easy-cone structure below 140 K leads to conversion of the Berry curvature, which influences both, anomalous and topological, Hall effects in the presence of an applied magnetic field and current. We compare and summarize the topological Hall effect in four categories with different mechanisms and have a discussion into the possible artificial fake effect of topological Hall effect in polycrystalline samples, which provides a deep understanding of the relation between spin structure and Hall properties.

skyrmions [9] with non-zero scalar spin chirality can also play the role of the magnetic field and contribute to the Hall signal, referred to as the topological Hall effect (THE) [10] .
A topological Hall effect was first observed in skyrmions in non-centrosymmetric materials, such as the B20 compounds MnSi [ 11 , 12 ] and FeGe [ 13 , 14 ] , in which it is stabilized by the Dzyaloshinsky-Moriya interaction. In these cubic systems, the topological Hall resistivity is usually as small as 10 -3 -10 -2 μΩ cm. In centrosymmetric materials with uniaxial magnetic anisotropy, such as MnNiGa, [15] , the biskyrmionic phase shows a large topological Hall effect of 0.15 μΩ cm. A topological Hall effect was also observed in systems with non-coplanar antiferromagnetic spin structure, such as Mn5Si3 [16] , MnP [17] , and YMn6Sn6 [18] . Under an applied magnetic field strong enough for a metamagnetic or spin-flop transition, the (partially) antiferromagnetic coupled or canted spins align to the field direction due to the Zeeman energy, a process during which a large topological Hall resistivity of up to 10 -1 μΩ cm has been observed. More recently, a topological Hall effect was also observed during the magnetization process along the hard axis of ferromagnets, such as in strong uniaxial Cr5Te8 [19] and Fe3GeTe2 [20] with a magnetic field applied in-plane. None of these materials, however, shows a topological Hall effect with a field along the easy axis (c-axis). This suggests a complex behaviour during magnetization along the hard axis in ferromagnets. Many Mnbased Heusler compounds crystallize in an inverse structure [21 -25] and have a non-collinear spin structure at low temperature. They exhibit a topological Hall effect that belongs to a mixed type of the above two cases. Recently, THE was also reported in frustrated magnets [26,27] . The topological Hall effect is one of the characteristics of skyrmions, and electrical transport is easy to measure. Therefore, it can be used to select materials for potential skyrmion applications. In addition, the topological Hall effect can be used to confirm some non-coplanar spin structures without need for expensive neutron studies.
Ferromagnetism exists in a large range of compositions in Cr1-xTe (0 < x < 0.4) with different Curie temperatures Tc and saturation magnetization Ms [ 28 ] . These compounds share a similar hexagonal structure, with Cr vacancies in every second Cr layer, while the Te layer is fully occupied.
The vacancies induce small deviations from the hexagonal symmetry leading to monoclinic Cr3Te4, trigonal Cr2Te3, and trigonal or monoclinic Cr5Te8. Trigonal Cr5Te8 is a strong uniaxial ferromagnet with a magnetocrystalline anisotropy constant K1 of 0.8 MJ m -3 [19,29] . However, for materials with higher Cr concentration and smaller anisotropy (K1 < 0.5 MJ m -3 ) [30,31] , the magnetic structure is much more complicated. A canted ferromagnetic structure at low temperature was observed by neutron diffraction [32] and magnetization measurements, [28] which could lead to a possible real-space Berry phase and a topological Hall effect, providing a candidate material for skyrmion bubbles. In a previous study, we reported the magnetic structure of (Cr0.9B0.1)Te [33] . Owing to the difficulty in synthesizing stoichiometric CrTe, the chromium vacancies are filled by boron, stabilizing the hexagonal structure as well as shifting the Fermi energy to modify the magnetism. The magnetic moment changes from collinear along c at high temperature to an easy-cone structure below the spin-reorientation transition temperature TSR = 140 K. The tilt angle varies with temperature.
Here we report the magneto-electronic transport properties of (Cr0.9B0.1)Te single crystals. The spin reorientation leads to a change in the Berry curvature that significantly influences both, anomalous and topological, Hall effects depending on the applied magnetic field and current direction.
Single crystals of (Cr0.9B0.1)Te were grown by an annealing process followed by water quenching. Details of the crystal growth, composition, crystal structure, magnetic properties, and electronic structure are published in Ref. [33]. The longitudinal and Hall resistivities were measured using a Quantum Design PPMS 9 with a standard four-or five-probe method. indicating a large number of dislocations (vacancies or B atoms) inside the crystals. For magnetization along the c-axis, the magnetoresistance is almost zero, and as the field increases further, its value gradually decreases during heating to -1.5% at 300 K under 3 T due to spin-disorder scattering. However, the magnetoresistance is positive (1.5%) in the ab plane at 2 K during magnetization. With this additional effect, the negative magnetoresistance region at 3 T rises to above 200 K. (Cr0.9B0.1)Te also exhibits a large, anisotropic anomalous Hall effect that depends strongly on temperature. When the applied field direction is along the c-axis, the anomalous Hall resistivity ρAHE is positive at high temperature with collinear spin structure. However, it decreases during cooling and then changes sign at TSR, finally reaching -2.3 μΩ cm at 2 K, as shown in Fig. 1c. When the field is in-plane, as shown in Fig. 1f, the anomalous Hall effect is always negative and changes during cooling from -3.5 μΩ cm at 300 K to about -0.7 μΩ cm at 2 K. Skew scattering is the dominant mechanism of the anomalous Hall effect for both I // ab and I // c [19] , as shown in the linear fitting of ρAHE versus longitudinal resistivity in Supplementary information. ρAHE offsets the trend when the temperature approaches Tc. The skew-scattering mechanism confirms (Cr0.9B0.1)Te as a bad metal with a large number of defects.
