Open Submitted: 12 June 2020 Accepted: 24 July 2020 Published Online: 07 August 2020
Appl. Phys. Lett. 117, 052409 (2020); https://doi.org/10.1063/5.0018229
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• Yangkun He
• Johannes Kroder
• Jacob Gayles
• Chenguang Fu
• Yu Pan
• Walter Schnelle
• Claudia Felser
• Gerhard H. Fecher

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 the topological Hall effect in polycrystalline samples, which provides a deep understanding of the relation between the spin structure and Hall properties.
In condensed matter physics, Berry phases have enabled a wider understanding of many physical concepts and phenomena, such as chiral anomalies,1,21. E. Liu, Y. Sun, N. Kumar, L. Muechler, A. Sun, L. Jiao, S. Y. Yang, D. Liu, A. Liang, Q. Xu, J. Kroder, V. Süß, H. Borrmann, C. Shekhar, Z. Wang, C. Xi, W. Wang, W. Schnelle, S. Wirth, Y. Chen, S. T. B. Goennenwein, and C. Felser, “ Giant anomalous Hall effect in a ferromagnetic kagome-lattice semimetal,” Nat. Phys. 14, 1125 (2018). https://doi.org/10.1038/s41567-018-0234-52. J. Gooth, A. C. Niemann, T. Meng, A. G. Grushin, K. Landsteiner, B. Gotsmann, F. Menges, M. Schmidt, C. Shekhar, V. Süß, R. Hühne, B. Rellinghaus, C. Felser, B. Yan, and K. Nielsch, “ Experimental signatures of the mixed axial–gravitational anomaly in the Weyl semimetal NbP,” Nature 547, 324 (2017). https://doi.org/10.1038/nature23005 magnetic monopoles,33. Z. Fang, N. Nagaosa, K. S. Takahashi, A. Asamitsu, R. Mathieu, T. Ogasawara, H. Yamada, M. Kawasaki, Y. Tokura, and K. Terakura, “ The anomalous Hall effect and magnetic monopoles in momentum space,” Science 302, 92–95 (2003). https://doi.org/10.1126/science.1089408 and the anomalous Nernst effect.44. A. Sakai, Y. P. Mizuta, A. A. Nugroho, R. Sihombing, T. Koretsune, M. T. Suzuki, N. Takemori, R. Ishii, D. Nishio-Hamane, R. Arita, P. Goswami, and S. Nakatsuji, “ Giant anomalous Nernst effect and quantum-critical scaling in a ferromagnetic semimetal,” Nat. Phys. 14, 1119 (2018). https://doi.org/10.1038/s41567-018-0225-6 Among them, the intrinsic anomalous Hall effect (AHE) requires the absence of time reversal symmetry and the orbital degeneracy to be lifted. The former not only is usually seen in ferromagnetic systems but also can be found in specific antiferromagnetic systems. The latter not only is due to relativistic effects such as the spin–orbit interaction but can also be induced by a non-collinear magnetic spin texture.5,65. S. Nakatsuji, N. Kiyohara, and T. Higo, “ Large anomalous Hall effect in a non-collinear antiferromagnet at room temperature,” Nature 527, 212 (2015). https://doi.org/10.1038/nature157236. X. Wang, Z. Feng, P. Qin, H. Yan, X. Zhou, H. Guo, Z. Leng, W. Chen, Q. Jia, Z. Hu, H. Wu, X. Zhang, C. Jiang, and Z. Liu, “ Integration of the noncollinear antiferromagnetic metal Mn3Sn onto ferroelectric oxides for electric-field control,” Acta Mater. 181, 537 (2019). https://doi.org/10.1016/j.actamat.2019.10.020 The combination of these phenomena leads to the momentum-space Berry curvature as a linear response to an applied electric field.7,87. N. Nagaosa, J. Sinova, S. Onoda, A. H. MacDonald, and N. P. Ong, “ Anomalous Hall effect,” Rev. Mod. Phys. 82, 1539 (2010). https://doi.org/10.1103/RevModPhys.82.15398. K. Manna, Y. Sun, L. Muechler, J. Kübler, and C. Felser, “ Heusler, Weyl and Berry,” Nat. Rev. Mater. 