When magnetic order is suppressed by frustrated interactions, spins form a highly correlated fluctuating ‘spin liquid’ state down to low temperatures. The magnetic order of local moments can also be suppressed when they are fully screened by conduction electrons through the Kondo effect. Thus, the combination of strong geometrical frustration and Kondo screening may lead to novel types of quantum phase transition. We report low-temperature thermodynamic measurements on the frustrated Kondo lattice Pr2Ir2O7, which exhibits a chiral spin liquid state below 1.5 K as a result of the frustrated interaction between Ising 4f local moments and their interplay with Ir conduction electrons. Our results provide a first clear example of zero-field quantum critical scaling that emerges in a spin liquid state of a highly frustrated metal.
Si, Q. Global magnetic phase diagram and local quantum criticality in heavy fermion metals. Physica B 378–380, 23–27 (2006).
Vojta, M. From itinerant to local-moment antiferromagnetism in Kondo lattices: Adiabatic continuity versus quantum phase transitions. Phys. Rev. B 78, 125109 (2008).
Custers, J. et al. Evidence for a non-Fermi-liquid phase in Ge-substituted Y bRh2Si2 . Phys. Rev. Lett. 104, 186402 (2010).
Coleman, P., Pepin, C., Si, Q. & Ramazashvili, R. How do Fermi liquids get heavy and die? J. Phys. Condens. Matter 13, R723–R738 (2001).
Si, Q., Rabello, S., Ingersent, K. & Smith, J. L. Locally critical quantum phase transitions in strongly correlated metals. Nature 413, 804–808 (2001).
Paschen, S. et al. Hall-effect evolution across a heavy-fermion quantum critical point. Nature 432, 881–885 (2004).
Senthil, T., Sachdev, S. & Vojta, M. Fractionalized Fermi liquids. Phys. Rev. Lett. 90, 216403 (2003).
Si, Q. & Paschen, S. Quantum phase transitions in heavy fermion metals and Kondo insulators. Phys. Status Solidi B 250, 425–438 (2013).
Nakatsuji, S. et al. Metallic spin-liquid behaviour of the geometrically frustrated Kondo lattice Pr2Ir2O7 . Phys. Rev. Lett. 96, 087204 (2006).
Machida, Y., Nakatsuji, S., Onoda, S., Tayama, T. & Sakakibara, T. Time-reversal symmetry breaking and spontaneous Hall effect without magnetic dipole order. Nature 463, 210–213 (2010).
Ritz, R. et al. Formation of a topological non-Fermi liquid in MnSi. Nature 497, 231–234 (2013).
Ramirez, A. P., Hayashi, A., Cava, R. J., Siddharthan, R. & Shastry, B. S. Zero-point entropy in ’spin ice’. Nature 399, 333–335 (1999).
Bramwell, S. T. et al. Spin correlations in Ho2Ti2O7: A dipolar spin ice system. Phys. Rev. Lett. 87, 047205 (2001).
Kimura, K. et al. Quantum fluctuations in spin-ice-like Pr2Zn2O7 . Nature Commun. 4, 1934 (2013).
Pomaranski, D. et al. Absence of Pauling’s residual entropy in thermally equilibrated Dy2Ti2O7 . Nature Phys. 9, 353–356 (2013).
Flint, R. & Senthil, T. Chiral RKKY interaction in Pr2Ir2O7 . Phys. Rev. B 87, 125147 (2013).
Lee, S., Paramekanti, A. & Kim, Y. B. RKKY interactions and the anomalous Hall effect in metallic rare-earth pyrochlores. Phys. Rev. Lett. 111, 196601 (2013).
Onoda, S. & Tanaka, Y. Quantum melting of spin ice: emergent cooperative quadrupole and chirality. Phys. Rev. Lett. 105, 047201 (2010).
Zhu, L., Garst, M., Rosch, A. & Si, Q. Universally diverging Grüneisen parameter and the magnetocaloric effect close to quantum critical points. Phys. Rev. Lett. 91, 066404 (2003).
Tokiwa, Y., Radu, T., Geibel, C., Steglich, F. & Gegenwart, P. Divergence of the magnetic Grüneisen ratio at the field-induced quantum critical point in Y bRh2Si2 . Phys. Rev. Lett. 102, 066401 (2009).
Gegenwart, P., Weickert, F., Garst, M., Perry, R. S. & Maeno, Y. Metamagnetic quantum criticality in Sr3Ru2O7 studied by thermal expansion. Phys. Rev. Lett. 96, 136402 (2006).
Schroeder, A. et al. Onset of antiferromagnetism in heavy-fermion metals. Nature 407, 351– 355 (2000).
Custers, J. et al. The break-up of heavy electrons at a quantum critical point. Nature 424, 524– 527 (2003).
Hiroi, Z., Matsuhira, K., Takagi, S., Tayama, T. & Sakakibara, T. Specific heat of kagomé ice in the pyrochlore oxide Dy2Ti2O7 . J. Phys. Soc. Jpn 72, 411–418 (2003).
Tokiwa, Y., Bauer, E. D. & Gegenwart, P. Zero-field quantum critical point in CeCoIn5 . Phys. Rev. Lett. 111, 107003 (2013).
Moon, E-G., Cenke, X., Kim, Y. B. & Balents, L. Non-Fermi-liquid and topological states with strong spin–orbit coupling. Phys. Rev. Lett. 111, 206401 (2013).
Mathur, N. D. et al. Magnetically mediated superconductivity in heavy fermion compounds. Nature 394, 39–43 (1998).
Borzi, R. A. et al. Formation of a nematic fluid at high fields in Sr3Ru2O7 . Science 315, 214–217 (2007).
Millican, J. N. et al. Crystal growth and structure of R2Ir2O7 (R = Pr, Eu) using molten KF. Mater. Res. Bull. 42, 928–934 (2007).
Tokiwa, Y. & Gegenwart, P. High-resolution alternating-field technique to determine the magnetocaloric effect of metals down to very low temperatures. Rev. Sci. Instrum. 82, 013905 (2011).
The authors acknowledge discussions with L. Balents, M. Brando, J.G. Donath, M. Garst, Yong-Baek Kim, K. Kimura, Q. Si, C. Stingl, M. Vojta and K. Winzer. This work has been supported by the German Science Foundation through FOR 960 (Quantum phase transitions), the Helmholtz Virtual Institute VH521, and by Grants-in-Aid for Scientific Research (No. 25707030) from JSPS, and by PRESTO of JST. The use of the Materials Design and Characterization Laboratory at ISSP is gratefully acknowledged. This work was supported also in part by the National Science Foundation under Grant No. PHYS-1066293 and the hospitality of the Aspen Center for Physics.
The authors declare no competing financial interests.
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Tokiwa, Y., Ishikawa, J., Nakatsuji, S. et al. Quantum criticality in a metallic spin liquid. Nature Mater 13, 356–359 (2014). https://doi.org/10.1038/nmat3900
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