The rare earth-transition metal intermetallic compounds RCo2 (R = rare earth) exhibit a rich variety of useful properties, including giant magnetostriction, giant magnetoresistance, and large magnetocaloric effects.1–31. N. K. Singh, K. G. Suresh, A. K. Nigam, S. K. Malik, A. A. Coelho, and S. Gama, J. Magn. Magn. Mater. 317, 68 (2007). https://doi.org/10.1016/j.jmmm.2007.04.0092. N. H. Duc, D. T. K. Anh, and P. E. Brommer, Physica B 319, 1–8 (2002). https://doi.org/10.1016/S0921-4526(02)01099-23. N. H. Duc and D. T. K. Anh, J. Magn. Magn. Mater. 242–245, 873 (2002). https://doi.org/10.1016/S0304-8853(01)01328-2 These properties are closely related to their crystal and magnetic structures. It was established that RCo2 compounds crystallize in a cubic MgCu2-type structure at ambient temperature.44. E. Gratz, A. Lindbaum, A. S. Markosyan, H. Muelleret, and A. Y. Sokolov, J. Phys.: Condens. Matter 6, 6699 (1994). https://doi.org/10.1088/0953-8984/6/33/017 The cubic structure becomes unstable after cooling below their magnetic ordering temperature, TC. As two examples, TbCo2 and DyCo2 crystallize in a rhombohedral structure and a tetragonal structure below TC, respectively.4,54. E. Gratz, A. Lindbaum, A. S. Markosyan, H. Muelleret, and A. Y. Sokolov, J. Phys.: Condens. Matter 6, 6699 (1994). https://doi.org/10.1088/0953-8984/6/33/0175. S. Yang, H. Bao, C. Zhou, Y. Wang, X. Ren, Y. Matsushita, Y. Katsuya, M. Tanaka, K. Kobayashi, X. Song, and J. Gao, Phys. Rev. Lett. 104, 197201 (2010). https://doi.org/10.1103/PhysRevLett.104.197201 These two types of structures are stabilized by highly anisotropic 4f–3d interactions in the crystal lattice. It is generally accepted that magnetic moments of Co atoms are induced by a strong molecular field of localized 4f moments of Tb or Dy atoms.66. R. M. Moon, W. C. Koehler, and J. Farrell, J. Appl. Phys. 36, 978 (1965). https://doi.org/10.1063/1.1714286 They are antiparallel to 4f moments of Tb or Dy atoms,7,87. Z. W. Ouyang, F. W. Wang, Q. Hang, W. F. Liu, G. Y. Liu, J. W. Lynn, J. K. Liang, and G. H. Rao, J. Alloys Compd. 390, 21 (2005). https://doi.org/10.1016/j.jallcom.2004.08.0288. D. P. Kozlenko, E. Burzo, P. Vlaic, S. E. Kichanov, A. V. Rutkauskas, and B. N. Savenko, Sci. Rep. 5, 8620 (2015). https://doi.org/10.1038/srep08620 as illustrated in Figs. 1(a) and 1(d). In the rhombohedral-type structure, R atoms occupy the 6c site and Co atoms occupy two nonequivalent sites, Co1 (3b) and Co2 (9e). In the tetragonal-type structure, R atoms occupy the 4b site and Co atoms occupy the 8c site. As shown in Figs. 1(b) and 1(e), Co atoms in the (101) plane form a Kagome lattice in the crystal lattice of each type of structure, i.e., they form interconnected triangles and hexagons. A similar Kagome lattice of Co atoms exists in other RCo2 compounds. It is of fundamental and technical interest to explore how the Kagome lattice of Co atoms in RCo2 compounds affects transport behavior.A recent study using first-principles calculations99. Y. Xu, L. Elcoro, Z. D. Song, B. J. Wieder, M. G. Vergniory, N. Regnault, Y. Chen, C. Felser, and B. A. Bernevig, Nature 586, 702 (2020). https://doi.org/10.1038/s41586-020-2837-0 suggested that TbCo2 with a Kagome lattice could be a magnetic topological material. However, this prediction has not been verified. On the other hand, the Kagome lattice is an excellent model system for studies of frustrated magnetism, electronic correlation, and topological electronic structure.1010. N. J. Ghimire and I. I. Mazin, Nat. Mater. 