3, 244 (2018). https://doi.org/10.1038/s41578-018-0036-5 However, a real-space Berry phase originating from non-coplanar spin texture or magnetic topological excitations like skyrmions99. A. Fert, N. Reyren, and V. Cros, “ Magnetic skyrmions: Advances in physics and potential applications,” Nat. Rev. Mater. 2, 17031 (2017). https://doi.org/10.1038/natrevmats.2017.31 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).1010. N. Nagaosa and Y. Tokura, “ Topological properties and dynamics of magnetic skyrmions,” Nat. Nanotechnol. 8, 899–911 (2013). https://doi.org/10.1038/nnano.2013.243
A topological Hall effect was first observed in skyrmions in non-centrosymmetric materials, such as the B20 compounds MnSi11,1211. A. Neubauer, C. Pfleiderer, B. Binz, A. Rosch, R. Ritz, P. G. Niklowitz, and P. Böni, “ Topological Hall effect in the a phase of MnSi,” Phys. Rev. Lett. 102, 186602 (2009). https://doi.org/10.1103/PhysRevLett.102.18660212. Y. Li, N. Kanazawa, X. Z. Yu, A. Tsukazaki, M. Kawasaki, M. Ichikawa, X. F. Jin, F. Kagawa, and Y. Tokura, Phys. Rev. Lett. 110, 117202 (2013). https://doi.org/10.1103/PhysRevLett.110.117202 and FeGe,13,1413. N. A. Porter, J. C. Gartside, and C. H. Marrows, “ Scattering mechanisms in textured FeGe thin films: Magnetoresistance and the anomalous Hall effect,” Phys. Rev. B 90, 024403 (2014). https://doi.org/10.1103/PhysRevB.90.02440314. N. Kanazawa, M. Kubota, A. Tsukazaki, Y. Kozuka, K. S. Takahashi, M. Kawasaki, M. Ichikawa, F. Kagawa, and Y. Tokura, “ Discretized topological Hall effect emerging from skyrmions in constricted geometry,” Phys. Rev. B 91, 041122(R) (2015). https://doi.org/10.1103/PhysRevB.91.041122 in which it is stabilized by the Dzyaloshinskii–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,,1515. W. Wang, Y. Zhang, G. Xu, L. Peng, B. Ding, Y. Wang, Z. Hou, X. Zhang, X. Li, E. Liu, S. Wang, J. Cai, F. Wang, J. Li, F. Hu, G. Wu, B. Shen, and X. X. Zhang, “ A centrosymmetric hexagonal magnet with superstable biskyrmion magnetic nanodomains in a wide temperature range of 100–340 K,” Adv. Mater. 28, 6887–6893 (2016). https://doi.org/10.1002/adma.201600889 the biskyrmionic phase shows a large topological Hall effect of 0.15 μΩ cm. A topological Hall effect was also observed in systems with a non-coplanar antiferromagnetic spin structure, such as Mn5Si3,1616. C. Sürgers, G. Fischer, P. Winkel, and H. V. Löhneysen, “ Large topological Hall effect in the non-collinear phase of an antiferromagnet,” Nat. Commun 5, 3400 (2014). https://doi.org/10.1038/ncomms4400 MnP,1717. Y. Shiomi, S. Iguchi, and Y. Tokura, “ Emergence of topological Hall effect from fanlike spin structure as modified by Dzyaloshinsky–Moriya interaction in MnP,” Phys. Rev. B 86, 180404(R) (2012). https://doi.org/10.1103/PhysRevB.86.180404 and YMn6Sn6.1818. Q. Wang, Q. Yin, S. Fujitsu, H. Hosono, and H. Lei, “ Near-room-temperature giant topological Hall effect in antiferromagnetic Kagome metal YMn6Sn6,” arXiv:1906.07986v1. 