- Open Access
Tunable band-filling effects on thermoelectric properties and anomalous Hall conductivity in Weyl semimetal
Phys. Rev. Research 8, 013215 – Published 26 February, 2026
DOI: https://doi.org/10.1103/71sm-3r2x
Abstract
The magnetic Weyl semimetal has garnered significant experimental and theoretical interest, particularly regarding its electronic structure and transport properties. In this study, we comprehensively investigated the effects of Fe and Ni substitution in . The temperature-dependent Seebeck coefficient () implies that the reduction of the band gap and the shift in the Fermi level () due to Fe and Ni substitution, which was supported by angle-resolved photoemission spectroscopy results. These band-structure modifications influence not only thermoelectric (TE) performance but also the anomalous Hall conductivity (). Specifically, Fe substitution increases via skew scattering, while Ni substitution increases via intrinsic deflection with minor skew scattering. Additionally, the Fe and Ni dopant-induced changes in the ratio were demonstrated using high-resolution powder synchrotron x-ray diffraction, which explains the different modulation in the magnetic anisotropy of due to the magnetostriction effect. Notably, the oxidation states of Co, Fe, and Ni in each single crystal were confirmed as 0 using x-ray absorption near-edge structure analysis, further explaining the dopant-induced suppression in ferromagnetism of . These findings provide deeper insight into the band-filling effects on both TE and anomalous Hall transport in , offering perspectives for topological spintronics and TE applications.
Physics Subject Headings (PhySH)
- Anomalous Hall effect
- Electronic structure
- Ferromagnetism
- Magnetostriction
- Seebeck effect
- Thermal conductivity
- Thermoelectrics
- Thermopower
- Transport phenomena
- Valence
- Single crystal materials
- Synchrotron radiation facilities
- Weyl semimetal
- Angle-resolved photoemission spectroscopy
- Crystal growth
- Thermal techniques
- Transport techniques
- X-ray absorption spectroscopy
- X-ray diffraction
Article Text
Supplemental Material
References (84)
- L. Balents, Spin liquids in frustrated magnets, Nature (London) 464, 199 (2010).
- Y. Guo, H. Liu, O. Janson, I. C. Fulga, J. van den Brink, and J. I. Facio, Spin-split collinear antiferromagnets: A large-scale ab initio study, Mater. Today Phys. 32, 100991 (2023).
- Y. H. Chang, A. Pal, P. T. W. Yen, C. W. Wang, S. Giri, G. R. Blake, J. Gainza, M. J. Hsieh, J. Y. Lin, C. Y. Huang, Y. J. Chen, T. W. Kuo, A. Tiwari, D. Chandrasekhar Kakarla, and H. D. Yang, Field-induced transformation of complex spin ordering and magnetodielectric and magnetoelastic coupling in , Phys. Rev. B 110, 064405 (2024).
- H. C. Wu, J. K. Yuan, K. D. Chandrasekhar, C. H. Lee, W. H. Li, C. W. Wang, J. M. Chen, J. Y. Lin, H. Berger, T. W. Yen, S. M. Huang, C. W. Chu, and H. D. Yang, Observation of charge-transfer-driven antiferroelectricity in -pyrochlore multiferroic , Mater. Today Phys. 8, 34 (2019).
- W. Shon, D. C. Ryu, K. Kim, B. I. Min, B. Kim, B. Kang, B. K. Cho, H. J. Kim, and J. S. Rhyee, Magnetic field–induced type II Weyl semimetallic state in geometrically frustrated Shastry-Sutherland lattice , Mater. Today Phys. 11, 100168 (2019).
- H. C. Wu, K. D. Chandrasekhar, J. K. Yuan, J. R. Huang, J. Y. Lin, H. Berger, and H. D. Yang, Anisotropic spin-flip-induced multiferroic behavior in kagome , Phys. Rev. B 95, 125121 (2017).
- M. K. Dasoundhi, S. Baral, I. Rajput, D. Kumar, and A. Lakhani, Extremely large magnetoresistance and non-trivial band topology in YSb semimetal, Mater. Today Phys. 40, 101310 (2024).
