A quantum spin liquid is a state of matter where unpaired electrons’ spins, although entangled, do not show magnetic order even at the zero temperature. The realization of a quantum spin liquid is a long-sought goal in condensed-matter physics. Although neutron scattering experiments on the two-dimensional spin-1/2 kagome lattice ZnCu3(OD)6Cl2 and triangular lattice YbMgGaO4 have found evidence for the hallmark of a quantum spin liquid at very low temperature (a continuum of magnetic excitations), the presence of magnetic and non-magnetic site chemical disorder complicates the interpretation of the data. Recently, the three-dimensional Ce3+ pyrochlore lattice Ce2Sn2O7 has been suggested as a clean, effective spin-1/2 quantum spin liquid candidate, but evidence of a spin excitation continuum is still missing. Here, we use thermodynamic, muon spin relaxation and neutron scattering experiments on single crystals of Ce2Zr2O7, a compound isostructural to Ce2Sn2O7, to demonstrate the absence of magnetic ordering and the presence of a spin excitation continuum at 35 mK. With no evidence of oxygen deficiency and magnetic/non-magnetic ion disorder seen by neutron diffraction and diffuse scattering measurements, Ce2Zr2O7 may be a three-dimensional pyrochlore lattice quantum spin liquid material with minimum magnetic and non-magnetic chemical disorder.
Access optionsAccess options
Subscribe to Journal
Get full journal access for 1 year
only $17.92 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
The data that support the plots in this paper and other findings of this study are available from the corresponding author on reasonable request.
Anderson, P. W. Resonating valence bonds: a new kind of insulator? Mater. Res. Bull. 8, 153–160 (1973).
Anderson, P. W. The resonating valence bond state in La2CuO4 and superconductivity. Science 235, 1196–1198 (1987).
Lee, P. A., Nagaosa, N. & Wen, X. G. Doping a Mott insulator: physics of high-temperature superconductivity. Rev. Mod. Phys. 78, 17–85 (2006).
Kitaev, A. Y. Fault-tolerant quantum computation by anyons. Ann. Phys. 303, 2–30 (2003).
Kitaev, A. Anyons in an exactly solved model and beyond. Ann. Phys. 321, 2–111 (2006).
Balents, L. Spin liquids in frustrated magnets. Nature 464, 199–208 (2010).
Gardner, J. S., Gingras, M. J. P. & Greedan, J. E. Magnetic pyrochlore oxides. Rev. Mod. Phys. 82, 53–107 (2010).
Zhou, Y., Kanoda, K. & Ng, T.-K. Quantum spin liquid states. Rev. Mod. Phys. 89, 025003 (2017).
Savary, L. & Balents, L. Quantum spin liquids: a review. Rep. Prog. Phys. 80, 016502 (2017).
Hallas, A. M., Gaudet, J. & Gaulin, B. D. Experimental insights into ground-state selection of quantum XY pyrochlores. Annu. Rev. Condens. Matter Phys. 9, 105–124 (2018).
Tennant, D. A., Perring, T. G., Cowley, R. A. & Nagler, S. E. Unbound spinons in the S=1/2 antiferromagnetic chain KCuF3. Phys. Rev. Lett. 70, 4003–4006 (1993).
Shimizu, Y., Miyagawa, K., Kanoda, K., Maesato, M. & Saito, G. Spin liquid state in an organic Mott insulator with a triangular lattice. Phys. Rev. Lett. 91, 107001 (2003).
Itou, T., Oyamada, A., Maegawa, S., Tamura, M. & Kato, R. Quantum spin liquid in the spin-1∕2 triangular antiferromagnet EtMe3Sb[Pd(dmit)2]2. Phys. Rev. B 77, 104413 (2008).
Han, T. H. et al. Fractionalized excitations in the spin-liquid state of a kagome-lattice antiferromagnet. Nature 492, 406–410 (2012).
Norman, M. R. Colloquium: Herbertsmithite and the search for the quantum spin liquid. Rev. Mod. Phys. 88, 041002 (2016).
Shen, Y. et al. Evidence for a spinon Fermi surface in a triangular-lattice quantum-spin-liquid candidate. Nature 540, 559–562 (2016).
Paddison, J. A. M. et al. Continuous excitations of the triangular-lattice quantum spin liquid YbMgGaO4. Nat. Phys. 13, 117 (2016).