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 Cr5Te81919. Y. Wang, J. Yan, J. Li, S. Wang, M. Song, J. Song, Z. Li, K. Chen, Y. Qin, L. Ling, H. Du, L. Cao, X. Luo, Y. Xiong, and Y. Sun, “ Magnetic anisotropy and topological Hall effect in the trigonal chromium tellurides Cr5Te8,” Phys. Rev. B 100, 024434 (2019). https://doi.org/10.1103/PhysRevB.100.024434 and Fe3GeTe22020. Y. Wang, C. Xian, J. Wang, B. Liu, L. Ling, L. Zhang, L. Cao, Z. Qu, and Y. Xiong, “ Anisotropic anomalous Hall effect in triangular itinerant ferromagnet Fe3GeTe2,” Phys. Rev. B 96, 134428 (2017). https://doi.org/10.1103/PhysRevB.96.134428 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 behavior during magnetization along the hard axis in ferromagnets. Many Mn-based Heusler compounds crystallize in an inverse structure21–2521. K. G. Rana, O. Meshcheriakova, J. Kübler, B. Ernst, J. Karel, R. Hillebrand, E. Pippel1, P. Werner, A. K. Nayak, C. Felser, and S. S. P. Parkin, “ Observation of topological Hall effect in Mn2RhSn films,” New J. Phys. 18, 085007 (2016). https://doi.org/10.1088/1367-2630/18/8/08500722. Y. Li, B. Ding, X. Wang, H. Zhang, W. Wang, and Z. Liu, “ Large topological Hall effect observed in tetragonal Mn2PtSn Heusler thin film,” Appl. Phys. Lett. 113, 062406. https://doi.org/10.1063/1.503992123. P. Vir, J. Gayles, A. S. Sukhanov, N. Kumar, F. Damay, Y. Sun, J. Kübler, C. Shekhar, and C. Felser, “ Anisotropic topological Hall effect with real and momentum space Berry curvature in the antiskyrmion-hosting Heusler compound Mn1.4PtSn,” Phys. Rev. B 99, 140406(R) (2018). https://doi.org/10.1103/PhysRevB.99.14040624. P. Swekis, A. Markou, D. Kriegner, J. Gayles, R. Schlitz, W. Schnelle, S. T. B. Goennenwein, and C. Felser, “ Topological Hall effect in thin films of Mn1.5PtSn,” Phys. Rev. Mater. 3, 013001(R) (2019). https://doi.org/10.1103/PhysRevMaterials.3.01300125. V. Kumar, N. Kumar, M. Reehuis, J. Gayles, A. S. Sukhanov, A. Hoser, F. Damay, C. Shekhar, P. Adler, and C. Felser, “ Detection of antiskyrmions by topological Hall effect in Heusler compounds,” Phys. Rev. B 101, 014424 (2020). https://doi.org/10.1103/PhysRevB.101.014424 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 THE was also reported in frustrated magnets.26,2726. T. Kurumaji, T. Nakajima, M. Hirschberger, A. Kikkawa, Y. Yamasaki, H. Sagayama, H. Nakao, Y. Taguchi, T. Arima, and Y. Tokura, “ Skyrmion lattice with a giant topological Hall effect in a frustrated triangular-lattice magnet,” Science 365, 914–918 (2019). https://doi.org/10.1126/science.aau096827. H. Li, B. Ding, J. Chen, Z. Li, Z. Hou, E. Liu, H. Zhang, X. Xi, G. Wu, and W. Wang, “ Large topological Hall effect in a geometrically frustrated kagome magnet Fe3Sn2,” Appl. Phys. Lett 114, 192408 (2019). https://doi.org/10.1063/1.5088173
