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Three-dimensional quantum spin liquids have remained elusive, hindered by reduced quantum fluctuations from larger lattice connectivity inherent to high-dimensional systems. Here, we investigate the remarkable persistence of dynamical short-range magnetic correlations in the nearly body-centered cubic garnet NaCa$_2$Cu$_2$(VO$_4$)$_3$ down to $T = 50$ mK, two orders of magnitude below its Curie-Weiss temperature. Using a combination of neutron and muon spectroscopies plus numerical simulations, we demonstrate that a spin-liquid phase emerges from the interplay of strongly frustrated exchange interactions and subtle temperature-dependent Jahn-Teller spin-lattice effects., Comment: 9 pages, 4 figures. Supplementary Information: 3 pages, 4 figures

Y3Cu9(OH)19Cl8 realizes an original anisotropic kagome model hosting a rich magnetic phase diagram [M. Hering et al, npj Computational Materials 8, 1 (2022)]. We present an improved synthesis of large phase-pure single crystals via an external gradient method. These crystals were investigated in details by susceptibility, specific heat, thermal expansion, neutron scattering and local muSR and NMR techniques. At variance with polycristalline samples, the study of single crystals gives evidence for subtle structural instabilities at 33K and 13K which preserve the global symmetry of the system and thus the magnetic model. At 2.1K the compound shows a magnetic transition to a coplanar (1/3,1/3) long range order as predicted theoretically. However our analysis of the spin wave excitations yields magnetic interactions which locate the compound closer to the phase boundary to a classical jammed spin liquid phase. Enhanced quantum fluctuations at this boundary may be responsible for the strongly reduced ordered moment of the Cu2+, estimated to be 0.075muB from muSR.

We report thermal conductivity measurements on single crystals of herbertsmithite, over a wide range of temperatures (0.05-120 K) in magnetic fields up to 15 T. We also report measurements of the thermal Hall effect, found to be vanishingly small. At high temperatures, in the paramagnetic regime, the thermal conductivity has a negligible field dependence. Upon cooling and the development of correlations, the onset of a clear monotonic field dependence below about 20 K signals a new characteristic temperature scale that may reflect the subtle crossover towards the quantum spin liquid regime. Deconfined spinons, if present, are not detected and phonons, as the main carriers of heat, are strongly scattered by the intrinsic spin excitations and the magnetic defects. In view of the colossal fields required to affect the intrinsic spins, most of the field-induced evolution is attributed to the progressive polarization of some magnetic defects. By elaborating a phenomenological model, we extract the magnetization of these main scattering centers which does not resemble the Brillouin function for free spins 1/2, requiring to go beyond the paradigm of isolated paramagnetic spins. Besides, the onset of a nonmonotonic field dependence below about 2 K underlines the existence of another characteristic temperature scale, previously highlighted with other measurements, and sheds new light on the phase diagram of herbertsmithite down to the lowest temperatures., Comment: 14 pages, 7 figures

Measuring the specific heat of herbertsmithite single crystals in high magnetic fields (up to $34$ T) allows us to isolate the low-temperature kagome contribution while shifting away extrinsic Schottky-like contributions. The kagome contribution follows an original power law $C_{p}(T\rightarrow0)\propto T^{\alpha}$ with $\alpha\sim1.5$ and is found field-independent between $28$ and $34$ T for temperatures $1\leq T\leq4$ K. These are serious constrains when it comes to replication using low-temperature extrapolations of high-temperature series expansions. We manage to reproduce the experimental observations if about $10$ % of the kagome sites do not contribute. Between $0$ and $34$ T, the computed specific heat has a minute field dependence then supporting an algebraic temperature dependence in zero field, typical of a critical spin liquid ground state. The need for an effective dilution of the kagome planes is discussed and is likely linked to the presence of copper ions on the interplane zinc sites. At very low temperatures and moderate fields, we also report some small field-induced anomalies in the total specific heat and start to elaborate a phase diagram., Comment: 10 pages, 5 figures

