- Open Access
Magnetic field dependence of the spin fluctuations in
Phys. Rev. B 113, 045154 – Published 28 January, 2026
DOI: https://doi.org/10.1103/bjgt-p16s
Abstract
Quantum phase transitions are among the most intriguing phenomena that can occur when the electronic ground state of correlated metals are tuned by external parameters such as pressure, magnetic field, or chemical substitution. Such transitions between distinct states of matter are driven by quantum fluctuations, and can give rise to macroscopically coherent phases that are at the forefront of condensed matter research. However, the nature of the critical fluctuations, and thus the fundamental physics controlling many quantum phase transitions, remain poorly understood in numerous strongly correlated metals. Here we study the model material to gain insight into the implications of critical fluctuations originating from different regions in reciprocal space. By employing an external magnetic field along the crystallographic and axis as auxiliary tuning parameter, we observe a pronounced anisotropy in the suppression of the quantum critical fluctuations, reflecting the spin anisotropy of the long-range ordered ground state at larger silver concentration. Coupled with the temperature dependence of the quantum fluctuations, these results suggest that the quantum phase transition in is driven by three-dimensional spin-density wave fluctuations.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (61)
- M. Vojta, Frustration and quantum criticality, Rep. Prog. Phys. 81, 064501 (2018).
- L. Savary and L. Balents, Quantum spin liquids: A review, Rep. Prog. Phys. 80, 016502 (2017).
- M. R. Norman, The challenge of unconventional superconductivity, Science 332, 196 (2011).
- A. Narayan, A. Cano, A. V. Balatsky, and N. A. Spaldin, Multiferroic quantum criticality, Nat. Mater. 18, 223 (2019).
- K. G. Wilson and J. Kogut, The renormalization group and the expansion, Phys. Rep. 12, 75 (1974).
- S. Sachdev, Quantum Phase Transitions, 2nd ed. (Cambridge University Press, Cambridge, UK, 2011).
- Y. Tokiwa, C. Stingl, M.-S. Kim, T. Takabatake, and P. Gegenwart, Characteristic signatures of quantum criticality driven by geometrical frustration, Sci. Adv. 1, e1500001 (2015).
- V. K. Anand, D. T. Adroja, A. D. Hillier, K. Shigetoh, T. Takabatake, J.-G. Park, K. A. McEwen, J. H. Pixley, and Q. Si, Zero-field ambient-pressure quantum criticality in the stoichiometric non-Fermi liquid system CeRhBi, J. Phys. Soc. Jpn. 87, 064708 (2018).
- D. K. Singh, A. Thamizhavel, J. W. Lynn, S. Dhar, J. Rodriguez-Rivera, and T. Herman, Field-induced quantum fluctuations in the heavy fermion superconductor , Sci. Rep. 1, 117 (2011).
- V. H. Tran, A. D. Hillier, D. T. Adroja, and D. Kaczorowski, Antiferromagnetic spin fluctuations in the heavy-fermion superconductor , Phys. Rev. B 86, 094525 (2012).
- W. Knafo, S. Raymond, P. Lejay, and J. Flouquet, Antiferromagnetic criticality at a heavy-fermion quantum phase transition, Nat. Phys. 5, 753 (2009).
- J. A. Hertz, Quantum critical phenomena, Phys. Rev. B 14, 1165 (1976).
- A. J. Millis, Effect of a nonzero temperature on quantum critical points in itinerant fermion systems, Phys. Rev. B 48, 7183 (1993).
- T. Moriya and T. Takimoto, Anomalous properties around magnetic instability in heavy electron systems, J. Phys. Soc. Jpn. 64, 960 (1995).
- Q. Si, S. Rabello, K. Ingersent, and J. L. Smith, Locally critical quantum phase transitions in strongly correlated metals, Nature (London) 413, 804 (2001).
- Q. Si and S. Paschen, Quantum phase transitions in heavy fermion metals and kondo insulators, physica Status Solidi (B) 250, 425 (2013).
- S. Sachdev, Universal relaxational dynamics near two-dimensional quantum critical points, Phys. Rev. B 59, 14054 (1999).
- T. R. Kirkpatrick and D. Belitz, Exponent relations at quantum phase transitions with applications to metallic quantum ferromagnets, Phys. Rev. B 91, 214407 (2015).
- A. Schröder, G. Aeppli, E. Bucher, R. Ramazashvili, and P. Coleman, Scaling of magnetic fluctuations near a quantum phase transition, Phys. Rev. Lett. 80, 5623 (1998).
- A. Schröder, G. Aeppli, R. Coldea, M. Adams, O. Stockert, H.v. Löhneysen, E. Bucher, R. Ramazashvili, and P. Coleman, Onset of antiferromagnetism in heavy-fermion metals, Nature (London) 407, 351 (2000).