19, 137 (2020). https://doi.org/10.1038/s41563-019-0589-8 Theoretically, a Kagome lattice can host non-trivial topological states with unusual physical properties because of the breaking of time-reversal symmetry of Kagome geometry frustration.11,1211. D. Zhang, Z. Hou, and W. Mi, J. Mater. Chem. C 10, 7748 (2022). https://doi.org/10.1039/D2TC01190E12. Z. Rao, H. Li, T. Zhang, S. Tian, C. Li, B. Fu, C. Tang, L. Wang, Z. Li, W. Fan, J. Li, Y. Huang, Z. Liu, Y. Long, C. Fang, H. Weng, Y. Shi, H. Lei, Y. Sun, T. Qian, and H. Ding, Nature 567, 496 (2019). https://doi.org/10.1038/s41586-019-1031-8 Indeed, a number of Kagome magnets, including Fe3Sn2, Co3Sn2S2, Mn3Sn, and RMn6Sn6,13–1613. Q. Wang, S. Sun, X. Zhang, F. Pang, and H. Lei, Phys. Rev. B 94, 075135 (2016). https://doi.org/10.1103/PhysRevB.94.07513514. 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, Nat. Phys. 14, 1125 (2018). https://doi.org/10.1038/s41567-018-0234-515. P. K. Rout, P. V. P. Madduri, S. K. Manna, and A. K. Nayak, Phys. Rev. B 99, 094430 (2019). https://doi.org/10.1103/PhysRevB.99.09443016. W. Ma, X. Xu, J. X. Yin, H. Yang, H. Zhou, Z. J. Cheng, Y. Huang, Z. Qu, F. Wang, M. Z. Hasan, and S. Jia, Phys. Rev. Lett. 126, 246602 (2021). https://doi.org/10.1103/PhysRevLett.126.246602 exhibit a large and intrinsic anomalous Hall effect (AHE) and negative magnetoresistance (MR) due to Berry phase effect and chiral anomaly, respectively. Following these studies, one may expect that the Kagome lattice plays a role in the magnetoelectric transport properties of RCo2 compounds as well. In this work, we investigated temperature dependence of transport behavior of TbCo2 and DyCo2 to reveal this role. Compared to TbCo2 with the rhombohedral structure, DyCo2 with the tetragonal structure has a larger angle between the Kagome plane and the Co magnetic moment direction. Moreover, Dy atoms have a larger 4f magnetic moment, which introduces a stronger 4f–3d interaction with Co atoms.7,177. Z. W. Ouyang, F. W. Wang, Q. Hang, W. F. Liu, G. Y. Liu, J. W. Lynn, J. K. Liang, and G. H. Rao, J. Alloys Compd. 390, 21 (2005). https://doi.org/10.1016/j.jallcom.2004.08.02817. E. Burzo, P. Vlaic, D. P. Kozlenko, S. E. Kichanov, A. V. Rutkauskas, and B. N. Savenko, J. Alloys Compd. 724, 1184 (2017). https://doi.org/10.1016/j.jallcom.2017.07.078 Thus, a comparative study of the two RCo2 compounds may provide insight into the role of the Kagome lattice in tuning the AHE and MR.Polycrystalline samples of TbCo2 and DyCo2 compounds were prepared by arc melting high-purity elements under the protection of a purified argon atmosphere.1818. D. Huang, J. Gao, S. H. Lapidus, D. Brown, and Y. Ren, Mater. Res. Lett. 8, 97 (2020). https://doi.org/10.1080/21663831.2019.1704454 A 5% excess amount of rare earth was used to compensate for mass losses due to evaporation. Magnetization, longitudinal, and Hall resistivity of the samples were measured using a Quantum Design physical property measuring system (PPMS). The magnetization vs temperature curves were measured in field-cooled (FC) and zero-field cooled (ZFC) modes under a magnetic field of 0.05 T. The isothermal magnetization curves were measured under a magnetic field of 5 T at temperatures of interest. The longitudinal and Hall resistivity of the samples were measured in magnetic fields up to μ0H = 5 T using a