- Open Access
Quantum geometry and elliptic optical dichroism in -wave magnets
Phys. Rev. B 112, 045302 – Published 1 July, 2025
DOI: https://doi.org/10.1103/z9gw-lppc
Abstract
The quantum geometric tensor is composed of the Berry curvature and the quantum metric, which is observable by means of optical absorption of elliptically polarized light. Especially, the quantum geometric tensor at the zero-momentum is observable by the optical absorption at the optical band edge. In this context, we study optical absorption of a -wave magnet under irradiation of elliptically polarized light. The -wave magnet has a band splitting along one axis, which we choose as the axis. We obtain exact analytic formulas for the optical conductivity when the Néel vector is along the , and axis. The optical conductivity strongly depends on the degree of ellipticity of light, which is an elliptic dichroism. Especially, there is a perfect elliptic optical dichroism when the Néel vector is along the axis. It is possible to determine the Néel vector by measuring the ellipticity of the perfect elliptic dichroism, which will be a key to future magnetic memory based on the -wave magnet.
Physics Subject Headings (PhySH)
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References (57)
- J. Ahn, G.-Y. Guo, and N. Nagaosa, Low-frequency divergence and quantum geometry of the bulk photovoltaic effect in topological semimetals, Phys. Rev. X 10, 041041 (2020).
- T. Holder, D. Kaplan, and B. Yan, Consequences of time-reversal-symmetry breaking in the light-matter interaction: Berry curvature, quantum metric, and diabatic motion, Phys. Rev. Res. 2, 033100 (2020).
- P. Bhalla, K. Das, D. Culcer, and A. Agarwal, Resonant second-harmonic generation as a probe of quantum geometry, Phys. Rev. Lett. 129, 227401 (2022).
- J. Ahn, G.-Y. Guo, N. Nagaosa, and A. Vishwanath, Riemannian geometry of resonant optical responses, Nat. Phys. 18, 290 (2022).
- I. Souza, T. Wilkens, and R. M. Martin, Polarization and localization in insulators: Generating function approach, Phys. Rev. B 62, 1666 (2000).
- W. Chen and G. von Gersdorff, Measurement of interaction-dressed Berry curvature and quantum metric in solids by optical absorption, SciPost Phys. Core 5, 040 (2022).
- M. S. M. de Sousa, A. L. Cruz, and W. Chen, Mapping quantum geometry and quantum phase transitions to real space by a fidelity marker, Phys. Rev. B 107, 205133 (2023).
- B. Ghosh, Y. Onishi, S.-Y. Xu, H. Lin, L. Fu, and A. Bansil, Probing quantum geometry through optical conductivity and magnetic circular dichroism, Sci. Adv. 10, eado1761 (2024).
- Y. Onishi and L. Fu, Fundamental bound on topological gap, Phys. Rev. X 14, 011052 (2024).
- W. Chen, Quantum geometrical properties of topological materials, J. Phys.: Condens. Matter 37, 025605 (2025).
- M. Ezawa, Analytic approach to quantum metric and optical conductivity in Dirac models with parabolic mass in arbitrary dimensions, Phys. Rev. B 110, 195437 (2024).
- C.-G. Oh, S.-W. Kim, K. W. Kim, B. Monserrat, and J.-W. Rhim, Universal optical conductivity from quantum geometry in quadratic band-touching semimetals, arXiv:2503.18372.
- Q. Ma et al., Observation of the nonlinear Hall effect under time-reversal-symmetric conditions, Nature (London) 565, 337 (2019).
- C. Wang, Y. Gao, and D. Xiao, Intrinsic nonlinear Hall effect in antiferromagnetic tetragonal CuMnAs, Phys. Rev. Lett. 127, 277201 (2021).
- K. Das, S. Lahiri, R. B. Atencia, D. Culcer, and A. Agarwal, Intrinsic nonlinear conductivities induced by the quantum metric, Phys. Rev. B 108, L201405 (2023).
- A. Gao, Y.-F. Liu, J.-X. Qiu, B. Ghosh, T. V. Trevisan, Y. Onishi, C. Hu, T. Qian, H.-J. Tien, S.-W. Chen et al., Quantum metric nonlinear Hall effect in a topological antiferromagnetic heterostructure, Science 381, 181 (2023).