Spin-orbit coupling (SOC) often gives rise to interesting electronic and magnetic phases in an otherwise ordinary pool of paramagnetic heavy metal oxides. In presence of strong SOC, assumed to be working in $j$-$j$ coupling regime, 5$d^4$ iridates are generally speculated to possess a nonmagnetic $J_{eff}$~=~0 singlet ground state, which invariably gets masked due to different solid-state effects (e.g. hopping). Here, we try to probe the trueness of the atomic SOC-based proposal in an apparently 1-dimensional system, Sr$_3$NaIrO$_6$, possessing a 2$H$ hexagonal structure with well separated Ir$^{5+}$ (5$d^4$) ions. But all the detailed experimental as well as theoretical characterizations reveal that the ground state of Sr$_3$NaIrO$_6$ is not nonmagnetic, rather accommodating a significantly high effective magnetic moment on Ir$^{5+}$ ion. However our combined dc susceptibility ($\chi$), ${}^{23}$Na nuclear magnetic resonance (NMR), muon-spin-relaxation/rotation ($\mu$SR) and heat capacity ($C_p$) measurements clearly refute any sign of spin-freezing or ordered magnetism among the Ir$^{5+}$ moments due to geometrical exchange frustration, while in-depth zero-field (ZF) and longitudinal field (LF) $\mu$SR investigations strongly point towards inhomogeneous quantum spin-orbital liquid (QSOL)-like ground state. In addition, the linear temperature dependence of both the NMR spin-lattice relaxation rate and the magnetic heat capacity at low temperatures suggest low-lying gapless spin excitations in the QSOL phase of this material. Finally, we conclude that the effective SOC realised in $d^4$ iridates are unlikely to offer a ground state which will be consistent with a purely atomic $j$-$j$ coupling description., Comment: 13 pages, 12 figures

We report x-ray diffraction, magnetic susceptibility, heat capacity, $^{1}$H nuclear magnetic resonance (NMR), and muon spin relaxation ($\mu$SR) measurements, as well as density-functional band-structure calculations for the frustrated $S=3/2$ triangular lattice Heisenberg antiferromagnet (TLHAF) $\alpha$-HCrO$_{2}$ (trigonal, space group: $R\bar{3}m$). This compound undergoes a clear magnetic transition at $T_{\rm N} \simeq 22.5$~K, as seen from the drop in the muon paramagnetic fraction and concurrent anomalies in the magnetic susceptibility and specific heat. Local probes (NMR and $\mu$SR) reveal a broad regime with slow fluctuations down to $0.7\,T_{\rm N}$, this temperature corresponding to the maximum in the $\mu$SR relaxation rate and in the NMR wipe-out. From the comparison with NaCrO$_{2}$ and $\alpha$-KCrO$_{2}$, the fluctuating regime and slow dynamics below $T_{\rm N}$ appear to be hallmarks of the TLHAF with $ABC$ stacking that leads to a frustration of interlayer couplings between the triangular planes. This interlayer frustration is a powerful lever to generate spin states with persistent dynamics and may bear implications to spin-liquid candidates with the triangular geometry., Comment: 14 pages, 11 figures, 2 tables

We investigate the low temperature magnetic properties of a $S=\frac{5}{2}$ Heisenberg kagom\'e antiferromagnet, the layered monodiphosphate Li$_9$Fe$_3$(P$_2$O$_7$)$_3$(PO$_4$)$_2$, using magnetization measurements and $^{31}$P nuclear magnetic resonance. An antiferromagnetic-type order sets in at $T_{\rm N}=1.3$ K and a characteristic magnetization plateau is observed at 1/3 of the saturation magnetization below $T^* \sim 5$ K. A moderate $^{31}$P NMR line broadening reveals the development of anisotropic short-range correlations within the plateau phase concomitantly with a gapless spin-lattice relaxation time $T_1 \sim k_B T / \hbar S$, which both point to the presence of a semiclassical nematic spin liquid state predicted for the Heisenberg kagom\'e antiferromagnetic model or to the persistence of the zero-energy modes of the kagome lattice under large magnetic fields., Comment: 6 pages, 5 figures

We present a microscopic study of a doped quantum spin liquid candidate, the hyperkagome Na$_3$Ir$_3$O$_8$ compound by using $^{23}$Na NMR. We determine the intrinsic behavior of the uniform \textbf{q} $ = 0$ susceptibility via shift measurements and the dynamical response by probing the spin-lattice relaxation rate. Throughout the studied temperature range, the susceptibility is consistent with a semimetal behavior, though with electronic bands substantially modified by correlations. Remarkably, the antiferromagnetic fluctuations present in the insulating parent compound Na$_4$Ir$_3$O$_8$ survive in the studied compound. The spin dynamics are consistent with 120$^o$ excitations modes displaying short-range correlations.