standard six-probe configuration [see the inset of Fig. 2(a)]. The longitudinal resistivity of the samples was determined using ρxx(μ0H) = [ρxx(+μ0H) + ρxx(−μ0H)]/2 to reduce errors due to voltage probe misalignment. The Hall resistivity of the samples was obtained using ρxy(μ0H) = [ρxy(+μ0H) − ρxy(−μ0H)]/2. The MR of the samples was determined using [ρxx(H) − ρxx(0)]/ρxx(0), where ρxx(H) and ρxx(0) are the resistivity with and without a magnetic field, respectively.Figures 1(c) and 1(f) show the M(T) curves of TbCo2 and DyCo2 samples, respectively. The TC of the samples was determined as 232 and 140 K, respectively, in terms of a steep rise of magnetization with temperature. These TC values are in good agreement with literature.5,185. S. Yang, H. Bao, C. Zhou, Y. Wang, X. Ren, Y. Matsushita, Y. Katsuya, M. Tanaka, K. Kobayashi, X. Song, and J. Gao, Phys. Rev. Lett. 104, 197201 (2010). https://doi.org/10.1103/PhysRevLett.104.19720118. D. Huang, J. Gao, S. H. Lapidus, D. Brown, and Y. Ren, Mater. Res. Lett. 8, 97 (2020). https://doi.org/10.1080/21663831.2019.1704454 There are significant differences between the ZFC and FC curves of each compound up to temperatures close to respective TC indicating thermomagnetic irreversibility. The thermomagnetic irreversibility was usually observed for spin-glass systems and interpreted by considering domain wall pinning.1919. A. Kowalczyk, J. Baszyński, A. Szajek, J. Kováč, and I. Škorvánek, J. Magn. Magn. Mater. 152, L279 (1996). https://doi.org/10.1016/0304-8853(95)00424-6 Its occurrence in the RCo2 compounds has been related to the formation of a spin freezing phase.20–2220. R. Kuentzler and A. Tari, J. Magn. Magn. Mater. 61, 29 (1986). https://doi.org/10.1016/0304-8853(86)90064-821. A. Kowalczyk, A. Szajek, J. Baszyński, J. Kováč, and G. Chełkowska, J. Magn. Magn. Mater. 166, 237 (1997). https://doi.org/10.1016/S0304-8853(96)00431-322. C. L. Wang, J. Liu, Y. Mudryk, K. A. Gschneidner, Y. Long, and V. K. Pecharsky, J. Magn. Magn. Mater. 405, 122 (2016). https://doi.org/10.1016/j.jmmm.2015.12.062 Following this relation, a fully spin freezing temperature can be defined, at which the difference between magnetization of ZFC and FC curves is abruptly enlarged. Here, the fully spin freezing temperature Tf was determined to be 35 and 33 K for TbCo2 and DyCo2, respectively. As described below, the electrical transport properties of each compound are changed rapidly at respective Tf indicating a strong correlation between magnetic and electrical transport.A negative MR is observed for each compound as shown in Figs. 2(a) and 2(b). The absolute magnitude of the negative MR increases with decreasing temperature until a maximum is attained at TC. As shown in Fig. 2(c), a maximum MR of −16.3% and −35.1% at μ0H = 5 T is observed near the TC of TbCo2 and DyCo2, respectively. These negative MR values near TC are attributed to the suppression of spin-dependent scattering by an applied magnetic field.2,232. N. H. Duc, D. T. K. Anh, and P. E. Brommer, Physica B 319, 1–8 (2002). https://doi.org/10.1016/S0921-4526(02)01099-223. B. Raquet, M. Viret, E. Sondergard, O. Cespedes, and R. Mamy, Phys. Rev. B 66, 024433 (2002). https://doi.org/10.1103/PhysRevB.66.024433 The larger MR of DyCo2 is related to its first-order ferrimagnetic transition in contrast to a second-order ferrimagnetic transition of TbCo2.24,2524. S. Khmelevskyi and P. Mohn, J. Phys.: Condens. Matter 12, 9453 (2000). https://doi.org/10.1088/0953-8984/12/45/30825. C. M. Bonilla, J. Herrero-Albillos, F. Bartolomé, L. M. García, M. Parra-Borderías, and V. Franco, Phys. Rev. B 81, 224424 (2010). https://doi.org/10.1103/PhysRevB.81.224424 Both compounds show a negative MR above TC, which can be attributed to scattering by spin fluctuations in a paramagnetic state.2,26,272. N. H. Duc, D. T. K. Anh, and P. E. Brommer, Physica B 319, 1–8 (2002). https://doi.org/10.1016/S0921-4526(02)01099-226. I. Balberg, Physica B C 91, 71 (1977). https://doi.org/10.1016/0378-4363(77)90169-327. F. Bartolomé, C. M. Bonilla, J. Herrero-Albillos, I. Calvo-Almazán, C. Castán, E. Weschke, D. Schmitz, D. Paudyal, Y. Mudryk, V. Pecharsky, K. A. Gschneidner, Jr., A. Stunault, and L. M. García, Eur. Phys. J. B 86, 489 (2013). https://doi.org/10.1140/epjb/e2013-30968-7 As temperature decreases well below TC, the MR of each compound shows a plateau in both positive and negative quadrants of critical field Hcr. This behavior is rare. It has been only observed in few compounds such as Mn2(Sb,Sn), CeMn2Ge2, and Ce(Fe,Al)2 and attributed to a field-induced metamagnetic transition.28–3028. Y. Zhang and Z. Zhang, Phys. Rev. B 67, 132405 (2003). https://doi.org/10.1103/PhysRevB.67.13240529. G. Xu, D. Liu, L. He, S. Wang, and L. Ma, Mater. Lett. 315, 131963 (2022). https://doi.org/10.1016/j.matlet.2022.13196330. S. Radha, S. B. Roy, A. K. Nigam, and G. Chandra, Phys. Rev. B 50, 6866 (1994). https://doi.org/10.1103/PhysRevB.50.6866 Unlike those compounds, neither of the two title compounds shows a pronounced metamagnetic transition in the M(H) curves (Fig. S1). Then, the MR plateau below TC can be understood in terms of two opposing scattering mechanisms related to magnetic sublattices of R and Co atoms under the action of a low magnetic field. According to Ref. 22. N. H. Duc, D. T. K. Anh, and P. E. Brommer, Physica B 319, 1–8 (2002). https://doi.org/10.1016/S0921-4526(02)01099-2, the spin-dependent scattering related to ferromagnetic ordering of Tb atoms should lead to a negative contribution to MR whereas the formation of 3d moments, i.e., the noncoplanar frustrated magnetic structure of Co atoms in the Kagome plane, should bring about a positive contribution to MR. These opposing scattering mechanisms can compensate each other leading to a nearly zero MR, i.e., the MR plateau. The MR shows a sharp decrease, i.e., a negative value, at a critical magnetic field of Hcr as shown in the diagram in Fig. 2(d). This sharp decrease in MR is due to the suppression of spin-related scattering as usually observed in magnetic systems.2323. B. Raquet, M. Viret, E. Sondergard, O. Cespedes, and R. Mamy, Phys. Rev. B 66, 024433 (2002). https://doi.org/10.1103/PhysRevB.66.024433 For each compound, the critical field Hcr has a small value around TC but has a much larger value at lower temperatures. The larger value of the Hcr below TC can be attributed to a rapid rise of the magnetic moment of Co atoms according to the neutron diffraction study.7,177. Z. W. Ouyang, F. W. Wang, Q. Hang, W. F. Liu, G. Y. Liu, J. W. Lynn, J. K. Liang, and G. H. Rao, J. Alloys Compd. 390, 21 (2005). https://doi.org/10.1016/j.jallcom.2004.08.02817. E. Burzo, P. Vlaic, D. P. Kozlenko, S. E. Kichanov, A. V. Rutkauskas, and B. N. Savenko, J. Alloys Compd. 