- N. Wang, D. Kaplan, Z. Zhang, T. Holder, N. Cao, A. Wang, X. Zhou, F. Zhou, Z. Jiang, C. Zhang et al., Quantum metric-induced nonlinear transport in a topological antiferromagnet, Nature (London) 621, 487 (2023).
- D. Kaplan, T. Holder and B. Yan, Unification of nonlinear anomalous Hall effect and nonreciprocal magnetoresistance in metals by the quantum geometry, Phys. Rev. Lett. 132, 026301 (2024).
- G. Sala et al., The quantum metric of electrons with spin-momentum locking, arXiv:2407.06659.
- Y. Fang, J. Cano, and S. A. A. Ghorashi, Quantum geometry induced nonlinear transport in altermagnets, Phys. Rev. Lett. 133, 106701 (2024).
- M. Ezawa, Detecting the Néel vector of altermagnets in heterostructures with a topological insulator and a crystalline valley-edge insulator, Phys. Rev. B 109, 245306 (2024).
- W. Yao, D. Xiao, and Q. Niu, Phys. Rev. B 77, 235406 (2008).
- D. Xiao, G.-B. Liu, W. Feng, X. Xu, and W. Yao, Coupled spin and valley physics in monolayers of and other group-VI dichalcogenides, Phys. Rev. Lett. 108, 196802 (2012).
- M. Ezawa, Spin-valley optical selection rule and strong circular dichroism in silicene, Phys. Rev. B 86, 161407(R) (2012).
- X. Li, T. Cao, Q. Niu, J. Shi, and J. Feng, Coupling the valley degree of freedom to antiferromagnetic order, Proc. Natl. Acad. Sci. USA 110, 3738 (2013).
- M. Ezawa, Elliptic Dichroism and Valley-Selective Optical Pumping in the Surface of Topological Crystalline Insulator, Phys. Rev. B 89, 195413 (2014).
- A. B. Hellenes, T. Jungwirth, J. Sinova, L. Šmejkal, Unconventional p-wave magnets, arXiv:2309.01607.
- R. Yamada, M. T. Birch, P. R. Baral, S. Okumura, R. Nakano, S. Gao, Y. Ishihara, K. K. Kolincio, I. Belopolski, H. Sagayama, H. Nakao, K. Ohishi, T. Nakajima, Y. Tokura, T.-H. Arima, Y. Motome, M. M. Hirschmann, and M. Hirschberger, Gapping the spin-nodal planes of an anisotropic p-wave magnet to induce a large anomalous Hall effect, arXiv:2502.10386.
- M. Ezawa, Topological insulators based on -wave altermagnets; Electrical control and detection of the altermagnetic domain wall, Phys. Rev. B 110, 165429 (2024).
- M. Ezawa, Purely electrical detection of the Néel vector of p-wave magnets based on linear and nonlinear conductivities, arXiv:2410.21854.
- M. Ezawa, Out-of-plane Edelstein effects: Electric-field induced magnetization in p-wave magnets, Phys. Rev. B 111, L161301 (2025).
- L. Šmejkal, A. H. MacDonald, J. Sinova, S. Nakatsuji and T. Jungwirth, Anomalous Hall antiferromagnets, Nat. Rev. Mater. 7, 482 (2022).
- L. Šmejkal, J. Sinova, and T. Jungwirth, Emerging research landscape of altermagnetism, Phys. Rev. X 12, 040501 (2022).
- D. Zhu, Z.-Y. Zhuang, Z. Wu, and Z. Yan, Topological superconductivity in two-dimensional altermagnetic metals, Phys. Rev. B 108, 184505 (2023).
- C. Sun, J. Linder, Spin pumping from a ferromagnetic insulator into an altermagnet, Phys. Rev. B 108, L140408 (2023).
- G. S. Diniz and E. Vernek, Suppressed Kondo screening in two-dimensional altermagnets, Phys. Rev. B 109, 155127 (2024).
- P. Rao, A. Mook, and J. Knolle, Tunable band topology and optical conductivity in altermagnets, Phys. Rev. B 110, 024425 (2024).