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 the 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.2828. J. Dijkstra, H. H. Weitering, C. F. Van Bruggen, C. Haas, and R. A. de Groot, “ Band-structure calculations, and magnetic and transport properties of ferromagnetic chromium tellurides (CrTe, Cr3Te4, Cr2Te3,” J. Phys.: Condens. Matter 1, 9141 (1989). https://doi.org/10.1088/0953-8984/1/46/008 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−3.19,2919. Y. Wang, J. Yan, J. Li, S. Wang, M. Song, J. Song, Z. Li, K. Chen, Y. Qin, L. Ling, H. Du, L. Cao, X. Luo, Y. Xiong, and Y. Sun, “ Magnetic anisotropy and topological Hall effect in the trigonal chromium tellurides Cr5Te8,” Phys. Rev. B 100, 024434 (2019). https://doi.org/10.1103/PhysRevB.100.02443429. X. H. Luo, W. J. Ren, and Z. D. Zhang, “ Magnetic properties and magnetocaloric effect of a trigonal Te-rich Cr5Te8 single crystal,” J. Magn. Magn. Mater. 445, 37–43 (2018). https://doi.org/10.1016/j.jmmm.2017.08.078 However, for materials with a higher Cr concentration and smaller anisotropy (K1 < 0.5 MJ m−3),30,3130. G. B. Street, E. Sawatzky, and K. Lee, “ Magnetic properties of vapor grown crystals of hexagonal chromium telluride,” J. Phys. Chem. Solids 34, 1453–1455 (1973). https://doi.org/10.1016/S0022-3697(73)80048-431. T. Hirone and S. Chiba, “ On the magnetic anisotropy of single crystal of chromium telluride,” J. Phys. Soc. Jpn. 15, 1991 (1960). https://doi.org/10.1143/JPSJ.15.1991 the magnetic structure is much more complicated. A canted ferromagnetic structure at low temperature was observed by neutron diffraction3232. A. F. Andersen, “ The magnetic structure of Cr2Te3, Cr3Te4, and Cr5Te6,” Acta Chem. Scand. 24, 3495–3509 (1970). https://doi.org/10.3891/acta.chem.scand.24-3495 and magnetization measurements,2828. J. Dijkstra, H. H. Weitering, C. F. Van Bruggen, C. Haas, and R. A. de Groot, “ Band-structure calculations, and magnetic and transport properties of ferromagnetic chromium tellurides (CrTe, Cr3Te4, Cr2Te3,” J. Phys.: Condens. Matter 1, 9141 (1989). https://doi.org/10.1088/0953-8984/1/46/008 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.3333. Y. He, G. H. Fecher, J. Kroder, H. Borrmann, X. Wang, L. Zhang, C. Kuo, C. Liu, C. Chen, K. Chen, F. Choueikani, P. Ohresser, A. Tanaka, Z. Hu, and C. Felser, “ Easy-cone magnetic structure in (Cr0.9B0.1)Te,” Appl. Phys. Lett. 116, 102404 (2020). https://doi.org/10.1063/5.0002118 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, which 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. The details of the crystal growth, composition, crystal structure, magnetic properties, and electronic structure are published in Ref. 3333. Y. He, G. H. Fecher, J. Kroder, H. Borrmann, X. Wang, L. Zhang, C. Kuo, C. Liu, C. Chen, K. Chen, F. Choueikani, P. Ohresser, A. Tanaka, Z. Hu, and C. Felser, “ Easy-cone magnetic structure in (Cr0.9B0.1)Te,” Appl. Phys. Lett. 116, 102404 (2020). https://doi.org/10.1063/5.0002118. The longitudinal and Hall resistivities were measured using a Quantum Design PPMS 9 by a standard four- or five-probe method.
(Cr0.9B0.1)Te crystallizes in a B81 structure (prototype: NiAs, hP4, P63mmc, 194) with alternating Cr and Te layers. The lattice constants are a = 4.0184(6) Å and c = 6.2684(7) Å. It is assumed that B replaces only Cr atoms of every second Cr layer. A collinear spin structure with an easy axis along c is observed at high temperature, whereas the magnetic moments localized at the Cr atoms become gradually tilted away from the c-axis at temperatures below 140 K.
