Muon spin relaxation and susceptibility studies of the pure and diluted spin 1/2 kagomé-like lattice system (CuxZn(1-x))3V2O7(OH2) 2H2O

Orbital Transitions and Frustrated Magnetism in the Kagome-Type Copper Mineral Volborthite

Volborthite Cu₃V₂O₇(OH)₂·2H₂O is a copper mineral that materializes a two-dimensional quantum magnet comprising a kagome net of spin-¹/₂ Cu²⁺ ions. We prepared single crystals of volborthite using hydrothermal conditions and investigated their crystal structures and magnetic properties. Unusual orbital "switching" and "flipping" transitions were observed: in the former type of transition (switching), the Cu 3d orbital occupied by an unpaired electron changes between the d(3z²-r²) and d(x²-y²) types, and in the latter type of transition (flipping), the d(x²-y²)-type orbitals change their directions. Their origin is ascribed to variations in the orientation of water molecules in the gap between the kagome layers and the accompanying changes of hydrogen bonding. These orbital transitions dramatically modify the magnetic interactions between Cu²⁺ spins, from the anisotropic kagome type to the formation of spin trimers over the kagome net. The effective spin ¹/₂ generated on the trimers exhibits a frustrated magnetism, resulting in a rich phase diagram in the magnetic fields. Volborthite is a unique compound showing an exceptional interplay between the orbital and spin degrees of freedom.

Electrodynamics of quantum spin liquids

Quantum spin liquids attract great interest due to their exceptional magnetic properties characterized by the absence of long-range order down to low temperatures despite the strong magnetic interaction. Commonly, these compounds are strongly correlated electron systems, and their electrodynamic response is governed by the Mott gap in the excitation spectrum. Here we summarize and discuss the optical properties of several two-dimensional quantum spin liquid candidates. First we consider the inorganic material herbertsmithite ZnCu₃(OH)₆Cl₂ and related compounds, which crystallize in a kagome lattice. Then we turn to the organic compounds [Formula: see text]-EtMe₃Sb[Pd(dmit)₂]₂, κ-(BEDT-TTF)₂Ag₂(CN)₃ and κ-(BEDT-TTF)₂Cu₂(CN)₃, where the spins are arranged in an almost perfect triangular lattice, leading to strong frustration. Due to differences in bandwidth, the effective correlation strength varies over a wide range, leading to a rather distinct behavior as far as the electrodynamic properties are concerned. We discuss the spinon contributions to the optical conductivity in comparison to metallic quantum fluctuations in the vicinity of the Mott transition.

Possible spin frustration in Nd2Ti2O7 probed by muon spin relaxation

Muon spin relaxation on Nd2Ti2O7 (NTO) and NdLaTi2O7 (NLTO) compounds are presented. The time spectra for both compounds are as expected for the paramagnetic state at high temperatures, but deviate from the exponential function below around 100 K. Firstly, the muon spin relaxation rate increases with decreasing temperature and then levels off below around 10 K, which is reminiscent of the frustrated systems. An enhancement of the relaxation rate by a longitudinal field in the paramagnetic state is observed for NTO and eliminated by a magnetic dilution for the NLTO sample. This suggests that the spectral density is modified by a magnetic dilution and thus indicates that the spins behave cooperatively rather than individually. The zero-field measurement at 0.3 K indicates that the magnetic ground state for NTO is ferromagnetic.

Neutron scattering and μSR investigations of the low temperature state of LuCuGaO₄

LuCuGaO₄ has magnetic Cu(2+) and diamagnetic Ga(3+) ions distributed on a triangular bilayer and is suggested to undergo a spin glass transition at Tg ∼ 0.4 K. Using μSR (muon spin rotation) and neutron scattering measurements, we show that at low temperature the spins form a short range correlated state with spin fluctuations detectable over a wide range of timescales: at 0.05 K magnetic fluctuations can be detected in both the μSR time window and also extending beyond 7 meV in the inelastic neutron scattering response, indicating magnetic fluctuations spanning timescales between ∼10(-5) and ∼10(-10) s. The dynamical susceptibility scales according to the form χ″(ω)T(α), with α = 1, throughout the measured temperature range (0.05-50 K). These effects are associated with quantum fluctuations and some degree of structural disorder in ostensibly quite different materials, including certain heavy fermion alloys, kagome spin liquids, quantum spin glasses, and valence bond glasses. We therefore suggest that LuCuGaO₄ is an interesting model compound for the further examination of disorder and quantum magnetism.

Possible quantum diffusion of polaronic muons in Dy(2)Ti(2)O(7) spin ice

We interpret recent measurements of the zero field muon relaxation rate in the magnetic pyrochlore Dy(2)Ti(2)O(7) as resulting from the quantum diffusion of muons in the material. In this scenario, the plateau observed at low temperature (< 7 K) in the relaxation rate is due to coherent tunneling of muons through a spatially disordered spin state and not to any magnetic fluctuations persisting at low temperature. Two further regimes either side of a maximum relaxation rate at T* = 50 K correspond to a crossover between tunneling and incoherent activated hopping motion of the muon. Our fit of the experimental data is compared with the case of muonium diffusion in KCl.