724, 1184 (2017). https://doi.org/10.1016/j.jallcom.2017.07.078 The critical field corresponds to a field that brings about a collapse of the itinerant moments of Co atoms with the help of a molecular field offered by R atoms.31,3231. A. T. Burkov, A. Y. Zyuzin, T. Nakama, and K. Yagasaki, Phys. Rev. B 69, 144409 (2004). https://doi.org/10.1103/PhysRevB.69.14440932. R. Hauser, E. Bauer, E. Gratz, H. Müller, M. Rotter, H. Michor, G. Hilscher, A. S. Markosyan, K. Kamishima, and T. Goto, Phys. Rev. B 61, 1198 (2000). https://doi.org/10.1103/PhysRevB.61.1198 Thus, one may expect that the MR plateau disappears when the magnetic sublattices of R and Co atoms are fully ordered at very low temperatures. The Hcr of DyCo2 is higher than that of TbCo2. This difference is understood because the stronger 4f–3d interactions induce a larger Co moment in DyCo2.7,177. Z. W. Ouyang, F. W. Wang, Q. Hang, W. F. Liu, G. Y. Liu, J. W. Lynn, J. K. Liang, and G. H. Rao, J. Alloys Compd. 390, 21 (2005). https://doi.org/10.1016/j.jallcom.2004.08.02817. E. Burzo, P. Vlaic, D. P. Kozlenko, S. E. Kichanov, A. V. Rutkauskas, and B. N. Savenko, J. Alloys Compd. 724, 1184 (2017). https://doi.org/10.1016/j.jallcom.2017.07.078 The MR of each compound becomes positive and shows a quadratic field dependence at 20 K or lower temperatures. This quadratic dependence is typical for MR of paramagnets. Its occurrence in a ferromagnetic state actually indicates a cluster spin glass behavior.3333. A. K. Nigam, G. Chandra, and S. Ramakrishnan, J. Phys. F 16, 1255 (1986). https://doi.org/10.1088/0305-4608/16/9/018 The cluster spin glass behavior is consistent with the observations of the increase in the thermomagnetic irreversibility below Tf (see Fig. 1).As shown in Figs. 3(a) and 3(b), the Hall resistivity (ρxy) of TbCo2 and DyCo2 exhibits a linear field dependence at 300 K. As the temperature decreases to TC, ρxy of each compound shows a nonlinear field dependence. It increases quickly at low fields and then increases slowly at high fields. This nonlinear dependence indicates an anomalous Hall effect (AHE) in each compound. The ρxy observed at TC actually is the maximum one for each compound, which can be attributed to the phase transition as in La(Fe, Co)13−xSix.3434. D. Y. Karpenkov, K. P. Skokov, I. A. Radulov, O. Gutfleisch, J. Weischenberg, and H. Zhang, Phys. Rev. B 100, 094445 (2019). https://doi.org/10.1103/PhysRevB.100.094445 The maximum of the ρxy of DyCo2 is nearly twice larger than that of TbCo2. This difference can be attributed to stronger magnetization in DyCo2. The high-field slope of ρxy changes its sign with decreasing temperature, suggesting a change in the carrier type.3535. S. Lin, B. S. Wang, P. Tong, L. Hu, Y. N. Huang, W. J. Lu, B. C. Zhao, W. H. Song, and Y. P. Sun, J. Appl. Phys. 113, 103906 (2013). https://doi.org/10.1063/1.4795139 To confirm the change in the carrier type, we fit an empirical formula of the Hall resistivity of a non-trivial spin structure using ρxy = R0μ0H + RHM + ρxyT, where R0, RH, and ρxyT are the ordinary Hall, the anomalous Hall coefficient, and the topological Hall resistivity, respectively.36,3736. K. Ueda, S. Iguchi, T. Suzuki, S. Ishiwata, Y. Taguchi, and Y. Tokura, Phys. Rev. Lett. 108, 156601 (2012). https://doi.org/10.1103/PhysRevLett.108.15660137. N. Nagaosa, J. Sinova, S. Onoda, A. H. MacDonald, and N. P. Ong, Rev. Mod. Phys. 82, 1539 (2010). https://doi.org/10.1103/RevModPhys.82.1539 The first item on the right hand of the formula represents the ordinary Hall resistivity (OHE) due to a Lorentz