Freedman, D. E. et al. Site specific X-ray anomalous dispersion of the geometrically frustrated kagomé magnet, herbertsmithite, ZnCu3(OH)6Cl2. J. Am. Chem. Soc. 132, 16185–16190 (2010).
Li, Y. et al. Gapless quantum spin liquid ground state in the two-dimensional spin-1/2 triangular antiferromagnet YbMgGaO4. Sci. Rep. 5, 16419 (2015).
Ma, Z. et al. Spin-glass ground state in a triangular-lattice compound YbZnGaO4. Phys. Rev. Lett. 120, 087201 (2018).
Zhu, Z., Maksimov, P. A., White, S. R. & Chernyshev, A. L. Topography of spin liquids on a triangular lattice. Phys. Rev. Lett. 120, 207203 (2018).
Kimchi, I., Nahum, A. & Senthil, T. Valence bonds in random quantum magnets: theory and application to YbMgGaO4. Phys. Rev. X 8, 031028 (2018).
Liu, L., Shao, H., Lin, Y.-C., Guo, W. & Sandvik, A. W. Random-singlet phase in disordered two-dimensional quantum magnets. Phys. Rev. X 8, 041040 (2018).
Li, Y.-D., Lu, Y.-M. & Chen, G. Spinon Fermi surface U(1) spin liquid in the spin–orbit-coupled triangular-lattice Mott insulator YbMgGaO4. Phys. Rev. B 96, 054445 (2017).
Balz, C. et al. Physical realization of a quantum spin liquid based on a complex frustration mechanism. Nat. Phys. 12, 942–949 (2016).
Chillal, S. et al. A quantum spin liquid based on a new three-dimensional lattice. Preprint at https://arxiv.org/abs/1712.07942 (2017).
Plumb, K. W. et al. Continuum of quantum fluctuations in a three-dimensional S=1 Heisenberg magnet. Nat. Phys. 15, 54–59 (2019).
Bramwell, S. T. et al. Spin correlations in Ho2Ti2O7: a dipolar spin ice system. Phys. Rev. Lett. 87, 047205 (2001).
Castelnovo, C., Moessner, R. & Sondhi, S. L. Spin ice, fractionalization, and topological order. Annu. Rev. Condens. Matter Phys. 3, 35–55 (2012).
Gingras, M. J. P. & McClarty, P. A. Quantum spin ice: a search for gapless quantum spin liquids in pyrochlore magnets. Rep. Prog. Phys. 77, 056501 (2014).
Benton, O., Sikora, O. & Shannon, N. Seeing the light: experimental signatures of emergent electromagnetism in a quantum spin ice. Phys. Rev. B 86, 075154 (2012).
Lee, S., Onoda, S. & Balents, L. Generic quantum spin ice. Phys. Rev. B 86, 104412 (2012).
Sibille, R. et al. Candidate quantum spin liquid in the Ce3+ pyrochlore stannate Ce2Sn2O7. Phys. Rev. Lett. 115, 097202 (2015).
Huang, Y.-P., Chen, G. & Hermele, M. Quantum spin ices and topological phases from dipolar–octupolar doublets on the pyrochlore lattice. Phys. Rev. Lett. 112, 167203 (2014).
Li, Y.-D. & Chen, G. Symmetry enriched U(1) topological orders for dipole–octupole doublets on a pyrochlore lattice. Phys. Rev. B 95, 041106 (2017).
Urban, S. et al. Synthesis and full characterization of the phase-pure pyrochlore Ce2Zr2O7 and the κ-Ce2Zr2O8 phases. Appl. Catal. B 197, 23–34 (2016).
Lhotel, E. et al. Fluctuations and all-in-all-out ordering in dipole–octupole Nd2Zr2O7. Phys. Rev. Lett. 115, 197202 (2015).
Sala, G. et al. Vacancy defects and monopole dynamics in oxygen-deficient pyrochlores. Nat. Mater. 13, 488–493 (2014).
Ross, K. A., Savary, L., Gaulin, B. D. & Balents, L. Quantum excitations in quantum spin ice. Phys. Rev. X 1, 021002 (2011).
Cao, H. et al. Ising versus XY anisotropy in frustrated R2Ti2O7 compounds as “seen” by polarized neutrons. Phys. Rev. Lett. 103, 056402 (2009).
Sibille, R. et al. Experimental signatures of emergent quantum electrodynamics in Pr2Hf2O7. Nat. Phys. 14, 711–715 (2018).
