- Letter
- Open Access
Temperature-dependent and magnetism-controlled Fermi surface changes in magnetic Weyl semimetals
Phys. Rev. Research 5, L022013 – Published 18 April, 2023
DOI: https://doi.org/10.1103/PhysRevResearch.5.L022013
Abstract
The coupling between band structure and magnetism can lead to intricate Fermi surface modifications. Here we report on the comprehensive study of the Shubnikov–de Haas (SdH) effect in two rare-earth-based magnetic Weyl semimetals, NdAlSi and . The results show that the temperature evolution of topologically nontrivial Fermi surfaces strongly depends on magnetic configurations. In NdAlSi, the SdH frequencies vary with temperature in both the paramagnetic state and the magnetically ordered state with a chiral spin texture, but become temperature independent in the high-field fully polarized state. In , SdH frequencies are temperature dependent only in the ferromagnetic state with magnetic fields applied along the axis. First-principles calculations suggest that the notable temperature and magnetic-configuration dependence of Fermi surface morphology can be attributed to strong exchange coupling between the conduction electrons and local magnetic moments.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (54)
- J. M. Luttinger, Fermi surface and some simple equilibrium properties of a system of interacting fermions, Phys. Rev. 119, 1153 (1960).
- N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart and Winston, New York, 1976).
- For an electronic system with parabolic bands, the Sommerfeld correction of chemical potential at nonzero can be given by [2] , thus the relative change of is less than one percent even in a low-carrier-density material with 25 meV at K. At this temperature, however, the quantum oscillation measurements are mostly hampered by the thermal broadening of Landau levels.
- C. Guo, A. Alexandradinata, C. Putzke, A. Estry, T. Tu, N. Kumar, F.-R. Fan, S. Zhang, Q. Wu, O. V. Yazyev, K. R. Shirer, M. D. Bachmann, H. Peng, E. D. Bauer, F. Ronning, Y. Sun, C. Shekhar, C. Felser, and P. J. W. Moll, Temperature dependence of quantum oscillations from non-parabolic dispersions, Nat. Commun. 12, 6213 (2021).
- G. Lonzarich and A. V. Gold, Temperature dependence of the exchange splitting in ferromagnetic metals I. Information from the de Haas-van Alphen effect in iron, Can. J. Phys. 52, 694 (1974).
- E. A. Yelland and S. M. Hayden, Magnetic Excitations in an Itinerant Ferromagnet near Quantum Criticality, Phys. Rev. Lett. 99, 196405 (2007).
- T. Suzuki, R. Chisnell, A. Devarakonda, Y.-T. Liu, W. Feng, D. Xiao, J. W. Lynn, and J. G. Checkelsky, Large anomalous Hall effect in a half-Heusler antiferromagnet, Nat. Phys. 12, 1119 (2016).
- S. Nie, Y. Sun, F. B. Prinz, Z. Wang, H. Weng, Z. Fang, and X. Dai, Magnetic Semimetals and Quantized Anomalous Hall Effect in , Phys. Rev. Lett. 124, 076403 (2020).
- J. Ma, H. Wang, S. Nie, C. Yi, Y. Xu, H. Li, J. Jandke, W. Wulfhekel, Y. Huang, D. West, P. Richard, A. Chikina, V. N. Strocov, J. Mesot, H. Weng, S. Zhang, Y. Shi, T. Qian, M. Shi, and H. Ding, Emergence of nontrivial low-energy Dirac fermions in antiferromagnetic , Adv. Mater. 32, 1907565 (2020).
- S. H. Lee, D. Graf, L. Min, Y. Zhu, H. Yi, S. Ciocys, Y. Wang, E. S. Choi, R. Basnet, A. Fereidouni, A. Wegner, Y.-F. Zhao, K. Verlinde, J. He, R. Redwing, V. Gopalan, H. O. H. Churchill, A. Lanzara, N. Samarth, C.-Z. Chang et al., Evidence for a Magnetic-Field-Induced Ideal Type-II Weyl State in Antiferromagnetic Topological Insulator Mn(, Phys. Rev. X 11, 031032 (2021).
