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, Ce2Sn2O7, 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 dipoleoctupole 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 Ce2Sn2O7 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. The composite 'dipole-octupole' nature of the degrees of freedom and their evolution as a function of temperature or magnetic field provide new ways of controlling emergent phenomena in quantum materials.

Magnetic topological phases of quantum matter are an emerging frontier in physics and materials science, of which kagome magnets appear as a highly promising platform. Here, we explore magnetic correlations in the recently identified topological kagome system TbMn6Sn6 using muon spin rotation, combined with local field analysis and neutron diffraction. Our studies identify an out-of-plane ferrimagnetic structure with slow magnetic fluctuations which exhibit a critical slowing down below $${T}_{{{{{{{{\rm{C1}}}}}}}}}^{* }$$ T C1 *  ≃ 120 K and finally freeze into static patches with ideal out-of-plane order below TC1 ≃ 20 K. We further show that hydrostatic pressure of 2.1 GPa stabilises the static out-of-plane topological ferrimagnetic ground state in the whole volume of the sample. Therefore the exciting perspective arises of a magnetically-induced topological system whose magnetism can be controlled through external parameters. The present results will stimulate theoretical investigations to obtain a microscopic understanding of the relation between the low-temperature volume-wise magnetic evolution of the static c-axis ferrimagnetic patches and the topological electronic properties in TbMn6Sn6.

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We report the synthesis of powder and single-crystal samples of cerium pyrohafnate and their characterization using neutron diffraction, thermogravimetry and x-ray absorption spectroscopy. We evaluate the amount of nonmagnetic Ce 4+ defects and use this result to interpret the spectrum of crystal-electric field transitions observed using inelastic neutron scattering. The analysis of these single-ion transitions indicates the dipole-octupole nature of the ground-state doublet and a significant degree of spin-lattice coupling. The single-ion properties calculated from the crystal-electric field parameters obtained spectroscopically are in good agreement with bulk magnetic susceptibility data down to about 1 K. Below this temperature, the behavior of the magnetic susceptibility indicates a correlated regime without showing any sign of magnetic long-range order or freezing down to 0.08 K. We conclude that Ce 2 Hf 2 O 7 is another candidate to investigate exotic correlated states of quantum matter, such as the octupolar quantum spin ice recently argued to exist in the isostructural compounds Ce 2 Sn 2 O 7 and Ce 2 Zr 2 O 7 .