- H. C. Wu, Y. C. Chung, T. W. Yen, H. J. Chen, T. W. Kuo, D. C. Kakarla, S. M. Huang, Y. Y. Wang, J. Y. Lin, J. J. Lee, Y. C. Lai, C. L. Chen, J. F. Lee, T. L. Chou, Y. C. Lai, M. W. Chu, M. M. C. Chou, and H. D. Yang, Evidence of a structural phase transition in the triangular-lattice compound , Phys. Rev. B 103, 104111 (2021).
- A. P. Ramirez, Strongly geometrically frustrated magnets, Annu. Rev. Mater. Res. 24, 453 (1994).
- H. J. Chen, C. H. Yeh, T. W. Kuo, D. C. Kakarla, H. C. Wu, T. W. Yen, S. M. Huang, H. Chou, M. C. Chou, H. W. Chen, S. W. Kuo, Y. C. Chuang, C. K. Chang, U. Eckstein, N. H. Khansur, K. G. Webber, and H. D. Yang, Unique multiferroics with tunable ferroelastic transition in antiferromagnet , Mater. Today Phys. 23, 100623 (2022).
- A. Pal, C. H. Huang, T. W. Yen, P. H. Lee, Y. H. Chang, C. H. Yeh, T. W. Kuo, A. Tiwari, D. C. Kakarla, S. M. Huang, M. C. Chou, H. S. Kunwar, S. Rana, V. G. Sathe, B. H. Chen, Y. C. Chuang, and H. D. Yang, Spin-induced strongly correlated magnetodielectricity, magnetostriction effect, and spin-phonon coupling in helical magnet , Phys. Rev. B 106, 094404 (2022).
- N. Nagaosa, J. Sinova, S. Onoda, A. H. MacDonald, and N. P. Ong, Anomalous Hall effect, Rev. Mod. Phys. 82, 1539 (2010).
- 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 (2003).
- D. Xiao, M.-C. Chang, and Q. Niu, Berry phase effects on electronic properties, Rev. Mod. Phys. 82, 1959 (2010).
- F. D. M. Haldane, Berry curvature on the Fermi surface: Anomalous Hall effect as a topological Fermi-liquid property, Phys. Rev. Lett. 93, 206602 (2004).
- E. Vilanova Vidal, G. Stryganyuk, H. Schneider, C. Felser, and G. Jakob, Exploring Heusler compound for anomalous Hall effect sensors, Appl. Phys. Lett. 99, 132509 (2011).
- C.-Z. Chang, J. Zhang, M. Liu, Z. Zhang, X. Feng, K. Li, L.-L. Wang, X. Chen, X. Dai, Z. Fang, X.-L. Qi, S.-C. Zhang, Y. Wang, K. He, X.-C. Ma, and Q.-K. Xue, Thin films of magnetically doped topological insulator with carrier-independent long-range ferromagnetic order, Adv. Mater. 25, 1065 (2013).
- K. Manna, L. Muechler, T.-H. Kao, R. Stinshoff, Y. Zhang, J. Gooth, N. Kumar, G. Kreiner, K. Koepernik, R. Car, J. Kübler, G. H. Fecher, C. Shekhar, Y. Sun, and C. Felser, From colossal to zero: Controlling the anomalous Hall effect in magnetic Heusler compounds via Berry curvature design, Phys. Rev. X 8, 041045 (2018).
- D. F. Liu, A. J. Liang, E. K. Liu, Q. N. Xu, Y. W. Li, C. Chen, D. Pei, W. J. Shi, S. K. Mo, P. Dudin, T. Kim, C. Cacho, G. Li, Y. Sun, L. X. Yang, Z. K. Liu, S. S. P. Parkin, C. Felser, and Y. L. Chen, Magnetic Weyl semimetal phase in a Kagomé crystal, Science 365, 1282 (2019).
- N. Morali, R. Batabyal, P. K. Nag, E. Liu, Q. Xu, Y. Sun, B. Yan, C. Felser, N. Avraham, and H. Beidenkopf, Fermi-arc diversity on surface terminations of the magnetic Weyl semimetal , Science 365, 1286 (2019).
