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Phonon spectrum in the spin-Peierls phase of
Phys. Rev. B 112, 184302 – Published 5 November, 2025
DOI: https://doi.org/10.1103/jz36-8kz9
Abstract
has long been studied as a prototypical example of the spin-Peierls transition in a Heisenberg chain. Despite intensive investigation of this quasi-one-dimensional material, systematic measurements and calculations of the phonon excitations in the dimerized phase have not to date been possible, leaving certain aspects of the spin-Peierls phenomenon unresolved. We perform state-of-the-art density functional theory (DFT) calculations to compute the electronic structure and phonon dynamics in the low-temperature dimerized phase. We also perform high-resolution neutron spectroscopy to measure the full phonon spectrum over multiple Brillouin zones. We find excellent agreement between our numerical and experimental results that extend to all measurement temperatures. Notable features of our phonon spectra include a number of steeply dispersive modes, nonmonotonic dispersion features, and specific phonon anticrossings, which we relate to the mode eigenvectors. By calculating the magnetic interactions within DFT and studying the effects of different phonon modes on the superexchange paths, we discuss the possibility of observing spin-phonon hybridization effects in experiments performed both in and out of equilibrium.
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References (95)
- R. E. Peierls, Quantum Theory of Solids (Oxford University Press, Oxford, UK, 1956), p. 108.
- H. M. McConnell, D. Pooley, and A. Bradbury, The paramagnetic resonance of Wurster's blue perchlorate, Proc. Natl. Acad. Sci. USA 48, 1480 (1962).
- D. D. Thomas, H. Keller, and H. M. McConnell, Exciton magnetic resonance in Wurster's blue perchlorate, J. Chem. Phys. 39, 2321 (1963).
- I. S. Jacobs, J. W. Bray, H. R. Hart, Jr., L. V. Interrante, J. S. Kasper, G. D. Watkins, D. E. Prober, and J. C. Bonner, Spin-Peierls transitions in magnetic donor-acceptor compounds of tetrathiafulvalene (TTF) with bisdithiolene metal complexes, Phys. Rev. B 14, 3036 (1976).
- M. Hase, I. Terasaki, and K. Uchinokura, Observation of the spin-Peierls transition in linear (spin-1/2) chains in an inorganic compound , Phys. Rev. Lett. 70, 3651 (1993).
- J. E. Lorenzo, K. Hirota, G. Shirane, J. M. Tranquada, M. Hase, K. Uchinokura, H. Kojima, I. Tanaka, and Y. Shibuya, Soft longitudinal modes in spin-singlet , Phys. Rev. B 50, 1278 (1994).
- K. Hirota, D. E. Cox, J. E. Lorenzo, G. Shirane, J. M. Tranquada, M. Hase, K. Uchinokura, H. Kojima, Y. Shibuya, and I. Tanaka, Dimerization of in the spin-Peierls state, Phys. Rev. Lett. 73, 736 (1994).
- J. P. Pouget, L. P. Regnault, M. Ain, B. Hennion, J. P. Renard, P. Veillet, G. Dhalenne, and A. Revcolevschi, Structural evidence for a spin Peierls ground state in the quasi-one-dimensional compound , Phys. Rev. Lett. 72, 4037 (1994).
- K. Hirota, G. Shirane, Q. J. Harris, Q. Feng, R. J. Birgeneau, M. Hase, and K. Uchinokura, Characterization of the structural and magnetic fluctuations near the spin-Peierls transition in , Phys. Rev. B 52, 15412 (1995).
- S. Sahling, J. C. Lasjaunias, P. Monceau, and A. Revcolevschi, Heat capacity of the spin-Peierls compound , Solid State Commun. 92, 423 (1994).
- H. Takahashi, N. Môri, O. Fujita, J. Akimitsu, and T. Matsumoto, Effect of pressure on the magnetic susceptibility in spin-Peierls cuprate, , Solid State Commun. 95, 817 (1995).
- X. Liu, J. Wosnitza, H. von Löhneysen, and R. K. Kremer, Specific heat analysis of the spin-Peierls transition in , Phys. Rev. Lett. 75, 771 (1995).
- M. Poirier, M. Castonguay, A. Revcolevschi, and G. Dhalenne, Magnetoelastic coupling and order parameter in the spin-Peierls system , Phys. Rev. B 52, 16058 (1995).
- M. Hase, I. Terasaki, K. Uchinokura, M. Tokunaga, N. Miura, and H. Obara, Magnetic phase diagram of the spin-Peierls cuprate , Phys. Rev. B 48, 9616 (1993).
