Toby Perring, E. Lhotel, Romain Sibille, Vladimir Pomjakushin, Andrew Wildes, Tom Fennell, Russell A. Ewings, Thomas C. Hansen, Sylvain Petit, Lukas Keller, David A. Keen, Clemens Ritter, Jacques Ollivier, Nicolas Gauthier, Gøran J. Nilsen, Victor Porée, Paul Scherrer Institute (PSI), SLAC National Accelerator Laboratory (SLAC), Stanford University, Magnétisme et Supraconductivité (NEEL - MagSup), Institut Néel (NEEL), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), STFC Rutherford Appleton Laboratory (RAL), Science and Technology Facilities Council (STFC), Institut Laue-Langevin (ILL), Laboratoire Léon Brillouin (LLB - UMR 12), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Magnétisme et Supraconductivité (MagSup), ILL, and Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Saclay
Spin liquids are highly correlated yet disordered states formed by the entanglement of magnetic dipoles$^1$. Theories typically define such states using gauge fields and deconfined quasiparticle excitations that emerge from a simple rule governing the local ground state of a frustrated magnet. For example, the '2-in-2-out' ice rule for dipole moments on a tetrahedron can lead to a quantum spin ice in rare-earth pyrochlores - a state described by a lattice gauge theory of quantum electrodynamics$^{2-4}$. However, f-electron ions often carry multipole degrees of freedom of higher rank than dipoles, leading to intriguing behaviours and 'hidden' orders$^{5-6}$. Here we show that the correlated ground state of a Ce$^{3+}$-based pyrochlore, Ce$_2$Sn$_2$O$_7$, is a quantum liquid of magnetic octupoles. Our neutron scattering results are consistent with the formation of a fluid-like state of matter, but the intensity distribution is weighted to larger scattering vectors, which indicates that the correlated degrees of freedom have a more complex magnetization density than that typical of magnetic dipoles in a spin liquid. The temperature evolution of the bulk properties in the correlated regime below 1 Kelvin is well reproduced using a model of dipole-octupole doublets on a pyrochlore lattice$^{7-8}$. The nature and strength of the octupole-octupole couplings, together with the existence of a continuum of excitations attributed to spinons, provides further evidence for a quantum ice of octupoles governed by a '2-plus-2-minus' rule. Our work identifies Ce$_2$Sn$_2$O$_7$ as a unique example of a material where frustrated multipoles form a 'hidden' topological order, thus generalizing observations on quantum spin liquids to multipolar phases that can support novel types of emergent fields and excitations.