Kapellasite: a kagome quantum spin liquid with competing interactions

Magnetic susceptibility, NMR, muon spin relaxation, and inelastic neutron scattering measurements show that kapellasite, Cu_{3}Zn(OH)_{6}Cl_{2}, a geometrically frustrated spin-1/2 kagome antiferromagnet polymorphic with herbertsmithite, is a gapless spin liquid showing unusual dynamic short-range correlations of noncoplanar cuboc2 type which persist down to 20?mK. The Hamiltonian is determined from a fit of a high-temperature series expansion to bulk susceptibility data and possesses competing exchange interactions. The magnetic specific heat calculated from these exchange couplings is in good agreement with experiment. The temperature dependence of the magnetic structure factor and the muon relaxation rate are calculated in a Schwinger-boson approach and compared to experimental results.     

Macroscopic signature of protected spins in a dense frustrated magnet

The inability of systems of interacting objects to satisfy all constraints simultaneously leads to frustration. A particularly important consequence of frustration is the ability to access certain protected parts of a system without disturbing the others. For magnets such "protectorates" have been inferred from theory and from neutron scattering, but their practical consequences have been unclear. We show that a magnetic analogue of optical hole-burning can address these protected spin clusters in a well-known, geometrically frustrated Heisenberg system, gadolinium gallium garnet. Our measurements additionally provide a resolution of a famous discrepancy between the bulk magnetometry and neutron diffraction results for this magnetic compound.     

Dy2Ti2O7 spin ice: a test case for emergent clusters in a frustrated magnet

Dy2Ti2O7 is a geometrically frustrated magnetic material with a strongly correlated spin ice regime that extends from 1 K down to as low as 60 mK. The diffuse elastic neutron scattering intensities in the spin ice regime can be remarkably well described by a phenomenological model of weakly interacting hexagonal spin clusters, as invoked in other geometrically frustrated magnets. We present a highly refined microscopic theory of Dy2Ti2O7 that includes long-range dipolar and exchange interactions to third nearest neighbors and which demonstrates that the clusters are purely fictitious in this material. The seeming emergence of composite spin clusters and their associated scattering pattern is instead an indicator of fine-tuning of ancillary correlations within a strongly correlated state.     

Domain-wall spin dynamics in kagome antiferromagnets

We report magnetization and neutron scattering measurements down to 60 mK on a new family of Fe based kagome antiferromagnets, in which a strong local spin anisotropy combined with a low exchange path network connectivity lead to domain walls intersecting the kagome planes through strings of free spins. These produce unfamiliar slow spin dynamics in the ordered phase, evolving from exchange-released spin flips towards a cooperative behavior on decreasing the temperature, probably due to the onset of long-range dipolar interaction. A domain structure of independent magnetic grains is obtained that could be generic to other frustrated magnets.     

Probing magnetic order in EELS of chromite spinels using both multiple scattering (FEFF8.2) and DFT (WIEN2k)

The electron energy loss near edge structure on the O K-edge from chromite spinels contains fine structure from the hybridisation of the O p-orbitals and the Cr d-orbitals. Unlike the aluminates, a non-spin polarised calculation of this fine structure differs significantly from experimental observations. This is due to the large magnetic moment on the Cr. Calculations using simplified collinear ordering of the spins and the local spin density approximation give much improved agreement. A real space multiple scattering formalism and a reciprocal space density functional formalism give results in substantial agreement. In general, the actual spin arrangement of these chromites is not known since they are typically frustrated magnetic systems with ordering temperatures in the 10–20 K range. The calculations are based on the hypothesis that dynamic short range order persists to room temperature over the time scale of the interaction with the fast electron. However, it is possible that the observed effects are due to the strong paramagnetism present at room temperatures but which it is not possible to simulate accurately at present.     

Spin-liquid correlations in the Nd-langasite anisotropic kagomé antiferromagnet

Dynamical magnetic correlations in the geometrically frustrated Nd(3)Ga(5)SiO(14) compound were probed by inelastic neutron scattering on a single crystal. A scattering signal with a ring shape distribution in reciprocal space and unprecedented dispersive features was discovered. Comparison with calculated static magnetic scattering from models of correlated spins suggests that the observed phase is a spin liquid inherent to an antiferromagnetic kagomé-like lattice of anisotropic Nd moments.     

Quantum spin fluctuations in the spin-liquid state of Tb?Ti?O?

Neutron scattering experiments on a polycrystalline sample of the frustrated pyrochlore magnet Tb(2)Ti(2)O(7), which does not show any magnetic order down to 50 mK, have revealed that it shows condensation behavior below 0.4 K from a thermally fluctuating paramagnetic state to a spin-liquid ground state with quantum spin fluctuations. Energy spectra change from quasielastic scattering to a continuum with a double-peak structure at energies of 0 and 0.8 K in the spin-liquid state. Specific heat shows an anomaly at the crossover temperature.     