- H. Hori, M. Furusawa, T. Takeuchi, S. Sugai, K. Kindo, and A. Yamagishi, Magnetic measurements of by means of high magnetic field, J. Phys. Soc. Jpn. 63, 18 (1994).
- M. Udagawa, H. Aoki, N. Ogita, O. Fujita, A. Sohma, A. Ogihara, and J. Akimitsu, Raman scattering of , J. Phys. Soc. Jpn. 63, 4060 (1994).
- M. Nishi, O. Fujita, and J. Akimitsu, Neutron-scattering study on the spin-Peierls transition in a quasi-one-dimensional magnet , Phys. Rev. B 50, 6508 (1994).
- H. Kuroe, T. Sekine, M. Hase, Y. Sasago, K. Uchinokura, H. Kojima, I. Tanaka, and Y. Shibuya, Raman-scattering study of in the spin-Peierls phase, Phys. Rev. B 50, 16468 (1994).
- I. Terasaki, R. Itti, N. Koshizuka, M. Hase, I. Tsukada, and K. Uchinokura, Spectroscopic study of the electronic states of single-crystal , Phys. Rev. B 52, 295 (1995).
- Z. V. Popović, S. D. Dević, V. N. Popov, G. Dhalenne, and A. Revcolevschi, Phonons in studied using polarized far-infrared and Raman-scattering spectroscopies, Phys. Rev. B 52, 4185 (1995).
- I. Loa, S. Gronemeyer, C. Thomsen, and R. K. Kremer, Spin gap and spin-phonon interaction in , Solid State Commun. 99, 231 (1996).
- M. Braden, G. Wilkendorf, J. Lorenzana, M. Aïn, G. J. McIntyre, M. Behruzi, G. Heger, G. Dhalenne, and A. Revcolevschi, Structural analysis of : Relation between nuclear structure and magnetic interaction, Phys. Rev. B 54, 1105 (1996).
- M. Braden, B. Hennion, W. Reichardt, G. Dhalenne, and A. Revcolevschi, Spin-phonon coupling in , Phys. Rev. Lett. 80, 3634 (1998).
- M. Braden, W. Reichardt, B. Hennion, G. Dhalenne, and A. Revcolevschi, Lattice dynamics of : Inelastic neutron scattering and model calculations, Phys. Rev. B 66, 214417 (2002).
- A. Damascelli, D. van der Marel, F. Parmigiani, G. Dhalenne, and A. Revcolevschi, Infrared signatures of the spin-Peierls transition in , Phys. Rev. B 56, R11373 (1997).
- M. N. Popova, A. B. Sushkov, S. A. Golubchik, A. N. Vasil'ev, and L. I. Leonyuk, Folded modes in the infrared spectra of the spin-Peierls phase of , Phys. Rev. B 57, 5040 (1998).
- K. Takehana, T. Takamasu, M. Hase, G. Kido, and K. Uchinokura, Far-infrared spectroscopy in the spin-Peierls compound under high magnetic fields, Phys. Rev. B 62, 5191 (2000).
- L. P. Regnault, M. Aïn, B. Hennion, G. Dhalenne, and A. Revcolevschi, Inelastic neutron scattering investigation of the spin-Peierls system , Phys. Rev. B 53, 5579 (1996).
- M. Arai, M. Fujita, M. Motokawa, J. Akimitsu, and S. M. Bennington, Quantum spin excitations in the spin-Peierls system , Phys. Rev. Lett. 77, 3649 (1996).
- V. N. Muthukumar, C. Gros, W. Wenzel, R. Valentí, P. Lemmens, B. Eisener, G. Güntherodt, M. Weiden, C. Geibel, and F. Steglich, Frustration-induced Raman scattering in , Phys. Rev. B 54, R9635 (1996).
- E. Pytte, Peierls instability in Heisenberg chains, Phys. Rev. B 10, 4637 (1974).
- M. C. Cross and D. S. Fisher, A new theory of the spin-Peierls transition with special relevance to the experiments on TTFCuBDT, Phys. Rev. B 19, 402 (1979).
- G. Castilla, S. Chakravarty, and V. J. Emery, Quantum magnetism of , Phys. Rev. Lett. 75, 1823 (1995).
- J. Riera and A. Dobry, Magnetic susceptibility in the spin-Peierls system , Phys. Rev. B 51, 16098 (1995).
