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Continuum of quantum fluctuations in a three-dimensional S = 1 Heisenberg magnet

Abstract

Conventional crystalline magnets are characterized by symmetry breaking and normal modes of excitation called magnons, with quantized angular momentum ħ. Neutron scattering correspondingly features extra magnetic Bragg diffraction at low temperatures and dispersive inelastic scattering associated with single magnon creation and annihilation. Exceptions are anticipated in so-called quantum spin liquids, as exemplified by the one-dimensional spin-1/2 chain, which has no magnetic order and where magnons accordingly fractionalize into spinons with angular momentum ħ/2. This is spectacularly revealed by a continuum of inelastic neutron scattering associated with two-spinon processes. Here, we report evidence for these key features of a quantum spin liquid in the three-dimensional antiferromagnet NaCaNi2F7. We show that despite the complication of random Na1+–Ca2+ charge disorder, NaCaNi2F7 is an almost ideal realization of the spin-1 antiferromagnetic Heisenberg model on a pyrochlore lattice. Magnetic Bragg diffraction is absent and 90% of the neutron spectral weight forms a continuum of magnetic scattering with low-energy pinch points, indicating NaCaNi2F7 is in a Coulomb-like phase. Our results demonstrate that disorder can act to freeze only the lowest-energy magnetic degrees of freedom; at higher energies, a magnetic excitation continuum characteristic of fractionalized excitations persists.

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Acknowledgements

We are grateful to Y. Wan for enlightening discussions. This work benefited from many discussions with, and insights passed by, O. Tchernyshyov. We would also like to thank R. Moessner, J. Chalker and S. Todadri for critical reading of this manuscript. Work at the Institute for Quantum Matter was supported by the US Department of Energy, Office of Basic Energy Sciences, Division of Material Sciences and Engineering under grant DE-FG02-08ER46544. A.S. and C.B. were funded by the Gordon and Betty Moore Foundation under the EPIQS program GBMF no. 4532. Access to MACS was provided by the Center for High Resolution Neutron Scattering, a partnership between the National Institute of Standards and Technology and the National Science Foundation under Agreement No. DMR-1508249. A portion of this research used resources at the Spallation/Neutron Source, a DOE Office of Science User Facility operated by the Oak Ridge National Laboratory. This work was supported by the Paul Scherrer Institut by providing the supermirror analyser as a temporary loan to Oak Ridge National Laboratory. We gratefully acknowledge the Johns Hopkins Homewood High Performance Cluster (HHPC) and the Maryland Advanced Research Computing Center (MARCC), funded by the State of Maryland, for computing resources.

Author information

K.W.P., A.S., B.W., J.A.R. and Y.Q. performed the neutron scattering experiments. K.W.P. performed the specific heat measurements and analysed all experimental data. J.W.K. and R.J.C. synthesized and characterized the single-crystal sample. H.J.C and S.Z. performed Monte Carlo simulations and self-consistent Gaussian approximation calculations, along with assisting with the theoretical interpretation. K.W.P., C.L.B. and H.J.C. wrote the manuscript with input from all co-authors. C.L.B. oversaw all aspects of the project.

Correspondence to K. W. Plumb.

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Fig. 1: Equal-time structure factor in NaCaNi2F7.
Fig. 2: Inelastic neutron scattering showing dynamic magnetic correlations in NaCaNi2F7.
Fig. 3: Momentum- and energy-resolved inelastic neutron scattering probing magnetic excitations in NaCaNi2F7.
Fig. 4: Specific heat and elastic neutron scattering revealing spin freezing in NaCaNi2F7.