Magnetic properties of strongly frustrated and correlated systems

While consequences of frustration of magnetic interactions are much studied in localized spin systems, much less studies have been performed on frustrated metallic systems. However, several effects of strong geometrical frustration in metallic correlated system have also been experimentally observed in rare-earth or transition metal compounds: coexistence of magnetic and non-magnetic sites in ordered magnetic structure, heavy fermion behaviour and anomalous Hall effect due to spin chirality are consequences of frustration. An overview of the experimental observations and of the proposed models is given. Other interesting effects due to magnetic frustration in metallic systems, which have been predicted theoretically, are also reviewed.     

Noncoplanar magnetic ordering driven by itinerant electrons on the pyrochlore lattice

Exchange interaction tends to favor collinear or coplanar magnetic orders in rotationally invariant spin systems. Indeed, such magnetic structures are usually selected by thermal or quantum fluctuations in highly frustrated magnets. Here we show that a complex noncoplanar magnetic order with a quadrupled unit cell is stabilized by itinerant electrons on the pyrochlore lattice. Specifically, we consider a Kondo-lattice model with classical localized moments at quarter filling. The electron Fermi "surface" at this filling factor is topologically equivalent to three intersecting Fermi circles. Perfect nesting of the Fermi lines leads to magnetic ordering with multiple wave vectors and a definite handedness. The chiral order might persist without magnetic order in a chiral spin liquid at finite temperatures.     

Molecular spin resonance in the geometrically frustrated magnet MgCr2O4 by inelastic neutron scattering

We measured two magnetic modes with finite and discrete energies in an antiferromagnetic ordered phase of a geometrically frustrated magnet MgCr2O4 by single-crystal inelastic neutron scattering, and clarified the spatial spin correlations of the two levels: one is an antiferromagnetic hexamer and the other is an antiferromagnetic heptamer. Since these correlation types are emblematic of quasielastic scattering with geometric frustration, our results indicate instantaneous suppression of lattice distortion in an ordered phase by spin-lattice coupling, probably also supported by orbital and charge. The common features in the two levels, intermolecular independence and discreteness of energy, suggest that the spin molecules are interpreted as quasiparticles (elementary excitations with energy quantum) of highly frustrated spins, in analogy with the Fermi liquid approximation.     

Nonmonotonic zero-point entropy in diluted spin ice

Water ice and spin ice are important model systems in which theory can directly account for "zero-point" entropy associated with quenched configurational disorder. Spin ice differs from water ice in the important respect that its fundamental constituents, the spins of the magnetic ions, can be removed through replacement with nonmagnetic ions while keeping the lattice structure intact. In order to investigate the interplay of frustrated interactions and quenched disorder, we have performed systematic heat capacity measurements on spin ice materials which have been thus diluted up to 90%. Investigations of both Ho and Dy spin ices reveal that the zero-point entropy depends nonmonotonically on dilution and approaches the value of Rln2 in the limit of high dilution. The data are in good agreement with a generalization of Pauling's theory for the entropy of ice.     

Low-temperature heat transport of spin-gapped quantum magnets

This article reviews low-temperature heat transport studies of spin-gapped quantum magnets in the last few decades. Quantum magnets with small spins and low dimensionality exhibit a variety of novel phenomena. Among them, some systems are characteristic of having quantum-mechanism spin gap in their magnetic excitation spectra, including spin-Peierls systems, S=1 Haldane chains, S= 1/2 spin ladders, and spin dimmers. In some particular spin-gapped systems, the XY-type antiferromagnetic state induced by magnetic field that closes the spin gap can be described as a magnon Bose-Einstein condensation (BEC). Heat transport is effective in probing the magnetic excitations and magnetic phase transitions, and has been extensively studied for the spin-gapped systems. A large and ballistic spin thermal conductivity was observed in the two-leg Heisenberg S=1/2 ladder compounds. The characteristic of magnetic thermal transport of the Haldane chain systems is quite controversial on both the theoretical and experimental results. For the spin-Peierls system, the spin excitations can also act as heat carriers. In spin-dimer compounds, the magnetic excitations mainly play a role of scattering phonons. The magnetic excitations in the magnon BEC systems displayed dual roles, carrying heat or scattering phonons, in different materials.     

Chiral-like critical behavior in the antiferromagnet cobalt glycerolate

Critical exponents closely matching those of the N=2 chiral universality class have been obtained for the layered magnetic system cobalt glycerolate using muon spin relaxation. This class was originally introduced to represent geometrically frustrated triangular stacked-layer XY magnets with chiral noncollinear spin structures. Since the present magnetic system is a canted XY system without geometrical frustration or chiral degeneracy, the results indicate that the order parameter for canting in this system plays a similar role to the chiral order parameter in the geometrically frustrated systems, strongly suggesting that both types of noncollinear system share the same universality class.     