The electric transport properties of (Cr0.9B0.1)Te single crystals are shown in Fig. 1 with H//c [0001], I//ab plane [01‐10] in Figs. 1(a)–1(c) and H//ab plane [2‐1-10], I//c [0001] in Figs. 1(d)–1(f). Along both the c-axis and the ab plane, the longitudinal resistance shows a metallic behavior with a kink at Tc = 336 K, although the value in the ab plane is almost twice as large as that along the c-axis. The small residual-resistance ratio (RRR) is about 1.7 in-plane and 2.1 along the c-axis, 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 a collinear spin structure. However, it decreases during cooling and then changes its sign at TSR, finally reaching −2.3 μΩ cm at 2 K, as shown in Fig. 1(c). When the field is in-plane, as shown in Fig. 1(f), 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,1919. Y. Wang, J. Yan, J. Li, S. Wang, M. Song, J. Song, Z. Li, K. Chen, Y. Qin, L. Ling, H. Du, L. Cao, X. Luo, Y. Xiong, and Y. Sun, “ Magnetic anisotropy and topological Hall effect in the trigonal chromium tellurides Cr5Te8,” Phys. Rev. B 100, 024434 (2019). https://doi.org/10.1103/PhysRevB.100.024434 as shown in the linear fitting of ρAHE vs longitudinal resistivity in the supplementary material. 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:
 $ρH=R0B+Rsμ0M+ρTHE,$ (1)
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 1022 cm−3; therefore, it is not shown here. A low mobility of <1 cm2 V−1 s−1 further demonstrates that it is a bad metal, which is also confirmed by the low residual resistivity ratio (RRR) and the 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 its sign during cooling, whereas it remains negative with the field along the a-axis, as shown in the supplementary material.
Moreover, the Hall signal during magnetization causes an additional effect, namely, the topological Hall effect, when H//[2-1-10] and I//[0001] with the easy-cone structure at low temperature, as shown in Fig. 2. At 250 K, with the collinear spin structure, there is no topological Hall effect. However, it appears below TSR of 140 K. At 2 K, the value is as large as 0.21 μΩ cm. A similar result is observed when both the current and the field are in two in-plane perpendicular directions. A large topological Hall effect appears near saturation, when the easy-cone structure has already been destroyed by the applied magnetic field. Note that the in-plane magnetization curve below 140 K is not linear before saturation, with a kink at around 0.2 T (supplementary material), which is also the field at which the topological Hall effect starts to show a large value. This indicates a non-coplanar spin structure before saturation, with a solid angle Ω showing spin chirality as sketched in Fig. 3.
However, when the field is parallel to the c-axis, the topological Hall effect is too small to be distinguished from the noise. This can be explained by the lack of a non-coplanar intermediate phase during magnetization along the c-axis, as indicated by the absence of a kink in the magnetization curve (see the supplementary material). The domain wall motion and spin reorientation occur simultaneously during magnetization instead. This collinear spin structure does not give rise to an additional contribution to the Hall signal from the Berry curvature with Ω = 0. Similar phenomena have been observed in Cr5Te81919. Y. Wang, J. Yan, J. Li, S. Wang, M. Song, J. Song, Z. Li, K. Chen, Y. Qin, L. Ling, H. Du, L. Cao, X. Luo, Y. Xiong, and Y. Sun, “ Magnetic anisotropy and topological Hall effect in the trigonal chromium tellurides Cr5Te8,” Phys. Rev. B 100, 024434 (2019). https://doi.org/10.1103/PhysRevB.100.024434 and Fe3GeTe2,2020. Y. Wang, C. Xian, J. Wang, B. Liu, L. Ling, L. Zhang, L. Cao, Z. Qu, and Y. Xiong, “ Anisotropic anomalous Hall effect in triangular itinerant ferromagnet Fe3GeTe2,” Phys. Rev. B 96, 134428 (2017). https://doi.org/10.1103/PhysRevB.96.134428 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.