- V. N. Muthukumar, C. Gros, R. Valentí, M. Weiden, C. Geibel, F. Steglich, P. Lemmens, M. Fischer, and G. Güntherodt, Model revisited: Phenomenology of , Phys. Rev. B 55, 5944 (1997).
- G. S. Uhrig, Symmetry and dimension of the dispersion of inorganic spin-Peierls systems, Phys. Rev. Lett. 79, 163 (1997).
- C. Knetter and G. S. Uhrig, Triplet dispersion in : Perturbative analysis, Phys. Rev. B 63, 094401 (2001).
- C. Gros and R. Werner, Dynamics of the Peierls-active phonon modes in , Phys. Rev. B 58, R14677 (1998).
- R. Werner, C. Gros, and M. Braden, Microscopic spin-phonon coupling constants in , Phys. Rev. B 59, 14356 (1999).
- S. Feldkemper and W. Weber, Superexchange via cluster states: Calculation of spin-phonon coupling constants for , Phys. Rev. B 62, 3816 (2000).
- L. F. Mattheiss, Band picture of the spin-Peierls transition in the spin-1/2 linear-chain cuprate , Phys. Rev. B 49, 14050 (1994).
- Z. S. Popović, F. R. Vukajlović, and Ž. V. Šljivančanin, Band structure of spin-Peierls cuprate , J. Phys.: Condens. Matter 7, 4549 (1995).
- V. I. Anisimov, F. Aryasetiawan, and A. I. Lichtenstein, First-principles calculations of the electronic structure and spectra of strongly correlated systems: The LDA + method, J. Phys.: Condens. Matter 9, 767 (1997).
- S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys, and A. P. Sutton, Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA + study, Phys. Rev. B 57, 1505 (1998).
- Ž. V. Šljivančanin, Z. S. Popović, and F. R. Vukajlović, Band picture of the spin-Peierls cuprate , Phys. Rev. B 56, 4432 (1997).
- H. Wu, M.-C. Qian, and Q.-Q. Zheng, Insulating band structure of , J. Phys.: Condens. Matter 11, 209 (1999).
- Y. Nisikawa, M. Usuda, and A. Oguri, Electronic structure of in the spin-Peierls phase: Calculation within the LDA and scheme, J. Magn. Magn. Mater. 310, 1632 (2007).
- A. Filippetti and V. Fiorentini, Magnetic ordering under strain and spin-Peierls dimerization in , Phys. Rev. Lett. 98, 196403 (2007).
- A. Marciniak, S. Marcantoni, F. Giusti, F. Glerean, G. Sparapassi, T. Nova, A. Cartella, S. Latini, F. Valiera, A. Rubio, J. van den Brink, F. Benatti, and D. Fausti, Vibrational coherent control of localized electronic excitation, Nat. Phys. 17, 368 (2021).
- T. Tohyama, Y. Mizuno, S. Maekawa, C. Kim, and Z.-X. Shen, Electronic states and effective Hamiltonian of , Phys. B (Amsterdam, Neth.) 237-238, 135 (1997).
- X. C. Zhang, A. Shkurinov, and Y. Zhang, Extreme terahertz science, Nat. Photon. 11, 16 (2017).
- P. Salén, M. Basini, S. Bonetti, J. Hebling, M. Krasilnikov, A. Y. Nikitin, G. Shamuilov, Z. Tibai, V. Zhaunerchyk, and V. Goryashko, Matter manipulation with extreme terahertz light: Progress in the enabling THz technology, Phys. Rep. 836-837, 1 (2019).
- A. de la Torre, D. M. Kennes, M. Claassen, S. Gerber, J. W. McIver, and M. A. Sentef, Nonthermal pathways to ultrafast control in quantum materials, Rev. Mod. Phys. 93, 041002 (2021).
- M. Först, C. Manzoni, S. Kaiser, Y. Tomioka, Y. Tokura, R. Merlin, and A. Cavalleri, Nonlinear phononics as an ultrafast route to lattice control, Nat. Phys. 7, 854 (2011).
- A. Subedi, A. Cavalleri, and A. Georges, Theory of nonlinear phononics for coherent light control of solids, Phys. Rev. B 89, 220301(R) (2014).
- D. M. Juraschek, M. Fechner, and N. A. Spaldin, Ultrafast structure switching through nonlinear phononics, Phys. Rev. Lett. 118, 054101 (2017).
- T. Kampfrath, A. Sell, G. Klatt, A. Pashkin, S. Mährlein, T. Dekorsy, M. Wolf, M. Fiebig, A. Leitenstorfer, and R. Huber, Coherent terahertz control of antiferromagnetic spin waves, Nat. Photon. 5, 31 (2011).