We report a comprehensive muon spectroscopy study of the Zn-barlowite series of $S={\frac{1}{2}}$ kagom\'e antiferromagnets, Zn$_x$Cu$_{4-x}$(OH)$_{6}$FBr, for $x=0.00$ to $0.99(1)$. By combining muon spin relaxation and rotation measurements with state-of-the-art density-functional theory muon-site calculations, we observe the formation of both $\mu$--F and $\mu$--OH complexes in Zn-barlowite. From these stopping sites, implanted muon spins reveal the suppression of long-range magnetic order into a possible quantum spin liquid state upon increasing concentration of Zn-substitution. In the parent compound ($x=0$), static long-range magnetic order below $T_{\mathsf{N}}=15$ K manifests itself in the form of spontaneous oscillations in the time-dependent muon asymmetry signal consistent with the dipolar fields expected from the calculated muon stopping sites and the previously determined magnetic structure of barlowite. Meanwhile, in the $x=1.0$ end-member of the series---in which antiferromagnetic kagom\'e layers of Cu$^{2+}$ $S={\frac{1}{2}}$ moments are decoupled by diamagnetic Zn$^{2+}$ ions---we observe that dynamic magnetic moment fluctuations persist down to at least 50 mK, indicative of a quantum disordered ground state. We demonstrate that this crossover from a static to dynamic magnetic ground state occurs for compositions of Zn-barlowite with $x>0.5$, which bears resemblance to dynamical behaviour of the widely studied Zn-paratacamite series that contains the quantum spin liquid candidate herbertsmithite., Comment: 11 pages, 5 figures, supplementary information

We report $^{51}$V NMR, $\mu$SR and zero applied field $^{63,65}$Cu NMR measurements on powder samples of Sr-vesignieite, SrCu$_3$V$_2$O$_8$(OH)$_2$, a $S = 1/2$ nearly-kagome Heisenberg antiferromagnet. Our results demonstrate that the ground state is a $\mathbf{q} = 0$ magnetic structure with spins canting either in or out of the kagome plane, giving rise to weak ferromagnetism. We determine the size of ordered moments and the angle of canting for different possible $\mathbf{q} = 0$ structures and orbital scenarios, thereby providing insight into the role of the Dzyaloshinskii-Moriya (DM) interaction in this material., Comment: Accepted in Physical Review B

Spin liquids are exotic phases of quantum matter challenging Landau's paradigm of symmetry-breaking phase transitions. Despite strong exchange interactions, spins do not order or freeze down to zero temperature. While well-established for 1D quantum antiferromagnets, in higher dimension where quantum fluctuations are less acute, realizing and understanding such states represent major issues, both theoretical and experimental. In this respect the simplest nearest-neighbor Heisenberg antiferromagnet Hamiltonian on the highly frustrated kagome lattice has proven to be a fascinating and inspiring model. The exact nature of its ground state remains elusive and the existence of a spin-gap is the first key-issue to be addressed to discriminate between the various classes of proposed spin liquids. Here, through low-temperature Nuclear Magnetic Resonance (NMR) contrast experiments on high quality single crystals, we single out the kagome susceptibility and the corresponding dynamics in the kagome archetype, the mineral herbertsmithite, ZnCu$_3$(OH)$_6$Cl$_2$. We firmly conclude that this material does not harbor any spin-gap, which restores a convergence with recent numerical results promoting a gapless Dirac spin liquid as the ground state of the Heisenberg kagome antiferromagnet., Comment: 8 pages main text, 4 figures, 21 pages supplementary information

We report on a detailed neutron diffraction and $^1$H-NMR study on the frustrated spin-1/2 chain material linarite, PbCuSO$_4$(OH)$_2$, where competing ferromagnetic nearest neighbor and antiferromagnetic next-nearest neighbor interactions lead to frustration. From the magnetic Bragg peak intensity studied down to 60 mK, the magnetic moment per Cu atom is obtained within the whole magnetic phase diagram for $H \parallel b$ axis. Further, we establish the detailed configurations of the shift of the SDW propagation vector in phase V with field and temperature. Finally, combining our neutron diffraction results with those from a low-temperature/high-field NMR study we find an even more complex phase diagram close to the quasi-saturation field suggesting that bound two-magnon excitations are the lowest energy excitations close to and in the quasi-saturation regime. Qualitatively and semi-quantitatively, we relate such behavior to $XYZ$ exchange anisotropy and contributions from the Dzyaloshinsky-Moriya interaction to affect the magnetic properties of linarite.