The total Hall effect can be regarded as the sum of the ordinary Hall effect due to the Lorenz force, the anomalous, and the topological Hall effect using the following formula for the Hall resistivity: T c where R0 and Rs are the ordinary and anomalous Hall coefficients, respectively. The fitted ordinary Hall resistivity is negligible, indicating a high charge carrier density of more than 10 22 cm -3 ; therefore, it is not shown here. A low mobility of <1 cm 2 V -1 s -1 further demonstrates that it is a bad metal, which is also confirmed by the low residual resistivity ratio (RRR) and low thermal conductivity of 3.8 W K -1 m -1 at 300 K. When the field is applied along the c-axis, Rs changes sign during cooling, whereas it remains negative with the field along the a-axis, as shown in  have been observed in Cr5Te8 [19] and Fe3GeTe2 [20] , which also show a topological Hall effect when the field is along the hard axis rather than the easy c-axis due to the non-coplanar spin structure.   We compare materials exhibiting a topological Hall effect in Table 1. Generally, a large topological Hall effect requires a large magnetic field (see Supplementary information). The first category consists of the skyrmion materials. However, in general the topological Hall effect induced by skyrmions is small. The cubic B20 compounds, such as MnSi [11,12] or FeGe [13,14] , only exhibit a topological Hall resistivity of 10 -3 -10 -2 μΩ cm. In Mn1.4PtSn above the spin-reorientation temperature, no topological Hall effect was found [23] , although skyrmions still existed [34 ] . The second category covers the possibility to realize metamagnetic or spin-flop transitions under applied magnetic fields in antiferromagnetic materials with non-coplanar spin structure, as in the cases of Mn5Si3 [16] , MnP [17] , and YMn6Sn6 [18] . The third category covers magnetization from the hard axis, including Cr5Te8 [19] , Fe3GeTe2 [20] , and (Cr0.9B0.1)Te. Many Mn-based Heusler compounds [21][22][23][24][25]35] have combined materials from all three categories. The topological Hall effects for the second and third categories are larger, with a large magnetic field, depending on the exchange coupling strength or magnetocrystalline anisotropy.  [36] , which disappear when the thickness increases, indicating that the topological Hall effect is sensitive to the lattice constant, which is easily affected by strain. The small applied field is due to vanishing small single-ion anisotropy of Cr 3+ ions (3d 3 ) with a negligible orbital moment [33] . Note that the B significantly increases the Cr moment from 2.7 μB in the binary compound [28] to 3.1 μB here, and decreases the magnetocrystalline anisotropy K1 from 500 kJ m -3 [31] to -100 kJ m -3 at 2 K.
This reduced field is important for potential applications.
The findings also allow us to interpret transport data from previously reported polycrystalline materials. We propose a topological-like anomalous Hall effect (topological AHE) that originates in polycrystals from two magnetic sublattices with different anisotropy constants, the values of which are approximately the same magnitude, but of opposite sign. We simulated a textured structure (80%c + 20%a) as an example using the data at 300 K in Fig. 1, as shown in the Supplementary information. Note that there is no topological Hall effect at this temperature. The magnetization along the c-axis saturates fast, dominating the initial magnetization curve and the anomalous Hall effect (positive). However, after saturation in the 'c'-texture in a higher field, an additional anomalous Hall effect only emerges from the 'a'-texture, giving a negative contribution.
As result, a bump, namely, a topological-like anomalous Hall effect appears near saturation. The topological-like anomalous Hall resistivity is 1.3 μΩ cm after fitting and thus much larger than the real topological Hall resistivity observed at low temperature. Dijkstra [28] also reported Hall measurements on polycrystalline Cr0.9Te and Cr0.8Te. Both samples, especially Cr0.8Te, showed similar behaviour of two kinks before saturation, which can now be explained by topological and topological-like anomalous Hall effects. The first kink might come from the competition between anomalous Hall effects with different signs, whereas the second kink should come from the topological Hall effect of the non-coplanar spin structure. Interestingly, this topological-like anomalous Hall effect has been also realized in films in which two materials with opposite signs of the anomalous Hall effect were selected [37] . Our study points out that this can be realized in one material as well. Owing to the topological-like anomalous Hall effect great care should be taken with the transport properties of polycrystalline materials with anisotropic crystal structure to exclude the possibility of an 'artificial topological Hall effect'. For this reason, some polycrystalline materials without texture, especially those with high magnetocrystalline anisotropy, are not included in Table 1.
In conclusion, the spin reorientation transition at 140 K has a significant effect on the transport properties in (Cr0.9B0.1)Te. The non-coplanar spin structure at low temperature leads to a nonvanishing Berry phase, further causing a highly anisotropic anomalous Hall effect and a topological Hall effect that strongly depends on the field direction. Consequently, a sign change of the anomalous Hall effect and a large topological Hall resistivity of 0.21 μΩ cm are observed. Our study provides a deep understanding of non-coplanar magnetic structure and topological Hall effect.

Supplementary Material
See supplementary material for the mechanism of anomalous Hall effect, topological-like anomalous Hall effect, magnetization curves and comparison of the topological Hall effect with other materials.