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Magnetoelastic properties in the high-temperature magnetic phase of the skyrmion compound
Phys. Rev. B 113, 134416 – Published 9 April, 2026
DOI: https://doi.org/10.1103/ht3d-1kj8
Abstract
We investigated the magnetoelastic properties of a single crystal under a magnetic field applied along the crystallographic [001] and [110] directions. We report a series of strong anomalies in the sound velocity that is consistent with the complex phase diagram reported previously for this compound. In particular, in our study we focus on the recently identified magnetic phase in the high-temperature region. We show that while this phase is easily destroyed for magnetic fields applied along [001], it is rather stable for fields along [110]. Furthermore, we introduce a Landau theory and a microscopic toy model describing the elastic response at zero field. We reproduce qualitatively the observed anomalies for different acoustic modes, which suggest that the high-temperature phase weakly breaks the symmetry between the [100] and [010] directions. We discuss candidate magnetic structures consistent with this high-temperature phase, based on the comparison of elastic anomalies for a few different magnetic states.
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References (36)
- M. Brando, D. Belitz, F. M. Grosche, and T. R. Kirkpatrick, Metallic quantum ferromagnets, Rev. Mod. Phys. 88, 025006 (2016).
- A. Szilva, Y. Kvashnin, E. A Stepanov, L. Nordström, O. Eriksson, A. I Lichtenstein, and M. I. Katsnelson, Quantitative theory of magnetic interactions in solids, Rev. Mod. Phys. 95, 035004 (2023).
- M. Ruderman and C. Kittel, Indirect exchange coupling of nuclear magnetic moments by conduction electrons, Phys. Rev. 96, 99 (1954).
- T. Kasuya, A theory of metallic ferro-and antiferromagnetism on Zener's model, Prog. Theor. Phys. 16, 45 (1956).
- K. Yosida, Magnetic properties of Cu-Mn alloys, Phys. Rev. 106, 893 (1957).
- J. Jensen and A. Mackintosh, Rare-Earth Magnetism: Structures and Excitations (Oxford University Press, New York, 1991).
- S. Hayami and Y. Motome, Topological spin crystals by itinerant frustration, J. Phys.: Condens. Matter 33, 443001 (2021).
- S. Muhlbauer, B. Binz, F. Jonietz, C. Pfleiderer, A. Rosch, A. Neubauer, R. Georgii, and P. Boni, Skyrmion lattice in a chiral magnet, Science 323, 915 (2009).
- S. Hayami and Y. Motome, Multiple- instability by -dimensional connections of Fermi surfaces, Phys. Rev. B 90, 060402(R) (2014).
- S. Hayami, R. Ozawa, and Y. Motome, Effective bilinear-biquadratic model for noncoplanar ordering in itinerant magnets, Phys. Rev. B 95, 224424 (2017).
- Y. Akagi and Y. Motome, Spin chirality ordering and anomalous Hall effect in the ferromagnetic Kondo lattice model on a triangular lattice, J. Phys. Soc. Jpn. 79, 083711 (2010).
- T. Kurumaji, T. Nakajima, M. Hirschberger, A. Kikkawa, Y. Yamasaki, H. Sagayama, H. Nakao, Y. Taguchi, T. Arima, and Y. Tokura, Skyrmion lattice with a giant topological Hall effect in a frustrated triangular-lattice magnet, Science 365, 914 (2019).
- T. Nomoto, T. Koretsune, and R. Arita, Formation mechanism of the helical structure in Gd-based skyrmion materials, Phys. Rev. Lett. 125, 117204 (2020).
- N. Matsuyama, T. Nomura, S. Imajo, T. Nomoto, R. Arita, K. Sudo, M. Kimata, N. D. Khanh, R. Takagi, Y. Tokura, S. Seki, K. Kindo, and Y. Kohama, Quantum oscillations in the centrosymmetric skyrmion-hosting magnet , Phys. Rev. B 107, 104421 (2023).
- A. Garnier, D. Gignoux, N. Iwata, D. Schmitt, T. Shigeoka, and F. Zhang, Anisotropic metamagnetism in , J. Magn. Magn. Mater. 140-144, 899 (1995).
- A. Garnier, D. Gignoux, D. Schmitt, and T. Shigeoka, Giant magnetic anisotropy in tetragonal and , Phys. B (Amsterdam, Neth.) 222, 80 (1996).
- M. Ślaski, A. Szytuła, J. Leciejewicz, and A. Zygmunt, Magnetic properties of (RE=Pr, Nd, Gd, Tb, Dy, Er) interm etallics, J. Magn. Magn. Mater. 46, 114 (1984).
- N. Khanh, T. Nakajima, X. Yu, S. Gao, K. Shibata, M. Hirschberger, Y. Yamasaki, H. Sagayama, H. Nakao, L. Peng, et al., Nanometric square skyrmion lattice in a centrosymmetric tetragonal magnet, Nat. Nanotechnol. 15, 444 (2020).
