- Open Access
Destabilization of local magnetic anisotropy in heavy-fermion compounds
Phys. Rev. Research 7, 043225 – Published 1 December, 2025
DOI: https://doi.org/10.1103/7zsl-4497
Abstract
The local magnetic anisotropy of a typical crystalline compound is usually attributed to the combined effect of crystal electric fields and spin-orbit coupling. We show that this simple local picture is transformed in heavy-fermion compounds by the development of coherent electron scattering from local spin degrees of freedom. Provided the dominance of the coherence energy scale over the magnetic energy scale is strong enough, the fractionalization and delocalization of the spins destabilizes their single-ion anisotropy by generating an opposing anisotropy in the exchange. Experimentally, this can manifest as competing splittings in the Curie-Weiss constants and effective moments. We show that in the presence of orthorhombic or tetragonal symmetry, the destabilization of the anisotropy can result in either ferromagnetic or antiferromagnetic order that is perpendicular to the high-temperature easy axis. In the absence of destabilization, we show that the order is more likely to be antiferromagnetic. In agreement with our theory, we also observe that the temperature at which the anisotropy of the uniform magnetic response changes tracks the coherence energy scale in a wide range of actinide and lanthanide compounds.
Physics Subject Headings (PhySH)
Article Text
References (56)
- W. Knafo, M. Nardone, M. Vališka, A. Zitouni, G. Lapertot, D. Aoki, G. Knebel, and D. Braithwaite, Comparison of two superconducting phases induced by a magnetic field in , Commun. Phys. 4, 40 (2021).
- S. K. Lewin, C. E. Frank, S. Ran, J. Paglione, and N. P. Butch, A review of at high magnetic fields, Rep. Prog. Phys. 86, 114501 (2023).
- D. Aoki, J.-P. Brison, J. Flouquet, K. Ishida, G. Knebel, Y. Tokunaga, and Y. Yanase, Unconventional superconductivity in , J. Phys.: Condens. Matter 34, 243002 (2022).
- D. Aoki, K. Ishida, and J. Flouquet, Review of U-based ferromagnetic superconductors: Comparison between , and , J. Phys. Soc. Jpn. 88, 022001 (2019).
- A. Miyake, Y. Shimizu, Y. J. Sato, D. Li, A. Nakamura, Y. Homma, F. Honda, J. Flouquet, M. Tokunaga, and D. Aoki, Metamagnetic transition in heavy fermion superconductor , J. Phys. Soc. Jpn. 88, 063706 (2019).
- Y.-f. Yang, Z. Fisk, H.-O. Lee, J. D. Thompson, and D. Pines, Scaling the Kondo lattice, Nature (London) 454, 611 (2008).
- G. Lonzarich, D. Pines, and Y.-F. Yang, Toward a new microscopic framework for Kondo lattice materials, Rep. Prog. Phys. 80, 024501 (2017).
- X. Ji, X. Luo, Q. Chen, W. Feng, Q. Hao, Q. Liu, Y. Zhang, Y. Liu, X. Wang, S. Tan, and X. Lai, Direct observation of coexisting Kondo hybridization and antiferromagnetic state in , Phys. Rev. B 106, 125120 (2022).
- Y.-f. Yang, Two-fluid model for heavy electron physics, Rep. Prog. Phys. 79, 074501 (2016).
- A. Gleis, S.-S. B. Lee, G. Kotliar, and J. von Delft, Emergent properties of the periodic Anderson model: A high-resolution, real-frequency study of heavy-fermion quantum criticality, Phys. Rev. X 14, 041036 (2024).
- M. Raczkowski and F. F. Assaad, Phase diagram and dynamics of the symmetric Kondo lattice model, Phys. Rev. Res. 2, 013276 (2020).
- N. B. Perkins, M. D. Núñez Regueiro, B. Coqblin, and J. R. Iglesias, Underscreened Kondo lattice model applied to heavy fermion uranium compounds, Phys. Rev. B 76, 125101 (2007).
