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The quantum spin liquid is a highly entangled magnetic state characterized by the absence of static magnetism in its ground state. Instead, the spins fluctuate in a highly correlated way down to the lowest temperatures. Quantum spin liquids are very rare and are confined to a few specific cases where the interactions between the magnetic ions cannot be simultaneously satisfied (known as frustration). Lattices with magnetic ions in triangular or tetrahedral arrangements, which interact via isotropic antiferromagnetic interactions, can generate such a frustration. Three-dimensional isotropic spin liquids have mostly been sought in materials where the magnetic ions form pyrochlore or hyperkagome lattices. Here we present a three-dimensional lattice called the hyper-hyperkagome that enables spin liquid behaviour and manifests in the compound PbCuTe 2 O 6 . Using a combination of experiment and theory, we show that this system exhibits signs of being a quantum spin liquid with no detectable static magnetism together with the presence of diffuse continua in the magnetic spectrum suggestive of fractional spinon excitations. Quantum spin liquids have magnetic moments that do not form magnetic order even as the temperature approaches zero, leading to the dominance of quantum fluctuations. Chillal et al. present evidence that the hyper-hyperkagome lattice of PbCuTe 2 O 6 hosts a three-dimensional quantum spin liquid.

Geometrical frustration among interacting spins combined with strong quantum fluctuations destabilize long-range magnetic order in favor of more exotic states such as spin liquids. By following this guiding principle, a number of spin liquid candidate systems were identified in quasi-two-dimensional (quasi-2D) systems. For 3D, however, the situation is less favorable as quantum fluctuations are reduced and competing states become more relevant. Here we report a comprehensive study of thermodynamic, magnetic and dielectric properties on single crystalline and pressed-powder samples of PbCuTe2O6, a candidate material for a 3D frustrated quantum spin liquid featuring a hyperkagome lattice. Whereas the low-temperature properties of the powder samples are consistent with the recently proposed quantum spin liquid state, an even more exotic behavior is revealed for the single crystals. These crystals show ferroelectric order at TFE ≈ 1 K, accompanied by strong lattice distortions, and a modified magnetic response—still consistent with a quantum spin liquid—but with clear indications for quantum critical behavior.

The quantum spin liquid is a highly entangled magnetic state characterized by the absence of static magnetism in its ground state. Instead, the spins fluctuate in a highly correlated way down to the lowest temperatures. Quantum spin liquids are very rare and are confined to a few specific cases where the interactions between the magnetic ions cannot be simultaneously satisfied (known as frustration). Lattices with magnetic ions in triangular or tetrahedral arrangements, which interact via isotropic antiferromagnetic interactions, can generate such a frustration. Three-dimensional isotropic spin liquids have mostly been sought in materials where the magnetic ions form pyrochlore or hyperkagome lattices. Here we present a three-dimensional lattice called the hyper-hyperkagome that enables spin liquid behaviour and manifests in the compound PbCuTe O . Using a combination of experiment and theory, we show that this system exhibits signs of being a quantum spin liquid with no detectable static magnetism together with the presence of diffuse continua in the magnetic spectrum suggestive of fractional spinon excitations.

Quantum spin liquids (QSL) are novel phases of matter which remain quantum disordered even at the lowest temperature. They are characterized by emergent gauge fields and fractionalized quasiparticles. Here we show that the sub-Kelvin thermal transport of the three-dimensional \\(S=1/2\\) hyper-hyperkagome quantum magnet PbCuTe\\(_2\\)O\\(_6\\) is governed by a sizeable charge-neutral fermionic contribution which is compatible with the itinerant fractionalized excitations of a spinon Fermi surface. We demonstrate that this hallmark feature of the QSL state is remarkably robust against sample crystallinity, large magnetic field, and field-induced magnetic order, ruling out the imitation of QSL features by extrinsic effects. Our findings thus reveal the characteristic low-energy features of PbCuTe\\(_2\\)O\\(_6\\) which qualify this compound as a true QSL material.

PbCuTe\\(_2\\)O\\(_6\\) is considered as one of the rare candidate materials for a three-dimensional quantum spin liquid (QSL). This assessment was based on the results of various magnetic experiments, performed mainly on polycrystalline material. More recent measurements on single crystals revealed an even more exotic behavior, yielding ferroelectric order below \\(T_FE 1\\,K\\), accompanied by distinct lattice distortions, and a somewhat modified magnetic response which is still consistent with a QSL. Here we report on low-temperature measurements of various thermodynamic, magnetic and dielectric properties of single crystalline PbCuTe\\(_2\\)O\\(_6\\) in magnetic fields \\(B 14.5\\,T\\). The combination of these various probes allows us to construct a detailed \\(B\\)-\\(T\\) phase diagram including a ferroelectric phase for \\(B \\) \\(8\\,T\\) and a \\(B\\)-induced magnetic phase at \\(B \\) \\(11\\,T\\). These phases are preceded by or coincide with a structural transition from a cubic high-temperature phase into a distorted non-cubic low-temperature state. The phase diagram discloses two quantum critical points (QCPs) in the accessible field range, a ferroelectric QCP at \\(B_c1\\) = \\(7.9\\,T\\) and a magnetic QCP at \\(B_c2\\) = \\(11\\,T\\). Field-induced lattice distortions, observed in the state at \\(T>\\) \\(1\\,K\\) and which are assigned to the effect of spin-orbit interaction of the Cu\\(^2+\\)-ions, are considered as the key mechanism by which the magnetic field couples to the dielectric degrees of freedom in this material.

We report a neutron scattering study of the ferroelectric phase transition in Sr\\(_{0.585}\\)Ce\\(_{0.025}\\)Ba\\(_{0.39}\\)Nb\\(_2\\)O\\(_6\\) (SBN-61:Ce). We find no evidence for a soft transverse optic phonon. We do, however, observe anisotropic diffuse scattering. This scattering has inelastic and elastic contributions. In the paraelectric phase the susceptibility associated with the elastic diffuse scattering follows well the anomaly of the dielectric susceptibility of SBN-61:Ce. In the ferroelectric phase the lineshape of the elastic scattering is consistent with the form expected for the ferroelectric domain walls. In contrast to the macroscopic observations, the scattering properties of Ce-doped crystal do not exhibit important changes with respect to those of pure Sr\\(_{0.61}\\)Ba\\(_{0.39}\\)Nb\\(_2\\)O\\(_6\\).

Geometrical frustration among interacting spins combined with strong quantum fluctuations destabilize long-range magnetic order in favour of more exotic states such as spin liquids. By following this guiding principle, a number of spin liquid candidate systems were identified in quasi-two-dimensional (quasi-2D) systems. For 3D, however, the situation is less favourable as quantum fluctuations are reduced and competing states become more relevant. Here we report a comprehensive study of thermodynamic, magnetic and dielectric properties on single crystalline and pressed-powder samples of PbCuTe\\(_2\\)O\\(_6\\), a candidate material for a 3D frustrated quantum spin liquid featuring a hyperkagome lattice. Whereas the low-temperature properties of the powder samples are consistent with the recently proposed quantum spin liquid state, an even more exotic behaviour is revealed for the single crystals. These crystals show ferroelectric order at \\(T_FE 1\\,K\\), accompanied by strong lattice distortions, and a modified magnetic response -- still consistent with a quantum spin liquid -- but with clear indications for quantum critical behaviour.