- S. Rathod, M. Malasi, A. Lakhani, and D. Kumar, Electron-magnon scattering in an anisotropic Half-metallic ferromagnetic Weyl semimetal , Phys. Rev. Mater. 6, 084202 (2022).
- R. Weihrich and I. Anusca, Half antiperovskites. III. Crystallographic and electronic structure effects in , Z. Anorg. Allg. Chem. 632, 1531 (2006).
- Q. Wang, Y. Xu, R. Lou, Z. Liu, M. Li, Y. Huang, D. Shen, H. Weng, S. Wang, and H. Lei, Large intrinsic anomalous Hall effect in half-metallic ferromagnet with magnetic Weyl fermions, Nat. Commun. 9, 3681 (2018).
- E. Liu, et al., Giant anomalous Hall effect in a ferromagnetic Kagome-lattice semimetal, Nat. Phys. 14, 1125 (2018).
- R. K. Gopal Shama and Y. Singh, Observation of planar Hall effect in the ferromagnetic Weyl semimetal , J. Magn. Magn. Mater. 502, 166547 (2020).
- M. Tanaka, Y. Fujishiro, M. Mogi, Y. Kaneko, T. Yokosawa, N. Kanazawa, S. Minami, T. Koretsune, R. Arita, S. Tarucha, M. Yamamoto, and Y. Tokura, Topological kagome magnet thin flakes with high electron mobility and large anomalous hall effect, Nano Lett. 20, 7476 (2020).
- E. A. Stern, Rigid-band model of alloys, Phys. Rev. 157, 544 (1967).
- D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Quantized Hall conductance in a two-dimensional periodic potential, Phys. Rev. Lett. 49, 405 (1982).
- G. S. Thakur, P. Vir, S. N. Guin, C. Shekhar, R. Weihrich, Y. Sun, N. Kumar, and C. Felser, Intrinsic anomalous Hall effect in Ni-substituted magnetic Weyl semimetal , Chem. Mater. 32, 1612 (2020).
- J. Shen, Q. Zeng, S. Zhang, H. Sun, Q. Yao, X. Xi, W. Wang, G. Wu, B. Shen, Q. Liu, and E. Liu, 33% giant anomalous Hall current driven by both intrinsic and extrinsic contributions in magnetic Weyl semimetal , Adv. Funct. Mater. 30, 2000830 (2020).
- J. Shen, Q. Yao, Q. Zeng, H. Sun, X. Xi, G. Wu, W. Wang, B. Shen, Q. Liu, and E. Liu, Local disorder-induced elevation of intrinsic anomalous Hall conductance in an electron-doped magnetic Weyl semimetal, Phys. Rev. Lett. 125, 086602 (2020).
- H. Zhou, G. Chang, G. Wang, X. Gui, X. Xu, J.-X. Yin, Z. Guguchia, S. S. Zhang, T.-R. Chang, H. Lin, W. Xie, M. Z. Hasan, and S. Jia, Enhanced anomalous Hall effect in the magnetic topological semimetal , Phys. Rev. B 101, 125121 (2020).
- Y. Li, W. Li, J. Lin, Z. Guo, F. Sun, X. Chen, Y. Luo, J. Yang, and W. Yuan, Electron doping and physical properties in the ferromagnetic semimetal , J. Phys. Chem. C 126, 7230 (2022).
- B. He, M. Yao, Y. Pan, K. E. Arpino, D. Chen, F. M. Serrano-Sanchez, S. Ju, M. Shi, Y. Sun, and C. Felser, Enhanced Weyl semimetal signature in kagome ferromagnet by chlorine doping, Commun. Mater. 5, 275 (2024).
- H. C. Wu, P. J. Sun, D. J. Hsieh, H. J. Chen, D. C. Kakarla, L. Z. Deng, C. W. Chu, and H. D. Yang, Observation of skyrmion-like magnetism in magnetic Weyl semimetal , Mater. Today Phys. 12, 100189 (2020).