- R. V. Mikhaylovskiy, E. Hendry, A. Secchi, J. H. Mentink, M. Eckstein, A. Wu, R. V. Pisarev, V. V. Kruglyak, M. I. Katsnelson, T. Rasing, and A. V. Kimel, Ultrafast optical modification of exchange interactions in iron oxides, Nat. Commun. 6, 8190 (2015).
- M. Först, A. D. Caviglia, R. Scherwitzl, R. Mankowsky, P. Zubko, V. Khanna, H. Bromberger, S. B. Wilkins, Y.-D. Chuang, W. S. Lee, W. F. Schlotter, J. J. Turner, G. L. Dakovski, M. P. Minitti, J. Robinson, S. R. Clark, D. Jaksch, J.-M. Triscone, J. P. Hill, S. S. Dhesi, and A. Cavalleri, Spatially resolved ultrafast magnetic dynamics initiated at a complex oxide heterointerface, Nat. Mater. 14, 883 (2015).
- M. Fechner, A. Sukhov, L. Chotorlishvili, C. Kenel, J. Berakdar, and N. A. Spaldin, Magnetophononics: Ultrafast spin control through the lattice, Phys. Rev. Mater. 2, 064401 (2018).
- A. S. Disa, M. Fechner, T. F. Nova, B. Liu, M. Först, D. Prabhakaran, P. G. Radaelli, and A. Cavalleri, Polarizing an antiferromagnet by optical engineering of the crystal field, Nat. Phys. 16, 937 (2020).
- D. Afanasiev, J. R. Hortensius, B. A. Ivanov, A. Sasani, E. Bousquet, Y. M. Blanter, R. V. Mikhaylovskiy, A. V. Kimel, and A. D. Caviglia, Ultrafast control of magnetic interactions via light-driven phonons, Nat. Mater. 20, 607 (2021).
- F. Giorgianni, B. Wehinger, S. Allenspach, N. Colonna, C. Vicario, P. Puphal, E. Pomjakushina, B. Normand, and Ch. Rüegg, Ultrafast frustration breaking and magnetophononic driving of singlet excitations in a quantum magnet, Phys. Rev. B 107, 184440 (2023).
- M. Yarmohammadi, M. Krebs, G. S. Uhrig, and B. Normand, Strong-coupling magnetophononics: Self-blocking, phonon-bitriplons, and spin-band engineering, Phys. Rev. B 107, 174415 (2023).
- The materials project, , https://next-gen.materialsproject.org/materials/mp-21344.
- T. Giamarchi, Quantum Physics in One Dimension (Clarendon Press, Oxford, 2004).
- G. Kresse and J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B 47, 558 (1993).
- J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
- P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
- G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
- S. Grimme, J. Antony, S. Ehrlich, and H. Krieg, A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu, J. Chem. Phys. 132, 154104 (2010).
- S. Grimme, S. Ehrlich, and L. Goerigk, Effect of the damping function in dispersion corrected density functional theory, J. Comput. Chem. 32, 1456 (2011).
- A. Togo, L. Chaput, T. Tadano, and I. Tanaka, Implementation strategies in phonopy and phono3py, J. Phys.: Condens. Matter 35, 353001 (2023).
- A. Togo, First-principles phonon calculations with phonopy and phono3py, J. Phys. Soc. Jpn. 92, 012001 (2023).
- S. Zagoulaev and I. I. Tupitsyn, Electronic structure and magnetic properties of the spin-Peierls compound , Phys. Rev. B 55, 13528 (1997).
- In the data repository L. Spitz, A. Razpopov, S. Biswas, Calculated phonon spectrum and superexchange interactions in the dimerized phase of CuGeO3, Zenodo (2025), doi:10.5281/zenodo.15768088, we have gathered the full phonon dispersion and eigenvector information from our DFT calculations, including the input files to reproduce these, a comparison table of measured and calculated phonon frequencies, and the input files for and results from our TEMA calculations of the superexchange interactions.
- L. Pisani and R. Valentí, Ab initio phonon calculations for the layered compound TiOCl, Phys. Rev. B 71, 180409(R) (2005).
- L. Pisani, R. Valentí, B. Montanari, and N. M. Harrison, Density functional study of the electronic and vibrational properties of TiOCl, Phys. Rev. B 76, 235126 (2007).