We present a successful synthesis method of the series Ga$_{x}$Cu$_{4-x}$(OD)$_{6}$Cl$_{2}$ with substitutions up to $x=0.8$. The compound remains a frustrated kagome system with an insulating ground state similar to herbertsmithite for these substitutions, as the additional charge of Ga$^{3+}$ is most likely bound to additional OH$^{-}$ and Cl$^{-}$. Besides infrared measurements, we present magnetic and specific-heat data down to 2 K for selected samples with $0\leq x\leq0.8$. With increasing $x$ the long-range magnetic order is suppressed, similar to what was observed in the series Zn$_{x}$Cu$_{4-x}$(OH)$_{6}$Cl$_{2}$, indicating that Ga goes predominantly to the inter-plane position of the layered crystal structure. The reduction of the frozen magnetic fraction with increasing substitution was followed by $\mu$SR measurements. $^{69,71}$Ga nuclear magnetic resonance (NMR) was applied as a local probe for Ga induced disorder. One well resolved Ga NMR line of moderate width is found for each isotope across the phase diagram which indicates a rather homogeneous distribution of the Ga isotopes on a single site in the lattice., Comment: submitted to physica status solidi

The ground state of the quantum kagome antiferromagnet Zn-brochantite, ZnCu$_3$(OH)$_6$SO$_4$, which is one of only a few known spin-liquid (SL) realizations in two or three dimensions, has been described as a gapless SL with a spinon Fermi surface. Employing nuclear magnetic resonance in a broad magnetic-field range down to millikelvin temperatures, we show that in applied magnetic fields this enigmatic state is intrinsically unstable against a SL with a full or a partial gap. A similar instability of the gapless Fermi-surface SL was previously encountered in an organic triangular-lattice antiferromagnet, suggesting a common destabilization mechanism that most likely arises from spinon pairing. A salient property of this instability is that an infinitesimal field suffices to induce it, as predicted theoretically for some other types of gapless SL's., Comment: minor corrections

While it was speculated that 5$d^4$ systems would possess non-magnetic $J$~=~0 ground state due to strong Spin-Orbit Coupling (SOC), all such systems have invariably shown presence of magnetic moments so far. A puzzling case is that of Ba$_2$YIrO$_6$, which in spite of having a perfectly cubic structure with largely separated Ir$^{5+}$ ($d^4$) ions, has consistently shown presence of weak magnetic moments. Moreover, we clearly show from Muon Spin Relaxation ($\mu$SR) measurements that a change in the magnetic environment of the implanted muons in Ba$_2$YIrO$_6$ occurs as temperature is lowered below 10~K. This observation becomes counterintuitive, as the estimated value of SOC obtained by fitting the RIXS spectrum of Ba$_2$YIrO$_6$ with an atomic $j-j$ model is found to be as high as 0.39~eV, meaning that the system within this model is neither expected to possess moments nor exhibit temperature dependent magnetic response. Therefore we argue that the atomic $j-j$ coupling description is not sufficient to explain the ground state of such systems, where despite having strong SOC, presence of hopping triggers delocalisation of holes, resulting in spontaneous generation of magnetic moments. Our theoretical calculations further indicate that these moments favour formation of spin-orbital singlets in the case of Ba$_2$YIrO$_6$, which is manifested in $\mu$SR experiments measured down to 60~mK., Comment: 20 Pages, 7 Figures

In the vanadium oxyfluoride compound (NH$_4$)$_2$[C$_7$H$_{14}$N][V$_7$O$_6$F$_{18}$] (DQVOF), the V$^{4+}$ (3d$^1$, $S=1/2$) ions realize a unique, highly frustrated breathing kagome lattice composed of alternately-sized, corner-sharing equilateral triangles. Here we present an $^{17}$O NMR study of DQVOF, which isolates the local susceptibility of the breathing kagome network. By a fit to series expansion we extract the ratio of the interactions within the breathing kagome plane, $J_\triangledown / J_\vartriangle = 0.55(4)$, and the mean antiferromagnetic interaction $\bar{J}=60(7)$~K. Spin lattice, $T_1$, measurements reveal an essentially gapless excitation spectrum with a maximum gap $\Delta / \bar{J}=0.007(7)$. Our study provides new impetus for further theoretical investigations in order to establish whether the gapless spin liquid behavior displayed by DQVOF is intrinsic to its breathing kagome lattice or whether it is due to perturbations to this model, such as a residual coupling of the V$^{4+}$ ions in the breathing kagome planes to the interlayer V$^{3+}$ ($S=1$) spins., Comment: 5 pages, 4 figures, to appear in Phys. Rev. Lett