- M. Amundsen, A. Brataas, and J. Linder, RKKY interaction in Rashba altermagnets, Phys. Rev. B 110, 054427 (2024).
- M. Ezawa, Third-order and fifth-order nonlinear spin-current generation in g-wave and i-wave altermagnets and perfect spin-current diode based on f-wave magnets, Phys. Rev. B 111, 125420 (2025).
- S. Okumura, T. Morimoto, Y. Kato, and Y. Motome, Quadratic optical responses in a chiral magnet, Phys. Rev. B 104, L180407 (2021).
- B. Brekke, P. Sukhachov, H. G. Giil, A. Brataas, and J. Linder, Minimal models and transport properties of unconventional p-wave magnets, Phys. Rev. Lett. 133, 236703 (2024).
- A. Chakraborty, A. B. Hellenes, R. Jaeschke-Ubiergo, T. Jungwirth, L. Šmejkal, J. Sinova, Highly Efficient Non-relativistic Edelstein effect in p-wave magnets, arXiv:2411.16378.
- J. Nitta, T. Akazaki, and H. Takayanagi, T. Enoki, Gate control of spin-orbit interaction in an inverted InGaAs/InAs heterostructure, Phys. Rev. Lett. 78, 1335 (1997).
- J. P. Provost and G. Vallee, Riemannian structure on manifolds of quantum states, Commun. Math. Phys. 76, 289 (1980).
- Y.-Q. Ma, S. Chen, H. Fan, and W.-M. Liu, Abelian and non-Abelian quantum geometric tensor, Phys. Rev. B 81, 245129 (2010).
- S. Matsuura and S. Ryu, Momentum space metric, nonlocal operator, and topological insulators, Phys. Rev. B 82, 245113 (2010).
- G. von Gersdorff and W. Chen, Measurement of topological order based on metric-curvature correspondence, Phys. Rev. B 104, 195133 (2021).
- W.-Y. Hsiang and D.-H. Lee, Chern-Simons invariant in the Berry phase of a Hamiltonians, Phys. Rev. A 64, 052101 (2001).
- D. Sticlet, F. Piechon, J.-N. Fuchs, P. Kalugin, and P. Simon, Geometrical engineering of a two-band Chern insulator in two dimensions with arbitrary topological index, Phys. Rev. B 85, 165456 (2012).
- C.-M. Jian, Z.-C. Gu, and X.-L. Qi, Momentum-space instantons and maximally localized flat-band topological Hamiltonians, Phys. Rapid Res. Lett. 7, 154 (2013).
- T. Jungwirth, X. Marti, P. Wadley and J. Wunderlich, Antiferromagnetic spintronics, Nat. Nanotechnol. 11, 231 (2016).
- V. Baltz, A. Manchon, M. Tsoi, T. Moriyama, T. Ono, and Y. Tserkovnyak Antiferromagnetic spintronics, Rev. Mod. Phys. 90, 015005 (2018).
- J. Han, R. Cheng, L. Liu, H. Ohno, and S. Fukami, Coherent antiferromagnetic spintronics, Nat. Mater. 22, 684 (2023).
- Z. Ni, A. V. Haglund, H. Wang, B. Xu, C. Bernhard, D. G. Mandrus, X. Qian, E. J. Mele, C. L. Kane and L. Wu, Imaging the Néel vector switching in the monolayer antiferromagnet MnPSe3 with strain-controlled Ising order, Nat. Nanotechnol. 16, 782 (2021).
- J. Godinho, H. Reichlov, D. Kriegner, V. Novak, K. Olejnik, Z. Kašpar, Z. Šoban, P. Wadley, R. P. Campion, R. M. Otxoa, P. E. Roy, J. Železnny, T. Jungwirth and J. Wunderlich, Electrically induced and detected Néel vector reversal in a collinear antiferromagnet, Nat. Commun. 9, 4686 (2018).
- K. Kimura, Y. Otake, and T. Kimura, Visualizing rotation and reversal of the Néel vector through antiferromagnetic trichroism, Nat. Commun. 13, 697 (2022).
- Y.-H. Zhang, T.-C. Chuang, D. Qu, and S.-Y. Huang, Detection and manipulation of the antiferromagnetic Néel vector in , Phys. Rev. B 105, 094442 (2022).