Calculation of the expected zero-field muon relaxation rate in the geometrically frustrated rare earth pyrochlore Gd(2)Sn(2)O(7) antiferromagnet

The magnetic insulator Gd(2)Sn(2)O(7) is one of many geometrically frustrated magnetic materials known to exhibit a nonzero muon spin polarization relaxation rate, λ(T), down to the lowest temperature (T) studied. Such behaviour is typically interpreted as signalling the presence of persistent spin dynamics (PSD) of the host material. In the case of Gd(2)Sn(2)O(7), such PSD comes as a surprise since magnetic specific heat measurements suggest conventional gapped magnons, which would naively lead to an exponentially vanishing λ(T) as T → 0. In contrast to most materials that display PSD, the ordered phase of Gd(2)Sn(2)O(7) is well characterized and both the nature and the magnitude of the interactions have been inferred from the magnetic structure and the temperature dependence of the magnetic specific heat. Based on this understanding, the temperature dependence of the muon spin polarization relaxation through the scattering of spin waves (magnons) is calculated. The result explicitly shows that, despite the unusual extensive number of weakly dispersive (gapped) excitations characterizing Gd(2)Sn(2)O(7), a remnant of the zero modes of the parent frustrated pyrochlore Heisenberg antiferromagnet, the temperature dependence of the calculated λ(T) differs dramatically from the experimental one. Indeed, the calculation conforms to the naive expectation of an exponential collapse of λ(T) at temperatures below ∼ 0.7 K. This result, for the first time, illustrates crisply and quantitatively the paradox that presents itself with the pervasive occurrence of PSD in highly frustrated magnetic systems as evinced by muon spin relaxation measurements.

The giant anomalous Hall effect in the ferromagnet Fe3Sn2--a frustrated kagome metal

The kagome-bilayer material Fe(3)Sn(2) has recently been shown to be an example of a rare class of magnet-a frustrated ferromagnetic metal. While the magnetism of Fe(3)Sn(2) appears to be relatively simple at high temperature, with localized moments parallel to the c-axis (T(C) = 640 K), upon cooling the competing exchange interactions and spin frustration become apparent as they cause the moments to become non-collinear and to rotate towards the kagome plane, forming firstly a canted ferromagnetic structure and then a re-entrant spin glass (T(f) approximately equal 80 K). In this work we show that Fe(3)Sn(2) possesses an unusual anomalous Hall effect. The saturated Hall resistivity of Fe(3)Sn(2) is 3.2 µΩ cm at 300 K, almost 20 times higher than that of typical itinerant ferromagnets such as Fe and Ni. The anomalous Hall coefficient R(s) is 6.7 × 10(-9) Ω cm G(-1) at 300 K, which is three orders of magnitude larger than that of pure Fe, and obeys an unconventional scaling with the longitudinal resistivity, ρ(xx), of R(s) is proportional to ρ(xx)(3.15). Such a relationship cannot be explained by either the conventional skew or side-jump mechanisms, indicating that the anomalous Hall effect in Fe(3)Sn(2) has an extraordinary origin that is presumed to be related to the underlying frustration of the magnetism. These findings demonstrate that frustrated ferromagnets, whether based on bulk materials or on artificial nanoscale structures, can provide new routes to room temperature spin-dependent electron transport properties suited to application in spintronics.

Phase diagram and spin dynamics in volborthite with a distorted kagome lattice

We report a (51)V-NMR study on a high-quality powder sample of volborthite Cu3V2O7(OH)2 . 2H2O, a spin-1/2 Heisenberg antiferromagnet on a distorted kagome lattice formed by isosceles triangles. In the magnetic fields below 4.5 T, a sharp peak in the nuclear spin-lattice relaxation rate 1/T(1) accompanied with line broadening revealed a magnetic transition near 1 K. The low temperature phase shows anomalies such as a Lorentzian line shape, a 1/T(1) proportional, variantT behavior indicating dense low-energy excitations, and a large spin-echo decay rate 1/T(2) pointing to unusually slow fluctuations. Another magnetic phase appears above 4.5 T with less anomalous spectral shape and dynamics.

Easy-axis kagome antiferromagnet: local-probe study of Nd3Ga5SiO14

We report a local-probe investigation of the magnetically anisotropic kagome compound Nd3Ga5SiO14. Our zero-field muon spin relaxation (muSR) results provide direct evidence of a fluctuating collective paramagnetic state down to 60 mK, supported by a wipeout of the Ga nuclear magnetic resonance (NMR) signal below 25 K. At 60 mK a dynamics crossover to a much more static state is observed by muSR in magnetic fields above 0.5 T. Accordingly, the NMR signal is recovered at low T above a threshold field, revealing a rapid temperature and field variation of the magnetic fluctuations.