Using thermodynamic measurements, neutron diffraction, nuclear magnetic resonance, and muon spin relaxation, we establish putative quantum spin-liquid behavior in Ba$_3$InIr$_2$O$_9$, where unpaired electrons are localized on mixed-valence Ir$_2$O$_9$ dimers with Ir$^{4.5+}$ ions. Despite the antiferromagnetic Curie-Weiss temperature on the order of 10 K, neither long-range magnetic order nor spin freezing are observed down to at least 20 mK, such that spins are short-range correlated and dynamic over nearly three decades in temperature. Quadratic power-law behavior of both the spin-lattice relaxation rate and specific heat indicates the gapless nature of the ground state. We envisage that this exotic behavior may be related to an unprecedented combination of the triangular and buckled honeycomb geometries of nearest-neighbor exchange couplings in the mixed-valence setting., Comment: published version + Supplemental material

Employing complementary torque magnetometry and electron spin resonance on single crystals of herbertsmithite, the closest realization to date of a quantum kagome antiferromagnet featuring a spin-liquid ground state, we provide novel insight into different contributions to its magnetism. At low temperatures, two distinct types of defects with different magnetic couplings to the kagome spins are found. Surprisingly, their magnetic response contradicts the three-fold symmetry of the ideal kagome lattice, suggesting the presence of a global structural distortion that may be related to the establishment of the spin-liquid ground state., Comment: Published version with minor text corrections

PbCuTe2O6 is a rare example of a spin liquid candidate featuring a three dimensional magnetic lattice. Strong geometric frustration arises from the dominant antiferromagnetic interaction which generates a hyperkagome network of Cu2+ ions although additional interactions enhance the magnetic lattice connectivity. Through a combination of magnetization measurements and local probe investigation by NMR and muSR down to 20 mK, we provide a robust evidence for the absence of magnetic freezing in the ground state. The local spin susceptibility probed by the NMR shift hardly deviates from the macroscopic one down to 1 K pointing to a homogeneous magnetic system with a low defect concentration. The saturation of the NMR shift and the sublinear power law temperature (T) evolution of the 1/T1 NMR relaxation rate at low T point to a non-singlet ground state favoring a gapless fermionic description of the magnetic excitations. Below 1 K a pronounced slowing down of the spin dynamics is witnessed, which may signal a reconstruction of spinon Fermi surface. Nonetheless, the compound remains in a fluctuating spin liquid state down to the lowest temperature of the present investigation., Comment: To appear in Physical Review Letters

We have studied by muon spin resonance ({\mu}SR) the helical ground state and fluctuating chiral phase recently observed in the MnGe chiral magnet. At low temperature, the muon polarization shows double period oscillations at short time scales. Their analysis, akin to that recently developed for MnSi [A. Amato et al., Phys. Rev. B 89, 184425 (2014)], provides an estimation of the field distribution induced by the Mn helical order at the muon site. The refined muon position agrees nicely with ab initio calculations. With increasing temperature, an inhomogeneous fluctuating chiral phase sets in, characterized by two well separated frequency ranges which coexist in the sample. Rapid and slow fluctuations, respectively associated with short range and long range ordered helices, coexist in a large temperature range below T$_{N}$ = 170 K. We discuss the results with respect to MnSi, taking the short helical period, metastable quenched state and peculiar band structure of MnGe into account., Comment: 13 pages, 11 figures

Solid-solutions of the "soft" quantum spin ice pyrochlore magnets Tb2B2O7 with B=Ti and Sn display a novel magnetic ground state in the presence of strong B-site disorder, characterized by a low susceptibility and strong spin fluctuations to temperatures below 0.1 K. These materials have been studied using ac-susceptibility and muSR techniques to very low temperatures, and time-of-flight inelastic neutron scattering techniques to 1.5 K. Remarkably, neutron spectroscopy of the Tb3+ crystal field levels appropriate to at high B-site mixing (0.5 < x < 1.5 in Tb2Sn2-xTixO7) reveal that the doublet ground and first excited states present as continua in energy, while transitions to singlet excited states at higher energies simply interpolate between those of the end members of the solid solution. The resulting ground state suggests an extreme version of a random-anisotropy magnet, with many local moments and anisotropies, depending on the precise local configuration of the six B sites neighboring each magnetic Tb3+ ion., Comment: 6 pages, 6 figures