- S. Rathod, M. Malasi, A. Lakhani, and D. Kumar, How to enhance anomalous Hall effects in magnetic Weyl semimetal ? Chem. Mater. 36, 7418 (2024).
- M. Kanagaraj, J. Ning, and L. He, Topological magnetic Weyl semimetal: From fundamental understanding to diverse fields of study, Rev. Phys. 8, 100072 (2022).
- Z. Shen, X. D. Zhu, R. R. Ullah, P. Klavins, and V. Taufour, Anomalous depinning of magnetic domain walls within the ferromagnetic phase of the Weyl semimetal , J. Phys. Condens. Matter 35, 045802 (2023).
- A. Rossi, V. Ivanov, S. Sreedhar, A. L. Gross, Z. Shen, E. Rotenberg, A. Bostwick, C. Jozwiak, V. Taufour, S. Y. Savrasov, and I. M. Vishik, Electronic structure and topology across in the magnetic Weyl semimetal , Phys. Rev. B 104, 155115 (2021).
- Y. Zhang, Z. Li, and C. Uher, Low-temperature thermal properties of Fe-doped , Mater. Today Commun. 34, 105100 (2023).
- Y. Xin, K. W. Wong, C. X. Fan, Z. Z. Sheng, and F. T. Chan, Thermoelectric power of the thallium-based superconductor , Phys. Rev. B 48, 557 (1993).
- P. Mangelis, P. Vaqueiro, J.-C. Jumas, I. da Silva, R. I. Smith, and A. V. Powell, The effect of electron and hole doping on the thermoelectric properties of shandite-type , J. Solid State Chem. 251, 204 (2017).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/71sm-3r2x for the details of the additional data of .
- J. Liu, Y. Yang, J. Shen, D. Liu, G. S. Thakur, C. Guillemard, A. Smekhova, H. Chen, D. Biswas, M. Valvidares, E. Liu, C. Felser, T.-L. Lee, T. Hesjedal, Y. Chen, and G. van der Laan, Unusually high occupation of Co state in magnetic Weyl semimetal , ACS Nano 19, 8561 (2025).
- J. Corps, P. Vaqueiro, A. Aziz, R. Grau-Crespo, W. Kockelmann, J.-C. Jumas, and A. V. Powell, Interplay of metal-atom ordering, Fermi level tuning, and thermoelectric properties in cobalt shandites ( Sn, In), Chem. Mater. 27, 3946 (2015).
- M. Yan, Y. Jin, X. Hou, Y. Guo, A. Tsaturyan, A. Makarova, D. Smirnov, Y. Dedkov, and E. Voloshina, Topological quasi-2D semimetal : Insights into electronic structure from NEXAFS and resonant photoelectron spectroscopy, J. Phys. Chem. Lett. 12, 9807 (2021).
- G. Li, Q. Xu, W. Shi, C. Fu, L. Jiao, M. E. Kamminga, M. Yu, H. Tüysüz, N. Kumar, V. Süß, R. Saha, A. K. Srivastava, S. Wirth, G. Auffermann, J. Gooth, S. Parkin, Y. Sun, E. Liu, and C. Felser, Surface states in bulk single crystal of topological semimetal toward water oxidation, Sci. Adv. 5, eaaw9867 (2019).
- Y. Zhao, Y. Zhu, F. Jiang, Y. Li, Y. Meng, Y. Guo, Q. Li, Z. Huang, S. Zhang, R. Zhang, J. C. Ho, Q. Zhang, W. Liu, and C. Zhi, Vacancy modulating topological semimetal for aqueous zinc-ion batteries, Angew. Chem. Int. Ed. 61, e202111826 (2022).
- T. Kubodera, H. Okabe, Y. Kamihara, and M. Matoba, Ni substitution effect on magnetic and transport properties in metallic ferromagnet , Phys. B Condens. Matter 378-380, 1142 (2006).
- P. Gütlich, K. J. Range, C. Felser, C. Schultz-Münzenberg, W. Tremel, D. Walcher, and M. Waldeck, The valence states of nickel, tin, and sulfur in the ternary chalcogenide –XPS, , and Mössbauer investigations, and band structure calculations, Angew. Chem. Int. Ed. 38, 2381 (1999).