63Cu, 35Cl, and 1H NMR in the S=1/2 Kagome lattice ZnCu3(OH)6Cl2

ZnCu(3)(OH)(6)Cl(2) (S=1/2) is a promising new candidate for an ideal Kagome Heisenberg antiferromagnet, because there is no magnetic phase transition down to approximately 50 mK. We investigated its local magnetic and lattice environments with NMR techniques. We demonstrate that the intrinsic local spin susceptibility decreases toward T=0, but that slow freezing of the lattice near approximately 50 K, presumably associated with OH bonds, contributes to a large increase of local spin susceptibility and its distribution. Spin dynamics near T=0 obey a power-law behavior in high magnetic fields.

Quantum magnetism in the paratacamite family: towards an ideal kagomé lattice

We report muon spin rotation measurements on the S=1/2 (Cu2+) paratacamite ZnxCu4-x(OH)6Cl2 family. Despite a Weiss temperature of approximately -300 K, the x=1 compound is found to have no transition to a magnetic frozen state down to 50 mK as theoretically expected for the kagomé Heisenberg antiferromagnet. We find that the limit between a dynamical and a partly frozen ground state occurs around x=0.5. For x=1, we discuss the relevance to a singlet picture.

Ground state of the kagomé-like S=1/2 antiferromagnet volborthite Cu3V2O7(OH)2 x 2H2O

The volborthite compound is one of the very few realizations of S=1/2 quantum spins on a highly frustrated kagomé-like lattice. Low-T SQUID measurements reveal a broad magnetic transition below 2 K which is further confirmed by a peak in the 51V nuclear spin relaxation rate (1/T1) at 1.4 K +/- 0.2 K. Through 51V NMR, the ground state (GS) appears to be a mixture of different spin configurations, among which 20% corresponds to a well defined short-range order, possibly of the sqrt(3) x sqrt(3) type. While the freezing involves all the Cu2+ spins, only 40% of the copper moment is actually frozen which suggests that quantum fluctuations strongly renormalize the GS.

Magnetic density of states at low energy in geometrically frustrated systems

Using muon-spin-relaxation measurements we show that the pyrochlore compound Gd(2)Ti(2)O(7), in its magnetically ordered phase below approximately 1 K, displays persistent spin dynamics down to temperatures as low as 20 mK. The characteristics of the induced muon relaxation can be accounted for by a scattering process involving two magnetic excitations, with a density of states characterized by an upturn at low energy and a small gap depending linearly on the temperature. We propose that such a density of states is a generic feature of geometrically frustrated magnetic materials.

Low-energy singlets in the Heisenberg antiferromagnet on the kagomé lattice

The spin-1/2 Heisenberg antiferromagnet on the kagomé lattice, is mapped by contractor renormalization to a spin-pseudospin Hamiltonian on the triangular superlattice. Variationally, we find a ground state with columnar dimer order. Dimer orientation fluctuations are described by an effective O(2) model at energies above an exponentially suppressed clock mass scale. Our results explain the large density of low-energy singlets observed numerically, and the nonmagnetic T2 specific heat observed experimentally.

muSR study of the quantum dynamics in the frustrated S=3/2 kagomé bilayers

We present muSR experiments in the S=3/2 kagomé bilayer compound Ba(2)Sn(2)ZnGa(10-7p)Cr(7p)O22 [BSZCGO(p)] and compare it to the isostructural SrCr(9p)Ga(12-9p)O19 [SCGO(p)], including for the latter new results for p > or =0.89. Quantum-dynamical low energy magnetic excitations are evidenced in this novel compound. We study the evolution of the muon relaxation rate with p, T, and field. A phenomenological model for the muon relaxation based on sporadic dynamics due to spin excitations in a singlet sea proposed by Uemura et al. is extended to all fields and T range. Its connection to the RVB picture is discussed, and we argue that such coherent states might mediate the interactions between "impurities" which induce the spin glass freezing.

Magnetic-field induced spin-Peierls instability in strongly frustrated quantum spin lattices

For a class of frustrated antiferromagnetic spin lattices (in particular, the square-kagomé and kagomé lattices) we discuss the impact of recently discovered exact eigenstates on the stability of the lattice against distortions. These eigenstates consist of independent localized magnons embedded in a ferromagnetic environment and become ground states in high magnetic fields. For appropriate lattice distortions fitting to the structure of the localized magnons the lowering of magnetic energy can be calculated exactly and is proportional to the displacement of atoms leading to a spin-Peierls lattice instability. Since these localized states are present only for high magnetic fields, this instability might be driven by magnetic-field. The hysteresis of the spin-Peierls transition is also discussed.