- R. Fair, A. Jackson, D. Voneshen, D. Jochym, D. Le, K. Refson, and T. Perring, Euphonic: Inelastic neutron scattering simulations from force constants and visualization tools for phonon properties, J. Appl. Crystallogr. 55, 1689 (2022).
- J. K. Glasbrenner, I. I. Mazin, H. O. Jeschke, P. J. Hirschfeld, R. M. Fernandes, and R. Valentí, Effect of magnetic frustration on nematicity and superconductivity in iron chalcogenides, Nat. Phys. 11, 953 (2015).
- J. S. Zhang, Y. Xie, X. Q. Liu, A. Razpopov, V. Borisov, C. Wang, J. P. Sun, Y. Cui, J. C. Wang, X. Ren, H. Deng, X. Yin, Y. Ding, Y. Li, J. G. Cheng, J. Feng, R. Valentí, B. Normand, and W. Yu, Giant pressure-enhancement of multiferroicity in , Phys. Rev. Res. 2, 013144 (2020).
- A. Razpopov, D. A. S. Kaib, S. Backes, L. Balents, S. D. Wilson, F. Ferrari, K. Riedl, and R. Valentí, A Kitaev material on the triangular lattice: The case of , npj Quantum Mater. 8, 36 (2023).
- K. Koepernik and H. Eschrig, Full-potential nonorthogonal local-orbital minimum-basis band-structure scheme, Phys. Rev. B 59, 1743 (1999).
- E. R. Ylvisaker, W. E. Pickett, and K. Koepernik, Anisotropy and magnetism in the method, Phys. Rev. B 79, 035103 (2009).
- R. Kajimoto, M. Nakamura, Y. Inamura, F. Mizuno, K. Nakajima, S. Ohira-Kawamura, T. Yokoo, T. Nakatani, R. Maruyama, K. Soyama, K. Shibata, K. Suzuya, S. Sato, K. Aizawa, M. Arai, S. Wakimoto, M. Ishikado, S. Shamoto, M. Fujita, H. Hiraka, K. Ohoyama, K. Yamada, and C.-H. Lee, The Fermi chopper spectrometer 4SEASONS at J-PARC, J. Phys. Soc. Jpn. 80, SB025 (2011).
- M. Nakamura, R. Kajimoto, Y. Inamura, F. Mizuno, M. Fujita, T. Yokoo, and M. Arai, First demonstration of novel method for inelastic neutron scattering measurement utilizing multiple incident energies, J. Phys. Soc. Jpn. 78, 093002 (2009).
- Y. Inamura, T. Nakatani, J. Suzuki, and T. Otomo, Development status of software “Utsusemi” for chopper spectrometers at MLF, J-PARC, J. Phys. Soc. Jpn. 82, SA031 (2013).
- R. A. Ewings, A. Buts, M. D. Le, J. van Duijn, I. Bustinduy, and T. G. Perring, HORACE: Software for the analysis of data from single crystal spectroscopy experiments at time-of-flight neutron instruments, Nucl. Instrum. Methods Phys. Res. Sect. A 834, 132 (2016).
- B. Demazure, M. Krebs, G. S. Uhrig, and B. Normand, Pulsed magnetophononics in gapped quantum magnets, Phys. Rev. B 112, 075112 (2025).
- F. Aryasetiawan, M. Imada, A. Georges, G. Kotliar, S. Biermann, and A. I. Lichtenstein, Frequency-dependent local interactions and low-energy effective models from electronic structure calculations, Phys. Rev. B 70, 195104 (2004).
- C. Honerkamp, H. Shinaoka, F. F. Assaad, and P. Werner, Limitations of constrained random phase approximation downfolding, Phys. Rev. B 98, 235151 (2018).
- R. Tesch and P. M. Kowalski, Hubbard parameters for transition metals from first principles, Phys. Rev. B 105, 195153 (2022).
- K. Ikeuchi, R. Kajimoto, F. Mizuno, M. Fujita, Y. Inamura, M. Nakamura, K. Nakajima, K. Aizawa, and M. Arai, Anisotropic spin excitations in spin-Peierls , J. Korean Phys. Soc. 63, 333 (2013).
- A. Liu, Multidimensional terahertz probes of quantum materials, npj Quantum Mater. 10, 18 (2025).
- E. A. Mashkovich, K. A. Grishunin, R. M. Dubrovin, A. K. Zvezdin, R. V. Pisarev, and A. V. Kimel, Terahertz light-driven coupling of antiferromagnetic spins to lattice, Science 374, 1608 (2021).