Sibille, R. et al. Coulomb spin liquid in anion-disordered pyrochlore Tb2Hf2O7. Nat. Commun. 8, 892 (2017).
Bovo, L. et al. Special temperatures in frustrated ferromagnets. Nat. Commun. 9, 1999 (2018).
Fennell, T. et al. Multiple Coulomb phase in the fluoride pyrochlore CsNiCrF6. Nat. Phys. 15, 60–66 (2019).
Gaudet, J. et al. Quantum spin ice dynamics in the dipole-octupole pyrochlore magnet Ce2Zr2O7. Phys. Rev. Lett. 122, 187201 (2019).
Chakoumakos, B. C. et al. Four-circle single-crystal neutron diffractometer at the High Flux Isotope Reactor. J. Appl. Crystallogr. 44, 655–658 (2011).
Cao, H. et al. DEMAND, a dimensional extreme magnetic neutron diffractometer at the High Flux Isotope Reactor. Crystals 9, 5 (2018).
Rodríguez-Carvajal, J. Recent advances in magnetic structure determination by neutron powder diffraction. Phys. B 192, 55–69 (1993).
Petrenko, O. A., Lees, M. R. & Balakrishnan, G. Magnetization process in the spin-ice compound Ho2Ti2O7. Phys. Rev. B 68, 012406 (2003).
Fukazawa, H., Melko, R. G., Higashinaka, R., Maeno, Y. & Gingras, M. J. P. Magnetic anisotropy of the spin-ice compound Dy2Ti2O7. Phys. Rev. B 65, 054410 (2002).
Zhou, H. D. et al. Spin liquid state in the S=1/2 triangular lattice Ba3CuSb2O9. Phys. Rev. Lett. 106, 147204 (2011).
Clark, L. et al. Gapless spin liquid ground state in the S=1/2 vanadium oxyfluoride kagome antiferromagnet [NH4]2[C7H14N][V7O6F18]. Phys. Rev. Lett. 110, 207208 (2013).
de Vries, M. A., Kamenev, K. V., Kockelmann, W. A., Sanchez-Benitez, J. & Harrison, A. Magnetic ground state of an experimental S=1/2 kagome antiferromagnet. Phys. Rev. Lett. 100, 157205 (2008).
Gauthier, N. et al. Evidence for spin liquid ground state in SrDy2O4 frustrated magnet probed by μSR. J. Phys. Conf. Ser. 828, 012014 (2017).
Uemura, Y. J. et al. Spin fluctuations in frustrated kagome lattice system SrCr8Ga4O19 studied by muon spin relaxation. Phys. Rev. Lett. 73, 3306–3309 (1994).
Ye, F., Liu, Y., Whitfield, R., Osborn, R. & Rosenkranz, S. Implementation of cross correlation for energy discrimination on the time-of-flight spectrometer CORELLI. J. Appl. Crystallogr. 51, 315–322 (2018).
We thank Y. Su, Y. J. Uemura, J. A. Rodriguez and Z. Ma for helpful discussions. The neutron scattering work at Rice is supported by US DOE BES DE-SC0012311 (P.D.). The single-crystal-growth work at Rice is supported by the Robert A. Welch. Foundation under grant no. C-1839 (P.D.). E.M. and C.-L.H. acknowledge the support from US DOE BES DE-SC0019503. A.H.N. acknowledges the support of the Robert A. Welch Foundation grant no. C-1818 and NSF CAREER grant no. DMR-1350237. Research at UCSD was supported by the US DOE BES DE-FG02-04ER46105 (M.B.M.). The work of J.-H.C. was supported by the National Research Foundation of Korea (NRF-2017K1A3A7A09016303). This research used resources at the Spallation Neutron Source and the High Flux Isotope Reactor, DOE Office of Science User Facilities operated by the ORNL. H.C. acknowledges the support of US DOE BES Early Career Award KC0402010 under contract DE-AC05-00OR22725. Crystal growth by B.G., X.X. and S.-W.C. at Rutgers was supported by the visitor programme at the Center for Quantum Materials Synthesis, funded by the Gordon and Betty Moore Foundation’s EPiQS initiative through grant GBMF6402, and by Rutgers University. G.C. acknowledges the support from the Ministry of Science and Technology of China with grant no. 2016YFA0301001 and 2016YFA0300500.
The authors declare no competing interests.
Peer review information: Nature Physics thanks Kazushi Kanoda and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.