- D. Hafner, B. K. Rai, J. Banda, K. Kliemt, C. Krellner, J. Sichelschmidt, E. Morosan, C. Geibel, and M. Brando, Kondo-lattice ferromagnets and their peculiar order along the magnetically hard axis determined by the crystalline electric field, Phys. Rev. B 99, 201109 (2019).
- Y. Ōnuki, M. Hedo, and F. Honda, Unique electronic states of -based compounds, J. Phys. Soc. Jpn. 89, 102001 (2020).
- E. C. Andrade, M. Brando, C. Geibel, and M. Vojta, Competing orders, competing anisotropies, and multicriticality: The case of co-doped , Phys. Rev. B 90, 075138 (2014).
- H. Jin, R. R. Ullah, P. Klavins, and V. Taufour, Importance of anisotropic interactions for hard-axis or hard-plane ordering of Ce-based ferromagnets, Phys. Rev. B 112, 024437 (2025).
- D. Li, A. Nakamura, F. Honda, Y. Sato, Y. Homma, Y. Shimizu, J. Ishizuka, Y. Yanase, G. Knebel, J. Flouquet, and D. Aoki, Magnetic properties under pressure in novel spin-triplet superconductor , J. Phys. Soc. Jpn. 90, 073703 (2021).
- D. Hovančík, A. Koriki, A. c. v. Bendová, P. Doležal, P. Proschek, M. Míšek, M. Reiffers, J. Prokleška, J. c. v. Pospíšil, and V. Sechovský, Alloying-driven transition between ferromagnetism and antiferromagnetism in UTGe compounds: , Phys. Rev. B 105, 014436 (2022).
- J. Pospíšil, Y. Haga, S. Kambe, Y. Tokunaga, N. Tateiwa, D. Aoki, F. Honda, A. Nakamura, Y. Homma, E. Yamamoto, and T. Yamamura, Switching of magnetic ground states across the alloy system, Phys. Rev. B 95, 155138 (2017).
- W. Iha, T. Yara, Y. Ashitomi, M. Kakihana, T. Takeuchi, F. Honda, A. Nakamura, D. Aoki, J. Gouchi, Y. Uwatoko, T. Kida, T. Tahara, M. Hagiwara, Y. Haga, M. Hedo, T. Nakama, and Y. Ōnuki, Electronic states in based on the Doniach phase diagram, J. Phys. Soc. Jpn. 87, 064706 (2018).
- M. Szlawska, M. Majewicz, D. Kowalska, and D. Kaczorowski, Metamagnetic transition in single-crystalline , Sci. Rep. 13, 14772 (2023).
- Y. Hiranaka, A. Nakamura, M. Hedo, T. Takeuchi, A. Mori, Y. Hirose, K. Mitamura, K. Sugiyama, M. Hagiwara, T. Nakama, and Y. Ōnuki, Heavy fermion state based on the Kondo effect in , J. Phys. Soc. Jpn. 82, 083708 (2013).
- N. Huy and A. de Visser, Ferromagnetic order in U(Rh, Co)Ge, Solid State Commun. 149, 703 (2009).
- M. O. Ajeesh, J. D. Thompson, E. D. Bauer, F. Ronning, S. M. Thomas, and P. F. S. Rosa, Hydrostatic pressure studies on non-superconducting , J. Phys. Soc. Jpn. 93, 055001 (2024).
- D. Aoki, A. Nakamura, F. Honda, D. Li, Y. Homma, Y. Shimizu, Y. J. Sato, G. Knebel, J.-P. Brison, A. Pourret, D. Braithwaite, G. Lapertot, Q. Niu, M. Vališka, H. Harima, and J. Flouquet, Unconventional superconductivity in heavy fermion , J. Phys. Soc. Jpn. 88, 043702 (2019).
- R. Troć, R. Wawryk, W. Miiller, H. Misiorek, and M. Samsel-Czekała, Bulk properties of the UCoGe Kondo-like system, Philos. Mag. 90, 2249 (2010).
- K. Prokeš, H. Nakotte, V. Sechovský, M. Mihalik, and A. Andreev, On the magnetic structure of UIrGe, Phys. B: Condens. Matter 350, E199 (2004).