Figure 4 shows the phase diagram according to the above data with the field in-plane. Here, Tc and TSR are collected from the M(T) curves, whereas the saturation field μ0Hs and the maximum field of the easy cone are collected from the M(H) curves. It is clearly shown that the topological Hall effect appears at low temperature with a non-coplanar spin structure near saturation, when the spin is already shifted away from the initial cone.
We compare materials exhibiting a topological Hall effect in Table I. Generally, a large topological Hall effect requires a large magnetic field (see the supplementary material). 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 MnSi11,1211. A. Neubauer, C. Pfleiderer, B. Binz, A. Rosch, R. Ritz, P. G. Niklowitz, and P. Böni, “ Topological Hall effect in the a phase of MnSi,” Phys. Rev. Lett. 102, 186602 (2009). https://doi.org/10.1103/PhysRevLett.102.18660212. Y. Li, N. Kanazawa, X. Z. Yu, A. Tsukazaki, M. Kawasaki, M. Ichikawa, X. F. Jin, F. Kagawa, and Y. Tokura, Phys. Rev. Lett. 110, 117202 (2013). https://doi.org/10.1103/PhysRevLett.110.117202 or FeGe,13,1413. N. A. Porter, J. C. Gartside, and C. H. Marrows, “ Scattering mechanisms in textured FeGe thin films: Magnetoresistance and the anomalous Hall effect,” Phys. Rev. B 90, 024403 (2014). https://doi.org/10.1103/PhysRevB.90.02440314. N. Kanazawa, M. Kubota, A. Tsukazaki, Y. Kozuka, K. S. Takahashi, M. Kawasaki, M. Ichikawa, F. Kagawa, and Y. Tokura, “ Discretized topological Hall effect emerging from skyrmions in constricted geometry,” Phys. Rev. B 91, 041122(R) (2015). https://doi.org/10.1103/PhysRevB.91.041122 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,2323. P. Vir, J. Gayles, A. S. Sukhanov, N. Kumar, F. Damay, Y. Sun, J. Kübler, C. Shekhar, and C. Felser, “ Anisotropic topological Hall effect with real and momentum space Berry curvature in the antiskyrmion-hosting Heusler compound Mn1.4PtSn,” Phys. Rev. B 99, 140406(R) (2018). https://doi.org/10.1103/PhysRevB.99.140406 although skyrmions still existed.3434. A. K. Nayak, V. Kumar, T. Ma, P. Werner, E. Pippel, R. Sahoo, F. Damay, U. K. Rößler, C. Felser, and S. S. P. Parkin, “ Magnetic antiskyrmions above room temperature in tetragonal Heusler materials,” Nature. 548, 561 (2017). https://doi.org/10.1038/nature23466 The second category covers the possibility to realize metamagnetic or spin-flop transitions under applied magnetic fields in antiferromagnetic materials with a non-coplanar spin structure, as in the cases of Mn5Si3,1616. C. Sürgers, G. Fischer, P. Winkel, and H. V. Löhneysen, “ Large topological Hall effect in the non-collinear phase of an antiferromagnet,” Nat. Commun 5, 3400 (2014). https://doi.org/10.1038/ncomms4400 MnP,1717. Y. Shiomi, S. Iguchi, and Y. Tokura, “ Emergence of topological