- Q. Jiang, C. Wang, P. Malinowski, Z. Liu, Y. Shi, Z. Lin, Z. Fei, T. Song, D. Graf, S. Chikara, X. Xu, J. Yan, D. Xiao, and J.-H. Chu, Quantum oscillations in the field-induced ferromagnetic state of Mn(, Phys. Rev. B 103, 205111 (2021).
- H. Masuda, H. Sakai, M. Tokunaga, M. Ochi, H. Takahashi, K. Akiba, A. Miyake, K. Kuroki, Y. Tokura, and S. Ishiwata, Impact of antiferromagnetic order on Landau-level splitting of quasi-two-dimensional Dirac fermions in , Phys. Rev. B 98, 161108(R) (2018).
- M. Lyu, J. Xiang, Z. Mi, H. Zhao, Z. Wang, E. Liu, G. Chen, Z. Ren, G. Li, and P. Sun, Nonsaturating magnetoresistance, anomalous Hall effect, and magnetic quantum oscillations in the ferromagnetic semimetal PrAlSi, Phys. Rev. B 102, 085143 (2020).
- J. Gaudet, H.-Y. Yang, S. Baidya, B. Z. Lu, G. Y. Xu, Y. Zhao, J. A. Rodriguez-Rivera, C. M. Hoffmann, D. E. Graf, D. H. Torchinsky, P. Nikolic, D. Vanderbilt, F. Tafti, and C. L. Broholm, Weyl-mediated helical magnetism in NdAlSi, Nat. Mater. 20, 1650 (2021).
- J.-F. Wang, Q.-X. Dong, Z.-P. Guo, M. Lv, Y.-F. Huang, J.-S. Xiang, Z.-A. Ren, Z.-J. Wang, P.-J. Sun, G. Li, and G.-F. Chen, NdAlSi: A magnetic Weyl semimetal candidate with rich magnetic phases and atypical transport properties, Phys. Rev. B 105, 144435 (2022).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.5.L022013 for detailed sample characterizations, more information about the DFT calculations, and supporting data and discussions, which includes Refs. [17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36].
- H.-Y. Yang, B. Singh, J. Gaudet, B. Lu, C.-Y. Huang, W.-C. Chiu, S.-M. Huang, B. Wang, F. Bahrami, B. Xu, J. Franklin, I. Sochnikov, D. E. Graf, G. Xu, Y. Zhao, C. M. Hoffman, H. Lin, D. H. Torchinsky, C. L. Broholm, A. Bansil, and F. Tafti, Noncollinear ferromagnetic Weyl semimetal with anisotropic anomalous Hall effect, Phys. Rev. B 103, 115143 (2021).
- Y. Sun, C. Lee, H.-Y. Yang, D. H. Torchinsky, F. Tafti, and J. Orenstein, Mapping domain-wall topology in the magnetic Weyl semimetal CeAlSi, Phys. Rev. B 104, 235119 (2021).
- D. C. Tsui and R. W. Stark, de Haas-van Alphen Effect in Ferromagnetic Nickel, Phys. Rev. Lett. 17, 871 (1966).
- R. Prozorov and V. G. Kogan, Effective Demagnetizing Factors of Diamagnetic Samples of Various Shapes, Phys. Rev. Appl. 10, 014030 (2018).
- W. Kohn and L. J. Sham, Self-Consistent Equations Including Exchange and Correlation Effects, Phys. Rev. 140, A1133 (1965).
- G. Kresse and J. Furthmuller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
- G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
- J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett. 77, 3865 (1996).
- A. I. Liechtenstein, V. I. Anisimov, and J. Zaanen, Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators, Phys. Rev. B 52, R5467 (1995).
- N. Marzari, A. A. Mosto, J. R. Yates, I. Souza, and D. Vanderbilt, Maximally localized Wannier functions: Theory and applications, Rev. Mod. Phys. 84, 1419 (2012).