- A. Huxley, E. Ressouche, B. Grenier, D. Aoki, J. Flouquet, and C. Pfleiderer, The co-existence of superconductivity and ferromagnetism in actinide compounds, J. Phys.: Condens. Matter 15, S1945 (2003).
- K. S. Nemkovski, D. P. Kozlenko, P. A. Alekseev, J.-M. Mignot, A. P. Menushenkov, A. A. Yaroslavtsev, E. S. Clementyev, A. S. Ivanov, S. Rols, B. Klobes, R. P. Hermann, and A. V. Gribanov, Europium mixed-valence, long-range magnetic order, and dynamic magnetic response in , Phys. Rev. B 94, 195101 (2016).
- Z. Hossain, C. Geibel, N. Senthilkumaran, M. Deppe, M. Baenitz, F. Schiller, and S. L. Molodtsov, Antiferromagnetism, valence fluctuation, and heavy-fermion behavior in , Phys. Rev. B 69, 014422 (2004).
- M. Bleckmann, A. Otop, S. Süllow, R. Feyerherm, J. Klenke, A. Loose, R. Hendrikx, J. Mydosh, and H. Amitsuka, Structural properties, magnetic order and electronic transport in single crystalline , J. Magn. Magn. Mater. 322, 2447 (2010).
- H. Amitsuka, T. Sakakibara, K. Sugiyama, T. Ikeda, Y. Miyako, M. Date, and A. Yamagishi, High field magnetism of single crystals, Phys. B: Condens. Matter 177, 173 (1992).
- J. Valenta, F. Honda, M. Vališka, P. Opletal, J. Kaštil, M. Míšek, M. Diviš, L. Sandratskii, J. Prchal, and V. Sechovský, Antiferromagnetism and phase transitions in noncentrosymmetric , Phys. Rev. B 97, 144423 (2018).
- F. Honda, J. Valenta, J. Prokleška, J. Pospíšil, P. Proschek, J. Prchal, and V. Sechovský, Magnetotransport as a probe of phase transformations in metallic antiferromagnets: The case of , Phys. Rev. B 100, 014401 (2019).
- C. Krellner, S. Lausberg, A. Steppke, M. Brando, L. Pedrero, H. Pfau, S. Tencé, H. Rosner, F. Steglich, and C. Geibel, Ferromagnetic quantum criticality in the quasi-one-dimensional heavy fermion metal , New J. Phys. 13, 103014 (2011).
- A. Steppke, R. Küchler, S. Lausberg, E. Lengyel, L. Steinke, R. Borth, T. Lühmann, C. Krellner, M. Nicklas, C. Geibel, F. Steglich, and M. Brando, Ferromagnetic quantum critical point in the heavy-fermion metal , Science 339, 933 (2013).
- C. Krellner and C. Geibel, Single crystal growth and anisotropy of CeRuPO, J. Cryst. Growth 310, 1875 (2008).
- C. Krellner, N. S. Kini, E. M. Brüning, K. Koch, H. Rosner, M. Nicklas, M. Baenitz, and C. Geibel, CeRuPO: A rare example of a ferromagnetic Kondo lattice, Phys. Rev. B 76, 104418 (2007).
- C. Krellner, T. Förster, H. Jeevan, C. Geibel, and J. Sichelschmidt, Relevance of ferromagnetic correlations for the electron spin resonance in Kondo lattice systems, Phys. Rev. Lett. 100, 066401 (2008).
- S. Lausberg, A. Hannaske, A. Steppke, L. Steinke, T. Gruner, L. Pedrero, C. Krellner, C. Klingner, M. Brando, C. Geibel, and F. Steglich, Doped : Not only ferromagnetic correlations but ferromagnetic order, Phys. Rev. Lett. 110, 256402 (2013).
- C. Klingner, C. Krellner, M. Brando, C. Geibel, F. Steglich, D. V. Vyalikh, K. Kummer, S. Danzenbächer, S. L. Molodtsov, C. Laubschat, T. Kinoshita, Y. Kato, and T. Muro, Evolution of magnetism in , Phys. Rev. B 83, 144405 (2011).