force imposed by a perpendicular magnetic field. The second item represents the anomalous Hall resistivity, and it includes extrinsic mechanisms such as skew scattering and side-jump and a Karplus–Luttinger (KL) intrinsic mechanism, which is related to the longitudinal resistivity according to the Tian–Ye–Jin (TYJ) scaling.3838. Y. Tian, L. Ye, and X. Jin, Phys. Rev. Lett. 103, 087206 (2009). https://doi.org/10.1103/PhysRevLett.103.087206 Given that a magnetic field larger than 2 T is applied, ρxyT decreases to zero. Then, the value of R0 and RH could be determined from the linear fit of ρxy/μ0H–M/μ0H in a high field regime following the previous study.3939. 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, Adv. Mater. 28, 6887 (2016). https://doi.org/10.1002/adma.201600889 They correspond to the intercepts at the y-axis and the slope of the linear fitting (Fig. S2). As shown in Fig. 3(c), the R0 of TbCo2 and DyCo2 changes from a negative value to a positive value at 150 and 112 K, respectively, during cooling. This sign change of R0 indicates a change of the dominant carriers from the electron (n-type) to the hole (p-type). However, the change of the dominant carriers has a trivial effect on the MR of either compound at a maximum field of 5 T [see Fig. 2(c)]. On the other hand, RH in Fig. 3(d) is decreased significantly upon the sign change of ρxy. At lower temperatures, the Hall resistivity of each compound shows a small ordinary Hall effect. This effect is consistent with the cluster spin glass behavior.The negative topological Hall resistivity ρxyT was obtained by subtracting the contributions of the ordinary Hall resistivity (OHE) and AHE contributions from the Hall resistivity (see Figs. S3 and S4). It is pronounced at low fields near and below TC for each compound. The negative value of the topological Hall effect (THE) is not unique because it has been observed in several ferromagnets with magnetocrystalline anisotropy.40–4240. J. Yu, L. Liu, J. Deng, C. Zhou, H. Liu, F. Poh, and J. Chen, J. Magn. Magn. Mater. 487, 165316 (2019). https://doi.org/10.1016/j.jmmm.2019.16531641. H. Li, B. Ding, J. Chen, Z. Li, E. Liu, X. Xi, G. Wu, and W. Wang, Appl. Phys. Lett. 116, 182405 (2020). https://doi.org/10.1063/5.000549342. J. Liu, S. Zuo, X. Zheng, Y. Zhang, T. Zhao, F. Hu, J. Sun, and B. Shen, Appl. Phys. Lett. 117, 052407 (2020). https://doi.org/10.1063/5.0011570 Despite a small absolute magnitude, it indicates a topological Hall effect in agreement with the prediction by the first-principles calculations.99. Y. Xu, L. Elcoro, Z. D. Song, B. J. Wieder, M. G. Vergniory, N. Regnault, Y. Chen, C. Felser, and B. A. Bernevig, Nature 586, 702 (2020). https://doi.org/10.1038/s41586-020-2837-0 Here, we define a critical field, μ0HS, at which the ρxyT is suppressed. Below this critical field, ρxyT shows a maximum at the magnetic field of μ0Hmax with a strong dependence on temperature. The topological Hall effect has a correlation with the plateau MR, because they are observed in the same temperature region. It can be attributed to a non-zero spin chirality related to the noncoplanar spin structure as explained below.A recent study showed that an AHE and a THE of Kagome magnets are related to the momentum-space and real-space Berry phases of conduction electrons, respectively,3737. N. Nagaosa, J. Sinova, S. Onoda, A. H. MacDonald, and N. P. Ong, Rev. Mod. Phys. 82, 1539 (2010). https://doi.org/10.1103/RevModPhys.82.1539 and their magnitudes are sensitive to the details of electronic and magnetic structures. Here, the THE in TbCo2 and DyCo2 is supposed to have the same origin as that of magnetically frustrated systems such as crystalline Fe3GeTe2 and Cr5Te8 materials and amorphous CoTb films,40,43,4440. J. Yu, L. Liu, J. Deng, C. Zhou, H. Liu, F. Poh, and J. Chen, J. Magn. Magn. Mater. 