Hall effect from fanlike spin structure as modified by Dzyaloshinsky–Moriya interaction in MnP,” Phys. Rev. B 86, 180404(R) (2012). https://doi.org/10.1103/PhysRevB.86.180404 and YMn6Sn6.1818. Q. Wang, Q. Yin, S. Fujitsu, H. Hosono, and H. Lei, “ Near-room-temperature giant topological Hall effect in antiferromagnetic Kagome metal YMn6Sn6,” arXiv:1906.07986v1. The third category covers magnetization from the hard axis, including Cr5Te8,1919. Y. Wang, J. Yan, J. Li, S. Wang, M. Song, J. Song, Z. Li, K. Chen, Y. Qin, L. Ling, H. Du, L. Cao, X. Luo, Y. Xiong, and Y. Sun, “ Magnetic anisotropy and topological Hall effect in the trigonal chromium tellurides Cr5Te8,” Phys. Rev. B 100, 024434 (2019). https://doi.org/10.1103/PhysRevB.100.024434 Fe3GeTe2,2020. Y. Wang, C. Xian, J. Wang, B. Liu, L. Ling, L. Zhang, L. Cao, Z. Qu, and Y. Xiong, “ Anisotropic anomalous Hall effect in triangular itinerant ferromagnet Fe3GeTe2,” Phys. Rev. B 96, 134428 (2017). https://doi.org/10.1103/PhysRevB.96.134428 and (Cr0.9B0.1)Te. Many Mn-based Heusler compounds21–25,3521. K. G. Rana, O. Meshcheriakova, J. Kübler, B. Ernst, J. Karel, R. Hillebrand, E. Pippel1, P. Werner, A. K. Nayak, C. Felser, and S. S. P. Parkin, “ Observation of topological Hall effect in Mn2RhSn films,” New J. Phys. 18, 085007 (2016). https://doi.org/10.1088/1367-2630/18/8/08500722. Y. Li, B. Ding, X. Wang, H. Zhang, W. Wang, and Z. Liu, “ Large topological Hall effect observed in tetragonal Mn2PtSn Heusler thin film,” Appl. Phys. Lett. 113, 062406. https://doi.org/10.1063/1.503992123. P. Vir, J. Gayles, A. S. Sukhanov, N. Kumar, F. Damay, Y. Sun, J. Kübler, C. Shekhar, and C. Felser, “ Anisotropic topological Hall effect with real and momentum space Berry curvature in the antiskyrmion-hosting Heusler compound Mn1.4PtSn,” Phys. Rev. B 99, 140406(R) (2018). https://doi.org/10.1103/PhysRevB.99.14040624. P. Swekis, A. Markou, D. Kriegner, J. Gayles, R. Schlitz, W. Schnelle, S. T. B. Goennenwein, and C. Felser, “ Topological Hall effect in thin films of Mn1.5PtSn,” Phys. Rev. Mater. 3, 013001(R) (2019). https://doi.org/10.1103/PhysRevMaterials.3.01300125. V. Kumar, N. Kumar, M. Reehuis, J. Gayles, A. S. Sukhanov, A. Hoser, F. Damay, C. Shekhar, P. Adler, and C. Felser, “ Detection of antiskyrmions by topological Hall effect in Heusler compounds,” Phys. Rev. B 101, 014424 (2020). https://doi.org/10.1103/PhysRevB.101.01442435. B. M. Ludbrook, G. Dubuis, A. H. Puichaud, B. J. Ruck, and S. Granville, “ Nucleation and annihilation of skyrmions in Mn2CoAl observed through the topological Hall effect,” Sci. Rep. 7, 13620 (2017). https://doi.org/10.1038/s41598-017-13211-8 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.
TABLE I. Comparison of different categories of materials showing a topological Hall effect.