- A. A. Mostofi, J. R. Yates, Y.-S. Lee, I. Souza, D. Vanderbilt, and N. Marzari, Wannier90: A tool for obtaining maximally-localised Wannier functions, Comput. Phys. Commun. 178, 685 (2008).
- D. Destraz, L. Das, S. S. Tsirkin, Y. Xu, T. Neupert, J. Chang, A. Schilling, A. G. Grushin, J. Kohlbrecher, L. Keller, P Puphal, E Pomjakushina, and J. S. White, Magnetism and anomalous transport in the Weyl semimetal PrAlGe: possible route to axial gauge fields, npj Quantum Mater. 5, 5 (2020).
- D. Shoenberg, Magnetic Oscillations in Metals (Cambridge University Press, Cambridge, 1984).
- J. Hajdu, The Shubnikov-de Haas effect: An introduction to the theory, in Landau Level Spectroscopy: Modern Problems in Condensed Matter Sciences, edited by G. Landwehr and E. I. Rashba (North-Holland, Amsterdam, 1991).
- F. Wu, C. Guo, M. Smidman, J. Zhang, Y. Chen, J. Singleton, and H. Yuan, Anomalous quantum oscillations and evidence for a non-trivial Berry phase in SmSb, npj Quantum Mater. 4, 20 (2019).
- T. Yamamizu, M. Endo, M. Nakayama, N. Kimura, H. Aoki, and S. Kunii, Uniaxial pressure effect on the magnetic phase diagram and Fermi-surface properties of , Phys. Rev. B 69, 014423 (2004).
- Y. Matsumoto, T. Terashima, S. Uji, N. Kimura, and H. Aoki, How are heavy and itinerant electrons born in a dilute Kondo alloy?, J. Phys. Soc. Jpn. 81, 054703 (2012).
- G. Chang, B. Singh, S.-Y. Xu, G. Bian, S.-M. Huang, C.-H. Hsu, I. Belopolski, N. Alidoust, D. S. Sanchez, H. Zheng, H. Lu, X. Zhang, Y. Bian, T.-R. Chang, H.-T. Jeng, A. Bansil, H. Hsu, S. Jia, T. Neupert, H. Lin, and M. Zahid Hasan, Magnetic and noncentrosymmetric Weyl fermion semimetals in the family of compounds ( = rare earth), Phys. Rev. B 97, 041104(R) (2018).
- P. M. Levy, Anisotropy in two-center exchange interactions, Phys. Rev. 177, 509 (1969).
- K. V. Kavokin, Anisotropic exchange interaction of localized conduction-band electrons in semiconductors, Phys. Rev. B 64, 075305 (2001).
- J.-F. Wang, Q.-X. Dong, Y.-F. Huang, Z.-S. Wang, Z.-P. Guo, Z.-J. Wang, Z.-A. Ren, G. Li, P.-J. Sun, X. Dai, and G.-F. Chen, New type of quantum oscillations stemmed from the strong Weyl fermions - electrons exchange interaction, arXiv:2201.06412.
- W. Kang, G. Montambaux, J. R. Cooper, D. Jérome, P. Batail, and C. Lenoir, Observation of Giant Magnetoresistance Oscillations in the High- Phase of the Two-Dimensional Organic Conductor -(BEDT-TTF), Phys. Rev. Lett. 62, 2559 (1989).
- The origin of this phenomenon is not clear yet. It is possible that the large spin splitting in band in the FIP state (with ) can be suppressed in a tilted magnetic field. Another explanation is that, with the breaking of the rotational symmetry caused by a tilted , the four pockets in the first Brillouin zone become inequivalent [53]. We mention that the shapes and sizes of FSs in the FIP state of NdAlSi may change with field orientation owing to the strong coupling with Nd magnetism. Further theoretical analysis is required to determine the most likely scenario.
- H. Su, X. Shi, J. Yuan, Y. Wan, E. Cheng, C. Xi, L. Pi, X. Wang, Z. Zou, Na. Yu, W. Zhao, S. Li, and Y. Guo, Multiple Weyl fermions in the noncentrosymmetric semimetal LaAlSi, Phys. Rev. B 103, 165128 (2021).