Transport in quasi one-dimensional spin-1/2 systems

We present numerical results for the spin and thermal conductivity of one-dimensional (1D) quantum spin systems. We contrast the properties of integrable models such as the spin-1/2 XXZ chain against nonintegrable ones such as frustrated and dimerized chains. The thermal conductivity of the XXZ chain is ballistic at finite temperatures, while in the nonintegrable models, this quantity is argued to vanish. For the case of frustrated and dimerized chains, we discuss the frequency dependence of the transport coefficients. Finally, we give an overview over related theoretical work on intrinsic and extrinsic scattering mechanisms of quasi-1D spin systems.     

Chiral spin pairing in helical magnets

A concept of chiral spin pairing is introduced to describe a vector-chiral liquid-crystal order in frustrated spin systems. It is found that the chiral spin pairing is induced by the coupling to phonons through the Dzyaloshinskii-Moriya interaction and the four-spin exchange interaction of the Coulomb origin under the edge-sharing network of magnetic and ligand ions. This produces two successive second-order phase transitions upon cooling: an O(2) chiral spin nematic, i.e., spin cholesteric, order appears with an either parity, and then the O(2) symmetry is broken to yield a helical magnetic order. Possible candidate materials are also discussed as new multiferroic systems.     

The apparent Dingle temperature in Zn−Mn,Zn−Cr,and Zn−Fe

The apparent Dingle temperature of the 3rd zone needles in several alloys of Zn?Mn, Zn?Cr and Zn?Fe has been determined from the absolute amplitude of the de Haas-van Alphen effect over the temperature range 1.6 K to 4.2 K and the field range 0 to 9 kG. The results show clearly that potential scatteringnot spin scattering dominates in all three systems. In addition, a “cross-over” behaviour in the de Haas-van Alphen amplitudes results from the scattering of the magnetic moments of the impurity spin.     

Magnetic structure of the GdAl3 intermetallic compound as seen via Mössbauer spectroscopy data for 119Sn impurity atoms

The magnetic hyperfine interaction for ¹¹⁹Sn impurity atoms in GdAl₃ frustrated antiferromagnetic compound has been investigated by Mössbauer spectroscopy technique. Two magnetic subspectra with the ratio of the intensities 2:1 were observed. At 4.5 K, the values of the magnetic hyperfine field are 4.00(2) and 1.35(2) T. The peculiarities of the Mössbauer spectrum provide an opportunity to propose a plausible model of the spin arrangement in the GdAl₃ lattice. In each GdAl₃ basal layer, the magnetic moments of the Gd atoms form three-sublattice 120° spin structure that is peculiar to magnetically frustrated compounds. The appearance of two magnetically nonequivalent Sn sites is a result of vector summation of the transferred polarizations from Gd moments located in two adjacent GdAl₃ planes. The anomalous temperature behavior of the hyperfine field is characteristic of frustrated systems with competing exchange interactions.     

Disordered and ordered states in a frustrated Heisenberg Hamiltonian with spatial anisotropy

We use a recently proposed perturbative numerical renormalization group algorithm to investigate ground-state properties of a frustrated three-dimensional Heisenberg model on an anisotropic lattice. We analyze the ground-state energy, the finite size spin gap and the static magnetic structure factor. We find in two dimensions a frustration-induced gapless spin liquid state which separates two magnetically ordered phases. In the spin liquid state, the magnetic structure factor shows evidence that this state is made of nearly disconnected chains reminiscent of a sliding Luttinger liquid. This spin liquid state is unstable against unfrustrated interplane couplings.     

Topological spin liquid on the hyperkagome lattice of Na4Ir3O8

Recent experiments on the "hyperkagome" lattice system Na4Ir3O8 have demonstrated that it is a rare example of a three-dimensional spin-1/2 frustrated antiferromagnet. We investigate the role of quantum fluctuations as the primary mechanism lifting the macroscopic degeneracy inherited by classical spins on this lattice. In the semiclassical limit we predict, based on large-N calculations, that an unusual q[over -->]=0 coplanar magnetically ordered ground state is stabilized with no local zero modes that correspond to local deformations of the spin configurations. This phase melts in the quantum limit and a gapped topological Z2 spin liquid phase emerges. In the vicinity of this quantum phase transition, we study the dynamic spin structure factor and comment on the relevance of our results for future neutron scattering experiments.     

Double-peak specific heat feature in frustrated antiferromagnetic clusters

We study the nature of a double-peak specific heat structure in kagome clusters. A cluster containing 12 spins is considered thoroughly by means of numerical diagonalization. On the basis of analysis of exact spectra, simple models are proposed to explain the nature of the low-T peak at T _l <δ(δ is the spin gap) in this case and in those of larger clusters studied so far. Using these models, we show that the rapid increase in density of states just above the spin gap gives rise to the peak and clarify the weak magnetic field sensitivity of the peak. Spin susceptibility and entropy are considered as well. Our approach could be appropriate for other frustrated antiferromagnetic systems.