- Y. Sakai, R. Tanakadate, M. Matoba, I. Yamada, N. Nishiyama, T. Irifune, K. Funakoshi, T. Kunimoto, Y. Higo, and Y. Kamihara, Magnetic properties of shandite-phase ( 0–1.0) obtained with high pressure synthesis, J. Phys. Soc. Jpn. 84, 044705 (2015).
- Y. Zhang and C. Uher, Magnetic and transport properties of Fe-doped Weyl semimetal , J. Alloys Compd. 911, 165089 (2022).
- F. Sun, T. Zhang, C. J. Yi, Y. L. Wu, H. Zhao, Q. Wu, Y. G. Shi, H. Weng, and J. Zhao, Spin-polarized gap in the magnetic Weyl semimetal , Phys. Rev. B 104, L100301 (2021).
- W. Schnelle, A. Leithe-Jasper, H. Rosner, F. M. Schappacher, R. Pöttgen, F. Pielnhofer, and R. Weihrich, Ferromagnetic ordering and half-metallic state of with the shandite-type structure, Phys. Rev. B 88, 144404 (2013).
- M. A. Kassem, Y. Tabata, T. Waki, and H. Nakamura, Single crystal growth and characterization of kagomé-lattice shandites , J. Cryst. Growth 426, 208 (2015).
- S. N. Guin, P. Vir, Y. Zhang, N. Kumar, S. J. Watzman, C. Fu, E. Liu, K. Manna, W. Schnelle, J. Gooth, C. Shekhar, Y. Sun, and C. Felser, Zero-field Nernst effect in a ferromagnetic Kagome-lattice Weyl-semimetal , Adv. Mater. 31, 1806622 (2019).
- M. B. Brodsky, Thermoelectricity in metals and alloys, Phys. Bull. 24, 620 (1973).
- P. Bag, W. Z. Liu, Y.-K. Kuo, C. N. Kuo, and C. S. Lue, Thermoelectric properties of chemically substituted Heusler-type and ( In, Ge, and Sn) alloys, J. Alloys Compd. 849, 156617 (2020).
- C. S. Lue and Y. K. Kuo, Thermoelectric properties of the semimetallic Heusler compounds (, Ga), Phys. Rev. B 66, 085121 (2002).
- S. Mondal, C. Mazumdar, R. Ranganathan, E. Alleno, P. C. Sreeparvathy, V. Kanchana, and G. Vaitheeswaran, Ferromagnetically correlated clusters in semimetallic Heusler alloy and its thermoelectric properties, Phys. Rev. B 98, 205130 (2018).
- Y. K. Kuo, K. M. Sivakumar, H. C. Chen, J. H. Su, and C. S. Lue, Anomalous thermal properties of the Heusler alloy near the martensitic transition, Phys. Rev. B 72, 054116 (2005).
- J. Bhattacharya, P. Sadhukhan, S. Sarkar, V. K. Singh, A. Gloskovskii, S. R. Barman, and A. Chakrabarti, Bulk electronic structure of studied by density functional theory and hard x-ray photoelectron spectroscopy, Phys. Rev. B 108, L121114 (2023).
- J. Barth, G. H. Fecher, B. Balke, S. Ouardi, T. Graf, C. Felser, A. Shkabko, A. Weidenkaff, P. Klaer, H. J. Elmers, H. Yoshikawa, S. Ueda, and K. Kobayashi, Itinerant half-metallic ferromagnets (, Ge, Sn): Ab initio calculations and measurement of the electronic structure and transport properties, Phys. Rev. B 81, 064404 (2010).
- S. Arsenijević, R. Gaál, A. S. Sefat, M. A. McGuire, B. C. Sales, D. Mandrus, and L. Forró, Pressure effects on the transport coefficients of , Phys. Rev. B 84, 075148 (2011).
- T. M. Tritt, Thermal Conductivity: Theory, Properties, and Applications (Springer Science+Business Media, Berlin/Heidelberg, Germany, 2005).