- T. Gruner, J. Sichelschmidt, C. Klingner, C. Krellner, C. Geibel, and F. Steglich, Electron spin resonance of the moment in , Phys. Rev. B 85, 035119 (2012).
- S. Ikeda, T. D. Matsuda, A. Galatanu, E. Yamamoto, Y. Haga, and Y. Ōnuki, Single crystal growth and magnetic property of , J. Magn. Magn. Mater. 272-276, 62 (2004).
- D. Kaczorowski, R. Kruk, J. P. Sanchez, B. Malaman, and F. Wastin, Magnetic and electronic properties of ternary uranium antimonides , Phys. Rev. B 58, 9227 (1998).
- T. D. Matsuda, S. Ikeda, E. Yamamoto, Y. Haga, and Y. Ōnuki, Magnetic property of a single crystal , J. Phys. Soc. Jpn. 76, 074708 (2007).
- I. Giannakis, J. Leshen, M. Kavai, S. Ran, C.-J. Kang, S. R. Saha, Y. Zhao, Z. Xu, J. W. Lynn, L. Miao, L. A. Wray, G. Kotliar, N. P. Butch, and P. Aynajian, Orbital-selective Kondo lattice and enigmatic electrons emerging from inside the antiferromagnetic phase of a heavy fermion, Sci. Adv. 5, eaaw9061 (2019).
- B. K. Rai, M. Stavinoha, J. Banda, D. Hafner, K. A. Benavides, D. A. Sokolov, J. Y. Chan, M. Brando, C.-L. Huang, and E. Morosan, Ferromagnetic ordering along the hard axis in the Kondo lattice , Phys. Rev. B 99, 121109 (2019).
- W.-H. Ko, H.-C. Jiang, J. G. Rau, and L. Balents, Ordering and criticality in an underscreened Kondo chain, Phys. Rev. B 87, 205107 (2013).
- We take it to be equal to the difference between the energy of the ground state and the Fermi gas state.
- H. D. J. Keen, Coupling of crystal, Electronic, and Magnetic Structures in Quantum Materials (The University of Edinburgh, Edinburgh, UK, 2021).
- D. S. Christovam, M. Sundermann, A. Marino, D. Takegami, J. Falke, P. Dolmantas, M. Harder, H. Gretarsson, B. Keimer, A. Gloskovskii, M. W. Haverkort, I. Elfimov, G. Zwicknagl, A. V. Andreev, L. Havela, M. M. Bordelon, E. D. Bauer, P. F. S. Rosa, A. Severing, and L. H. Tjeng, Stabilization of U configuration in through U dimers in the presence of chains, Phys. Rev. Res. 6, 033299 (2024).
- S. Doniach, The Kondo lattice and weak antiferromagnetism, Physica B+C 91, 231 (1977).
- K. Umeo, H. Yamane, H. Kubo, Y. Muro, F. Nakamura, T. Suzuki, T. Takabatake, K. Sengupta, M. K. Forthaus, and M. M. Abd-Elmeguid, Interplay between crystal electric field and magnetic exchange anisotropies in the heavy-fermion antiferromagnet YbRhSb under pressure, Phys. Rev. B 85, 024412 (2012).
- S. Hamann, J. Zhang, D. Jang, A. Hannaske, L. Steinke, S. Lausberg, L. Pedrero, C. Klingner, M. Baenitz, F. Steglich, C. Krellner, C. Geibel, and M. Brando, Evolution from ferromagnetism to antiferromagnetism in , Phys. Rev. Lett. 122, 077202 (2019).
- M. Kanász-Nagy, Y. Ashida, T. Shi, C. P. Moca, T. N. Ikeda, S. Fölling, J. I. Cirac, G. Zaránd, and E. A. Demler, Exploring the anisotropic Kondo model in and out of equilibrium with alkaline-earth atoms, Phys. Rev. B 97, 155156 (2018).
- M. P. Kwasigroch, H. Hu, F. Krüger, and A. G. Green, Magnetic hard-direction ordering in anisotropic Kondo systems, Phys. Rev. B 105, 224418 (2022).