MaterialsMnSi, FeGeMn5Si3, MnP, YMn6Sn6Cr5Te8, Fe3GeTe2, Cr0.9B0.1TeMn1.4PtSn, Mn2RhSn
Ground stateHelical (AFM)Non-collinear AFMFMNon-collinear FM
ProcessSkyrmionMetamagnetic transitionHard-axis magnetizationMixture
Field directionAllAllHard axisAll
Max THE (μΩ cm)10-3–10−210-1–10010-2–10110-2–10−1
Magnetic fieldSmallLargeAnisotropy dependentAnisotropy dependent
(Cr0.9B0.1)Te belongs to the third group and is one of the materials that can achieve a large anomalous Hall effect with a mild field owing to its small magnetocrystalline anisotropy. Note that the topological Hall resistivity of 0.21 μΩ cm is already comparable to the anomalous Hall resistivity of 0.75 μΩ cm. Larger values of the topological Hall effect are also observed in thin films,3636. D. Zhao, L. Zhang, I. A. Malik, M. Liao, W. Cui, X. Cai1, C. Zheng, L. Li, X. Hu, D. Zhang, J. Zhang, X. Chen, W. Jiang, and Q. Xue, “ Observation of unconventional anomalous Hall effect in epitaxial CrTe thin films,” Nano Res. 11, 3116 (2018). https://doi.org/10.1007/s12274-017-1913-8 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 Cr3+ ions (3d3) with a negligible orbital moment.3333. Y. He, G. H. Fecher, J. Kroder, H. Borrmann, X. Wang, L. Zhang, C. Kuo, C. Liu, C. Chen, K. Chen, F. Choueikani, P. Ohresser, A. Tanaka, Z. Hu, and C. Felser, “ Easy-cone magnetic structure in (Cr0.9B0.1)Te,” Appl. Phys. Lett. 116, 102404 (2020). https://doi.org/10.1063/5.0002118 Note that B significantly increases the Cr moment from 2.7 μB in the binary compound2828. J. Dijkstra, H. H. Weitering, C. F. Van Bruggen, C. Haas, and R. A. de Groot, “ Band-structure calculations, and magnetic and transport properties of ferromagnetic chromium tellurides (CrTe, Cr3Te4, Cr2Te3,” J. Phys.: Condens. Matter 1, 9141 (1989). https://doi.org/10.1088/0953-8984/1/46/008 to 3.1 μB here and decreases the magnetocrystalline anisotropy K1 from 500 kJ m−33131. T. Hirone and S. Chiba, “ On the magnetic anisotropy of single crystal of chromium telluride,” J. Phys. Soc. Jpn. 15, 1991 (1960). https://doi.org/10.1143/JPSJ.15.1991 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 a 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 et al.2828. J. Dijkstra, H. H. Weitering, C. F. Van Bruggen, C. Haas, and R. A. de Groot, “ Band-structure calculations, and magnetic and transport properties of ferromagnetic chromium tellurides (CrTe, Cr3Te4, Cr2Te3,” J. Phys.: Condens. Matter 1, 9141 (1989). https://doi.org/10.1088/0953-8984/1/46/008 also reported Hall measurements on polycrystalline Cr0.9Te and Cr0.8Te. Both samples, especially Cr0.8Te, showed similar behavior 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 also been realized in films in which two materials with opposite signs of the anomalous Hall effect were selected.3737. A. Gerber, “ Interpretation of experimental evidence of the topological Hall effect,” Phys. Rev. B 98, 214440 (2018). https://doi.org/10.1103/PhysRevB.98.214440 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 an 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 I.
In conclusion, the spin reorientation transition at 140 K has a significant effect on the transport properties of (Cr0.9B0.1)Te. The non-coplanar spin structure at low temperature leads to a non-vanishing 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 the non-coplanar magnetic structure and topological Hall effect.
See the supplementary material for the mechanism of the anomalous Hall effect, topological-like anomalous Hall effect, magnetization curves, and comparison of the topological Hall effect with other materials.
This work was financially supported by the European Research Council Advanced Grant (No. 742068) “TOPMAT,” the European Union's Horizon 2020 Research and Innovation Programme (No. 824123) “SKYTOP,” the European Union's Horizon 2020 Research and Innovation Programme (No. 766566) “ASPIN,” the Deutsche Forschungsgemeinschaft (Project-ID No. 258499086) “SFB 1143,” the Deutsche Forschungsgemeinschaft (Project-ID No. FE 633/30-1) “SPP Skyrmions,” and the DFG through the Würzburg–Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter ct.qmat (EXC 2147, Project-ID No. 39085490).
Data are available on request from the authors.
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