487, 165316 (2019). https://doi.org/10.1016/j.jmmm.2019.16531643. Y. Wang, C. Xian, J. Wang, B. Liu, L. Ling, L. Zhang, L. Cao, Z. Qu, and Y. Xiong, Phys. Rev. B 96, 134428 (2017). https://doi.org/10.1103/PhysRevB.96.13442844. 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, Phys. Rev. B 100, 024434 (2019). https://doi.org/10.1103/PhysRevB.100.024434 i.e., it originates from a non-zero spin chirality. As shown in Figs. 4(a) and 4(b), the nearest three spins of Co atoms in the (101) plane have a non-zero spin chirality. This chirality is induced by a noncoplanar spin structure in the Co Kagome lattice and the 4f–3d interactions. The noncoplanar spin structure of the Co Kagome lattice is due to different responses of spin moment and orbital moments of Co atoms to a low external magnetic field.4545. B. L. Ahuja, H. S. Mund, J. Sahariya, A. Dashora, M. Halder, S. M. Yusuf, M. Itou, and Y. Sakurai, J. Alloys Compd. 633, 430 (2015). https://doi.org/10.1016/j.jallcom.2015.02.029 It causes a real-space Berry phase, which acts as an emergent magnetic field leading to an additional Hall signal, namely, the THE.36,4636. K. Ueda, S. Iguchi, T. Suzuki, S. Ishiwata, Y. Taguchi, and Y. Tokura, Phys. Rev. Lett. 108, 156601 (2012). https://doi.org/10.1103/PhysRevLett.108.15660146. Y. Taguchi, Y. Oohara, H. Yoshizawa, N. Nagaosa, and Y. Tokura, Science 291, 2573 (2001). https://doi.org/10.1126/science.1058161 Here, the emergent magnetic field is opposite to the external magnetic field because of the ferrimagnetic configuration of TbCo2 and DyCo2. Thus, a negative THE is expected. As the external magnetic field exceeds a critical field (μ0H > μ0HS), the spins in the Co Kagome lattice will arrange themselves in a parallel way while antiferromagnetically coupled with 4f moment of Tb atoms. As a result, the chirality is suppressed leading to the disappearance of the real-space Berry phase and the THE. This explanation is consistent with the fact that the topological Hall resistivity and the critical field for the THE of DyCo2 are larger than those of TbCo2. It was determined in previous neutron diffraction studies that Co atoms building the Kagome lattice of DyCo2 have larger moments when compared with those in TbCo2.7,177. Z. W. Ouyang, F. W. Wang, Q. Hang, W. F. Liu, G. Y. Liu, J. W. Lynn, J. K. Liang, and G. H. Rao, J. Alloys Compd. 390, 21 (2005). https://doi.org/10.1016/j.jallcom.2004.08.02817. E. Burzo, P. Vlaic, D. P. Kozlenko, S. E. Kichanov, A. V. Rutkauskas, and B. N. Savenko, J. Alloys Compd. 724, 1184 (2017). https://doi.org/10.1016/j.jallcom.2017.07.078 Thus, the non-zero spin chirality is stronger for DyCo2 as indicated by the observation of the larger topological Hall resistivity. The stronger THE of DyCo2 is consistent with a larger magnetovolume effect at its TC.44. E. Gratz, A. Lindbaum, A. S. Markosyan, H. Muelleret, and A. Y. Sokolov, J. Phys.: Condens. Matter 6, 6699 (1994). https://doi.org/10.1088/0953-8984/6/33/017 The THE disappears at low temperatures because a stable collinear ferrimagnetic structure is formed.7,177. Z. W. Ouyang, F. W. Wang, Q. Hang, W. F. Liu, G. Y. Liu, J. W. Lynn, J. K. Liang, and G. H. Rao, J. Alloys Compd. 