- J. W. Yan, F. Liu, G.-h. Ma, B. Gong, J. Zhu, X. G. Wang, W. Ao, C. Zhang, Y. Li, and J. Li, Suppression of the lattice thermal conductivity in NbFeSb-based half-Heusler thermoelectric materials through high entropy effects, Scr. Mater. 157, 129 (2018).
- D. M. Rowe, CRC Handbook of Thermoelectrics (CRC Press, Boca Raton, Florida, 1995).
- G. J. Snyder and E. S. Toberer, Complex thermoelectric materials, Nat. Mater. 7, 105 (2008).
- C.-C. Chang, C.-H. Liu, C.-C. Wu, P. Bag, and Y.-K. Kuo, Thermoelectric properties of eutectic composite with In doping, Mater. Res. Bull. 129, 110916 (2020).
- B. Ramachandran, K. K. Wu, Y. K. Kuo, L. S. Guo, and L. M. Wang, Compositional effects on the low-temperature transport properties of non-stoichiometric -based crystals, J. Phys. D Appl. Phys. 50, 025302 (2017).
- H.-S. Kim, Z. M. Gibbs, Y. Tang, H. Wang, and G. J. Snyder, Characterization of Lorenz number with Seebeck coefficient measurement, APL Mater. 3, 041506 (2015).
- P. Bag, Y. H. Lin, Y. K. Kuo, C. N. Kuo, and C. S. Lue, Physical properties of the full Heusler-type ( 0.00–0.50) alloys, J. Alloys Compd. 945, 169318 (2023).
- P. Bag, Y.-C. Su, Y.-K. Kuo, Y.-C. Lai, and S.-K. Wu, Physical properties of face-centered cubic structured high-entropy alloys: Effects of NiCo, NiFe, and NiCoFe alloying with Mn, Cr, and Pd, Phys. Rev. Mater. 5, 085003 (2021).
- J. Callaway, Model for lattice thermal conductivity at low temperatures, Phys. Rev. 113, 1046 (1959).
- A. Saadi, L. e. H. Omari, and A. Boudali, Sn replacement influence on magnetic, electronic, thermodynamic, thermoelectric and transport properties in shandite compounds of , Eur. Phys. J. B 93, 180 (2020).
- K. Ciesielski, K. Synoradzki, I. Veremchuk, P. Skokowski, D. Szymański, Y. Grin, and D. Kaczorowski, Thermoelectric performance of the half-Heusler phases ( Sc, Dy, Er, Tm, Lu): High mobility ratio between majority and minority charge carriers, Phys. Rev. Appl. 14, 054046 (2020).
- M. Ohta, H. Obara, and A. Yamamoto, Preparation and thermoelectric properties of chevrel-phase (2.0 ≤ ≤ 4.0), Mater. Trans. 50, 2129 (2009).
- D. Guo, C. Hu, and C. Zhang, First-principles study on doping and temperature dependence of thermoelectric property of thermoelectric material, Mater. Res. Bull. 48, 1984 (2013).
- M. R. Burton, S. Mehraban, J. McGettrick, T. Watson, N. P. Lavery, and M. J. Carnie, Earth abundant, non-toxic, 3D printed with high thermoelectric figure of merit, J. Mater. Chem. A 7, 25586 (2019).
- A. Damascelli, Probing the electronic structure of complex systems by ARPES, Phys. Scr. 2004, 61 (2004).
- J. M. D. Coey, Magnetism and Magnetic Materials (Cambridge University Press, Cambridge, 2010).
- S. Onoda, N. Sugimoto, and N. Nagaosa, Intrinsic versus extrinsic anomalous Hall effect in ferromagnets, Phys. Rev. Lett. 97, 126602 (2006).
- T. Miyasato, N. Abe, T. Fujii, A. Asamitsu, S. Onoda, Y. Onose, N. Nagaosa, and Y. Tokura, Crossover behavior of the anomalous Hall effect and anomalous Nernst effect in itinerant ferromagnets, Phys. Rev. Lett. 99, 086602 (2007).
- Y. Tian, L. Ye, and X. Jin, Proper scaling of the anomalous Hall effect, Phys. Rev. Lett. 103, 087206 (2009).