- H.v. Löhneysen, O. Stockert, and M. Enderle, Magnetic fluctuations at the field-tuned vs. concentration-tuned quantum phase transition in , J. Magn. Magn. Mater. 310, 822 (2007), proceedings of the 17th International Conference on Magnetism.
- J.-G. Park, D. T. Adroja, K. A. McEwen, and A. P. Murani, Non-Fermi liquid behavior in the dynamic susceptibility of Ce()Sb, J. Phys.: Condens. Matter 14, 3865 (2002).
- M. C. Aronson, R. Osborn, R. A. Robinson, J. W. Lynn, R. Chau, C. L. Seaman, and M. B. Maple, Non-Fermi-liquid scaling of the magnetic response in , Phys. Rev. Lett. 75, 725 (1995).
- C. Stock, C. Broholm, F. Demmel, J. Van Duijn, J. W. Taylor, H. J. Kang, R. Hu, and C. Petrovic, From incommensurate correlations to mesoscopic spin resonance in , Phys. Rev. Lett. 109, 127201 (2012).
- M. A. 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. Kondo, Resistance minimum in dilute magnetic alloys, Prog. Theor. Phys. 32, 37 (1964),.
- H. Wang, T. B. Park, J. Kim, H. Jang, E. D. Bauer, J. D. Thompson, and T. Park, Evidence for charge delocalization crossover in the quantum critical superconductor , Nat. Commun. 14, 7341 (2023).
- P. Coleman and A. J. Schofield, Quantum criticality, Nature (London) 433, 226 (2005).
- S. Paschen and Q. Si, Quantum phases driven by strong correlations, Nat. Rev. Phys. 3, 9 (2021).
- L. Poudel, J. M. Lawrence, L. S. Wu, G. Ehlers, Y. Qiu, A. F. May, F. Ronning, M. D. Lumsden, D. Mandrus, and A. D. Christianson, Multicomponent fluctuation spectrum at the quantum critical point in , npj Quantum Mater. 4, 52 (2019).
- O. Stockert, M. Enderle, and H. v. Löhneysen, Magnetic fluctuations at a field-induced quantum phase transition, Phys. Rev. Lett. 99, 237203 (2007).
- J. Rossat-Mignod, L. P. Regnault, J. L. Jacoud, C. Vettier, P. Lejay, J. Flouquet, E. Walker, D. Jaccard, and A. Amato, Inelastic neutron scattering study of cerium heavy fermion compounds, J. Magn. Magn. Mater. 76-77, 376 (1988).
- L. Poudel, C. de la Cruz, E. A. Payzant, A. F. May, M. Koehler, V. O. Garlea, A. E. Taylor, D. S. Parker, H. B. Cao, M. A. McGuire, W. Tian, M. Matsuda, H. Jeen, H. N. Lee, T. Hong, S. Calder, H. D. Zhou, M. D. Lumsden, V. Keppens, D. Mandrus, et al., Structural and magnetic phase transitions in , Phys. Rev. B 92, 214421 (2015).
- A. Amato, D. Jaccard, J. Flouquet, F. Lapierre, J. L. Tholence, R. A. Fisher, S. E. Lacy, J. A. Olsen, and N. E. Phillips, Thermodynamic and transport properties of , J. Low Temp. Phys. 68, 371 (1987).
- H. G. Schlager, A. Schröder, M. Welsch, and H. v. Löhneysen, Magnetic ordering in single crystals: Thermodynamic and transport properties, J. Low Temp. Phys. 90, 181 (1993).
- E.-W. Scheidt, D. Maurer, A. Weber, T. Götzfried, K. Heuser, S. Kehrein, and R. Tidecks, Quantum phase transitions: Experimental facts—a challenge for theory, Phys. B: Condens. Matter 321, 133 (2002), Proceedings of the Second Regional Conference on Magnetic and Superconducting Materials.
- R. I. Bewley, J. W. Taylor, and S. M. Bennington, LET, a cold neutron multi-disk chopper spectrometer at ISIS, Nucl. Instrum. Methods Phys. Res. Sect. A 637, 128 (2011).
- J. Lass, H. Jacobsen, K. M. L. Krighaar, D. Graf, F. Groitl, F. Herzog, M. Yamada, C. Kägi, R. A. Müller, R. Bürge, M. Schild, M. S. Lehmann, A. Bollhalder, P. Keller, M. Bartkowiak, U. Filges, U. Greuter, G. Theidel, H. M. Rønnow, Ch. Niedermayer, et al., Commissioning of the novel continuous angle multi-energy analysis spectrometer at the Paul Scherrer Institut, Rev. Sci. Instrum. 94, 023302 (2023),.