390, 21 (2005). https://doi.org/10.1016/j.jallcom.2004.08.02817. E. Burzo, P. Vlaic, D. P. Kozlenko, S. E. Kichanov, A. V. Rutkauskas, and B. N. Savenko, J. Alloys Compd. 724, 1184 (2017). https://doi.org/10.1016/j.jallcom.2017.07.078Following these relations of the magnetoelectric transport properties, we propose a magnetic phase diagram for each compound. As shown in Figs. 4(c) and 4(d), each magnetic phase diagram is divided into four regions: paramagnetic, trivial ferrimagnetic, noncoplanar, and spin frozen regions. According to the phase diagrams, the noncoplanar region is stable below a critical magnetic field of μ0HS. This small magnitude of the critical magnetic field means that the THE in the two compounds can be switched using a commercial permanent magnet. On the other hand, a similar configuration between the phase diagrams suggests that the noncoplanar spin structure is more related to the Co Kagome lattice than to the species of R atoms. From this point of view, it is plausible to increase the upper limit temperature of this spin structure close to room temperature using partial substitution of Tb or Dy by other rare earth, e.g., Gd. With these possibilities, the THE in the RCo2 compounds with a Co Kagome lattice is considered to be promising for technological applications in spintronic devices.

In conclusion, we have observed a low-field induced plateau-like MR and THE in TbCo2 and DyCo2 below respective TC. The THE has been suggested to have a close correlation to the plateau MR, because they occur in the same temperature region. Fundamentally, these transport phenomena of RCo2 compounds at low magnetic fields have been attributed to the non-zero spin chirality induced by the noncoplanar spin structures of the Co Kagome lattice. The critical field for the suppression of the plateau MR and the THE is higher in DyCo2 than in TbCo2, and this difference is consistent with stronger 4f–3d interactions between Dy and Co atoms. A magnetic phase diagram, including different types of spin structures at low temperatures, has been proposed for the two compounds. In a general sense, the phase diagrams indicate that the RCo2 compounds are promising for functional applications in spintronic devices.

See the supplementary material for the isothermal magnetization (Fig. S1), the linear fit of ρxy/H vs M/H curves (Fig. S2), and the topological Hall resistivity of TbCo2 and DyCo2 at various temperatures (Figs. S3 and S4).

This work was financially supported by the National Key R&D Program of China (Grant Nos. 2022YFA1402600 and 2018YFA0703603) and the National Natural Science Foundation of China (Grant No. 51831003).

Conflict of Interest

The authors have no conflicts to disclose.

Author Contributions

Dan Huang: Data curation (lead); Investigation (lead); Writing – original draft (lead); Writing – review & editing (equal). Hang Li: Investigation (equal); Methodology (equal). Bei Ding: Data curation (equal). Xuekui Xi: Supervision (equal). Jianrong Gao: Data curation (equal); Writing – review & editing (lead). Yong-Chang Lau: Investigation (equal). Wenhong Wang: Funding acquisition (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within the article and its supplementary material.

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