- G. D. A. Wood, D. D. Khalyavin, D. A. Mayoh, J. Bouaziz, A. E. Hall, S. J. R. Holt, F. Orlandi, P. Manuel, S. Blügel, J. B. Staunton, O. A. Petrenko, M. R. Lees, and G. Balakrishnan, Double- ground state with topological charge stripes in the centrosymmetric skyrmion candidate , Phys. Rev. B 107, L180402 (2023).
- L. Gries, T. Kleinbeck, D. A. Mayoh, G. D. A. Wood, G. Balakrishnan, and R. Klingeler, Uniaxial pressure effects, phase diagram, and tricritical point in the centrosymmetric skyrmion lattice magnet , Phys. Rev. B. 111, 064419 (2025).
- B. Lüthi, Physical Acoustics in the Solid State (Springer, Berlin, Heidelberg, 2006), Vol. 148.
- A. Hauspurg, S. Zherlitsyn, T. Helm, V. Felea, J. Wosnitza, V. Tsurkan, K.-Y. Choi, S.-H. Do, M. Ye, W. Brenig, and N. B. Perkins, Fractionalized excitations probed by ultrasound, Phys. Rev. B 109, 144415 (2024).
- J. Prokleška, J. Vejpravová, and V. Sechovský, Magnetostriction measurement of single crystal, J. Phys.: Conf. Ser. 51, 127 (2006).
- N. Khanh, T. Nakajima, S. Hayami, S. Gao, Y. Yamasaki, H. Sagayama, H. Nakao, R. Takagi, Y. Motome, Y. Tokura, et al., Zoology of multiple- spin textures in a centrosymmetric tetragonal magnet with itinerant electrons, Adv. Sci. 9, 2105452 (2022).
- J. Paddison, J. Bouaziz, A. May, Q. Zhang, S. Calder, D. Abernathy, J. Staunton, S. Blügel, and A. Christianson, Spin dynamics of the centrosymmetric skyrmion material , Cell Rep. Phys. Sci. 5, 102280 (2024).
- J. N. Reimers, A. J. Berlinsky, and A.-C. Shi, Mean-field approach to magnetic ordering in highly frustrated pyrochlores, Phys. Rev. B 43, 865 (1991).
- T. Okubo, S. Chung, and H. Kawamura, Multiple- states and the skyrmion lattice of the triangular-lattice heisenberg antiferromagnet under magnetic fields, Phys. Rev. Lett. 108, 017206 (2012).
- G. Quirion, X. Han, and M. L. Plumer, Magnetoelastic coupling within a landau model of phase transitions: Application to the frustrated triangular antiferromagnet , Phys. Rev. B 84, 014408 (2011).
- J. Bouaziz, E. Mendive-Tapia, S. Blügel, and J. B. Staunton, Fermi-surface origin of skyrmion lattices in centrosymmetric rare-earth intermetallics, Phys. Rev. Lett. 128, 157206 (2022).
- S. Eremeev, D. Glazkova, G. Poelchen, A. Kraiker, K. Ali, A. Tarasov, S. Schulz, K. Kliemt, E. Chulkov, V. Stolyarov, et al., Insight into the electronic structure of the centrosymmetric skyrmion magnet , Nano. Adv. 5, 6678 (2023).
- H. Weber and M. Vojta, Heavy-fermion metals with hybridization nodes: Unconventional Fermi liquids and competing phases, Phys. Rev. B 77, 125118 (2008).
- J. Sourd, S. Tencé, E. Gaudin, and S. Burdin, Nonlocal Kondo coupling and selective doping from cerium electrons in iron-based superconductors, Phys. Rev. B 109, 045117 (2024).
- I. Eremin, P. Thalmeier, P. Fulde, R. K. Kremer, K. Ahn, and A. Simon, Large magnetoresistance and critical spin fluctuations in , Phys. Rev. B 64, 064425 (2001).
- A. Abanov, A. Chubukov, and J. Schmalian, Quantum-critical theory of the spin-fermion model and its application to cuprates: Normal state analysis, Adv. Phys. 52, 119 (2003).
- G. Wood, J. Stewart, D. Mayoh, J. Paddison, J. Bouaziz, S. Tobin, O. Petrenko, M. Lees, P. Manuel, J. Staunton, et al., A magnon band analysis of in the field-polarized state, npj Quantum Mater. 10, 39 (2025).
- Y. Yasui, C. Butler, N. Khanh, S. Hayami, T. Nomoto, T. Hanaguri, Y. Motome, R. Arita, T. Arima, Y. Tokura, et al., Imaging the coupling between itinerant electrons and localised moments in the centrosymmetric skyrmion magnet , Nat. Commun. 11, 5925 (2020).