- J. Lass, H. Jacobsen, D. G. Mazzone, and K. Lefmann, MJOLNIR: A software package for multiplexing neutron spectrometers, SoftwareX 12, 100600 (2020).
- A. Furrer, J. Mesot, and T. Strässle, Neutron Scattering in Condensed Matter Physics (World Scientific, 5 Toh Tuck Link, Singapore, 2009).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/bjgt-p16s for more detailed results and additional information on the data analysis, which also includes Refs. [59, 60, 61].
- M. T. Glossop and K. Ingersent, Magnetic quantum phase transition in an anisotropic Kondo lattice, Phys. Rev. Lett. 99, 227203 (2007).
- D. R. Grempel and Q. Si, Locally critical point in an anisotropic Kondo lattice, Phys. Rev. Lett. 91, 026401 (2003).
- J.-X. Zhu, S. Kirchner, R. Bulla, and Q. Si, Zero-temperature magnetic transition in an easy-axis Kondo lattice model, Phys. Rev. Lett. 99, 227204 (2007).
- K. Heuser, J. S. Kim, E. W. Scheidt, T. Schreiner, and G. R. Stewart, Inducement of non-Fermi-liquid behavior with magnetic field in heavy-fermion antiferromagnets, Phys. B: Condens. Matter 259-261, 392 (1999).
- R. Küchler, P. Gegenwart, K. Heuser, E.-W. Scheidt, G. R. Stewart, and F. Steglich, Grüneisen ratio divergence at the quantum critical point in , Phys. Rev. Lett. 93, 096402 (2004).
- H. v. Löhneysen, Fermi-liquid instability at magnetic–nonmagnetic quantum phase transitions, J. Magn. Magn. Mater. 200, 532 (1999).
- U. Witte, O. Stockert, R. Schedler, L. P. Regnault, and M. Loewenhaupt, Crystalline electric field excitations in studied by single crystal measurements with polarized neutrons, Phys. B: Condens. Matter 397, 20 (2007).
- E. A. Goremychkin and R. Osborn, Neutron-spectroscopy study of the heavy-fermion compound , Phys. Rev. B 47, 14580 (1993).
- S. Chapman, M. Hunt, P. Meeson, P. H. P. Reinders, M. Springford, and M. Norman, Heavy quasiparticles in studied using magnetic quantum oscillations, J. Phys.: Condens. Matter 2, 8123 (1990).
- H. Harima and A. Yanase, Fermi surfaces of and , J. Magn. Magn. Mater. 108, 145 (1992).
- P. Coleman and A. H. Nevidomskyy, Frustration and the Kondo effect in heavy fermion materials, J. Low Temp. Phys. 161, 182 (2010).
- H. Zhao, J. Zhang, M. Lyu, S. Bachus, Y. Tokiwa, P. Gegenwart, S. Zhang, J. Cheng, Y.-f. Yang, G. Chen, Y. Isikawa, Q. Si, F. Steglich, and P. Sun, Quantum-critical phase from frustrated magnetism in a strongly correlated metal, Nat. Phys. 15, 1261 (2019).
- Y. Tokiwa, M. Garst, P. Gegenwart, S. L. Bud'ko, and P. C. Canfield, Quantum bicriticality in the heavy-fermion metamagnet YbAgGe, Phys. Rev. Lett. 111, 116401 (2013).
- D. G. Mazzone, M. Janoschek, C. Balz, Ch. Niedermayer, and X. Boraley, Understanding multicomponent quantum criticality in , STFC ISIS Neutron and Muon Source, doi:10.5286/ISIS.E.RB2210367.
- X. Boraley, A. Christianson, J. Lass, C. Balz, M. Bartkowiak, Ch. Niedermayer, J. M. Lawrence, L. Poudel, D. Mandrus, F. Ronning, M. Janoschek, and D. G. Mazzone, Data for “Magnetic field dependence of critical fluctuations in ”, Zenodo (2025), doi: 10.5281/zenodo.16939914.
- W. Knafo and S. Raymond, Artificial scaling laws of the dynamical magnetic susceptibility in heavy-fermion systems, Phys. Lett. A 341, 251 (2005).
- O. Arnold, J. C. Bilheux, J. M. Borreguero, A. Buts, S. I. Campbell, L. Chapon, M. Doucet, N. Draper, R. Ferraz Leal, M. A. Gigg, V. E. Lynch, A. Markvardsen, D. J. Mikkelson, R. L. Mikkelson, R. Miller, K. Palmen, P. Parker, G. Passos, T. G. Perring, R. F. Peterson, et al., Mantid—data analysis and visualization package for neutron scattering and experiments, Nucl. Instrum. Methods Phys. Res. Sect. A 764, 156 (2014).
- 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).