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.

The disordered antiferromagnet PbFe 1/2 Nb 1/2 O3 (PFN ) is investigated in a wide temperature range by combining Mössbauer spectroscopy and neutron diffraction experiments. It is demonstrated that the magnetic ground state is a microscopic coexistence of antiferromagnetic and a spin-glass orders. This speromagnet-like phase features frozen-in short-range fluctuations of the Fe 3+ magnetic moments that are transverse to the long-range ordered antiferromagnetic spin component.Phase transitions in the presence of disorder and/or competing interactions are one of the central unresolved problems in modern condensed matter physics 1-4 . With both effects present, one may encounter a freezing of microscopic degrees of freedom without conventional longrange order. In magnetic systems, the corresponding phenomenon is referred to as a spin-glass (SG) transition 5 . By now, spin glasses are reasonably well understood for models with discrete (Ising) symmetries and long-range interactions 6,7 . In contrast, for continuous (Heisenberg and XY) symmetries with short-range coupling, the properties and sometimes the very existence of the SG phase remain a matter of debate [8][9][10][11][12] . An important outstanding question is whether the SG phase can coexist with true long-range order (LRO) 12,13 ? Theory 14-16 and numerical studies 17-20 have consistently provide an affirmative answer; see Ref.21 for a review. Both ferromagnetic (FM) 15 and AF 16 models demonstrate a SG freezing of spin components transverse to the long range order parameter. The problem gained a particular urgency in the context of cuprate superconductors, where SG and AF phases are adjacent on the concentrationtemperature phase diagram but appear to be mutually exclusive 22,23 .On the experimental side though, the situation is much less clear-cut and hotly debated. Most hurdles on this route are the known measurement issues endemic to spin glasses 1,24,25 . In addition, even if long range order and SG are shown to appear simultaneously, it may be extremely difficult to establish their co-existence on the microscopic scale, as opposed to an inhomogeneous phase separation. A great deal of work was done on amorphous, ferromagnetic Fe X Zr 100−X alloys. While strong support for uniformly coexisting SG and LRO in these systems have been presented 20,[26][27][28] , evidence pointing to a cluster-based scenario also exist 29 . In crystalline materials, simultaneous antiferromagnetic (AF) and SG states have been observed in Fe 0.6 Mn 0.4 TiO 3 30,31 and Co 2 (OH)PO 4 32 . However, even in these Ising systems, the microscopic nature of such coexistence is not unambiguous 31,32 .A solid experimental proof of microscopic SG and LRO coexistence in a crystalline material remains elu- sive. Besides finding an appropriate model compound, one has to strategically choose the experimental techniques. Momentum-resolved (scattering) experiments are well-suited to probe microscopic quantities averaged over the entire sample, but do not provide spatiallyresolved information. I...

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We investigate the structural and magnetic properties of the quantum magnet BaCuTe 2 O 6 . This compound is synthesized in powder and single crystal form for the first time. Synchrotron x-ray and neutron diffraction reveal a cubic crystal structure (P4 1 32) where the magnetic Cu 2+ ions form a complex network. Heat capacity and static magnetic susceptibility measurements suggest the presence of antiferromagnetic interactions with a Curie-Weiss temperature of ≈− 33 K, while long-range magnetic order occurs at the much lower temperature of ≈6.3 K. The magnetic structure, solved using neutron diffraction, reveals antiferromagnetic order along chains parallel to the a, b, and c crystal axes. This is consistent with the magnetic excitations which resemble the multispinon continuum typical of the spin-1/2 Heisenberg antiferromagnetic chain. A consistent intrachain interaction value of ≈34 K is achieved from the various techniques. Finally the magnetic structure provides evidence that the chains are coupled together in a noncollinear arrangement by a much weaker antiferromagnetic, frustrated hyperkagome interaction.

SrCuTe 2 O 6 consists of a three-dimensional arrangement of spin-1 2 Cu 2+ ions. The first-, second-, and third-neighbor interactions, respectively, couple Cu 2+ moments into a network of isolated triangles, a highly frustrated hyperkagome lattice consisting of corner-sharing triangles and antiferromagnetic chains. Of these, the chain interaction dominates in SrCuTe 2 O 6 while the other two interactions lead to frustrated interchain coupling giving rise to long-range magnetic order at suppressed temperatures. In this paper, we investigate the magnetic properties in SrCuTe 2 O 6 using muon relaxation spectroscopy and neutron diffraction and present the low-temperature magnetic structure as well as the directional-dependent magnetic phase diagram as a function of field.