- According to the model presented in [4], the topological correction , with the maximum . Taking = [14], = 70 T for SdH branch in NdAlSi, and = 20 K, is at most . We cannot verify the presence or absence of such a small contribution.
- A general example of the Hamiltonian of the exchange coupling between the local magnetic moments and conduction electron spins takes the form [46, 54] ; here, is the effective exchange integral, and and describe the spin density of conduction electrons and the -electron angular momentum, respectively. Note that the exchange coupling in NdAlSi cannot be taken as a two-spin interaction due to the nonzero orbital angular momentum () of the ion. We thus consider the local moment corresponding to the multiplet.
- It was pointed out in [14] that the SdH frequency shifts in the canted u-d-d state of NdAlSi are linked to the RKKY interaction between the itinerant Weyl fermions and localized electrons, with the frequency shifts coinciding with the changes of ordering vectors. Such scenario does not suffice to explain the -dependent SdH patterns in the PM state.
- N. Kozlova, J. Hagel, M. Doerr, J. Wosnitza, D. Eckert, K.-H. Müller, L. Schultz, I. Opahle, S. Elgazzar, M. Richter, G. Goll, H. v. Löhneysen, G. Zwicknagl, T. Yoshino, and T. Takabatake, Magnetic-Field-Induced Band-Structure Change in CeBiPt, Phys. Rev. Lett. 95, 086403 (2005).
- J. Wosnitza, G. Goll, A. D. Bianchi, B. Bergk, N. Kozlova, I. Opahle, S. Elgazzar, M. Richter, O. Stockert, H. v. Löhneysen, T. Yoshino, and T. Takabatake, Magnetic-field- and temperature-dependent Fermi surface of CeBiPt, New J. Phys. 8, 174 (2006).
- Y. Nakanishi, T. Sakon, M. Motokawa, M. Ozawa, and T. Suzuki, De Haas–van Alphen study of the spin splitting of the Fermi surface in TbSb, Phys. Rev. B 69, 024412 (2004).
- R. G. Goodrich, N. Harrison, and Z. Fisk, Fermi Surface Changes across the Néel Phase Boundary of , Phys. Rev. Lett. 97, 146404 (2006).
- J. Y. Liu, J. Hu, Q. Zhang, D. Graf, H. B. Cao, S. M. A. Radmanesh, D. J. Adams, Y. L. Zhu, G. F. Cheng, X. Liu, W. A. Phelan, J. Wei, M. Jaime, F. Balakirev, D. A. Tennant, J. F. DiTusa, I. Chiorescu, L. Spinu, and Z. Q. Mao, A magnetic topological semimetal ( 0.1), Nat. Mater. 16, 905 (2017).
- K. Zhao, X. Chen, Z. Wang, J. Liu, J. Wu, C. Xi, X. Lv, L. Li, Z. Zhong, and P. Gegenwart, Magnetic tuning of band topology evidenced by exotic quantum oscillations in the Dirac semimetal , Phys. Rev. B 107, L081112 (2023).
- H.-R. Chang, J. Zhou, S.-X. Wang, W.-Y. Shan, and D. Xiao, RKKY interaction of magnetic impurities in Dirac and Weyl semimetals, Phys. Rev. B 92, 241103(R) (2015).
- S.-X. Wang, H.-R. Chang, and J. Zhou, RKKY interaction in three-dimensional electron gases with linear spin-orbit coupling, Phys. Rev. B 96, 115204 (2017).
- P. Nikolić, Dynamics of local magnetic moments induced by itinerant Weyl electrons, Phys. Rev. B 103, 155151 (2021)
- T. Suzuki, L. Savary, J.-P. Liu, J. W. Lynn, L. Balents, and J. G. Checkelsky, Singular angular magnetoresistance in a magnetic nodal semimetal, Science 365, 377 (2019).
- M. Wulff, G. G. Lonzarich, D. Fort, and H. L. Skriver, Strong quasi-particle renormalization in praseodymium, Europhys. Lett. 7, 629 (1988).