Table of contents

The Highly Frustrated Magnetism 2003 conference took place on 26 - 30 August 2003 at the Institut Laue Langevin, Grenoble, France. This meeting was a follow-up to the HFM2000 meeting held in Waterloo, Canada, while another topical meeting took place in Santa Fe, New Mexico, USA, in 2002. The HFM2003 conference attracted participants from all over the world, with notable delegations from USA, Canada and Japan, as well as from several European countries. Both theoretical and experimental aspects of the physics of frustrated magnets were treated by the plenary and invited speakers as well as in the contributed talks and posters. This special issue of Journal of Physics: Condensed Matter provides a timely presentation of the recent progress and important topics in the field of frustrated magnetism. At the start of this issue we have included a comprehensive overview on strategies of materials synthesis by A~Harrison. Reviews on the topics treated have recently been published by two of the plenary speakers and their collaborators (Claire~Lhuillier [1, 2], A~Ramirez [3]) and the proceedings of the HFM2000 [4] remain a valuable source of reference.

The organization of the conference was financed through the support of the Institut Laue Langevin (ILL), the Centre National de la R\'echerche Scientifique (CNRS), Grenoble, France, the City Council of Grenoble and the Neutron Round Table (European Union Framework Programme 5). We wish to thank all these bodies for their generous help.

In addition we would also like to thank the following people who helped during both the organization and running of the conference: Laurence Tellier, Alison Mader and Serge Claisse.

References

[1] Lhuillier C and Misguich G 2002 High Magnetic Fields ed C Berthier, L P Levy and G Martinez (Berlin: Springer)

[2] Misguich G and Lhuillier C Frustrated Spin Systems ed H T Diep (New York: World Scientific) to be published Preprint cond-mat 0310405

[3] Ramirez A P 2001 Handbook of Magnetic Materials vol 13 ed K H J Buschow (Amsterdam: Elsevier) pp 423--520

[4] Gingras M (ed) 2000 Can. J. Phys.79 1283-1597

The PDF gives details of the International Programme Committee, the Local Organizing Committee and a full list of participants.

A major constraint on experimental studies of geometrically frustrated magnets (GFMs) is the availability of suitable samples that provide tangible models to inspire or test theory. Most model GFMs studied to date have been ionic compounds, for which simple models of sphere packing predict an abundance of frustrated motifs—triangular plaquettes within close-packed layers, and nets of tetrahedra in three dimensions. The various frustrated topologies that arise naturally in such systems when they are decorated with moments and exchange interactions are reviewed. An alternative approach to the design of GFMs is to build networks of magnetic species from building blocks whose geometry or valence electron configuration lead to a strong preference for a particular connectivity. This strategy may be used to build relatively dense, mainly covalently bound networks of atoms or small molecules, or more open networks in which the building blocks are larger units. Most of the applications of this type of material have been in the field of catalysis so far, but they also present new opportunities to provide GFMs with rare or new lattice topologies.

The A-site-ordered/disordered manganese perovskites, RBaMn₂O₆/ R_0.5 Ba_0.5MnO₃ (R = Y and rare earth elements), are reviewed. RBaMn₂O₆ displays remarkable features: (1) the charge/orbital order (CO) transition at relatively high temperatures far above 300 K, (2) a new stacking variation of the CE-type CO with a fourfold periodicity along the c-axis, (3) the presence of structural transition possibly accompanied by d_x²−y² orbital order and (4) electronic phase segregation. These novel structural and electromagnetic properties are discussed in terms of the structural characteristic that the MnO₂ square sublattice is sandwiched by two types of rock-salt layer, R O and BaO, with different lattice sizes. Such structure introduces a strong frustration to the MnO₂ sublattice and gives a new perturbation to the competition of multiple degrees of freedom among charge, orbital, spin and lattice. In R_0.5Ba_0.5MnO₃ with a primitive cubic perovskite cell, on the other hand, the magnetic glassy states are dominant as the ground state. A peculiar behaviour, steplike ultrasharp magnetization and resistivity changes, has been observed in Pr_0.5Ba_0.5MnO₃.

New layered magnetic materials, (MCl)Ca₂Ta₃O₁₀ (M = Cu, Fe), have been prepared by ion-exchange reactions of non-magnetic perovskite derivatives, ACa₂Ta₃O₁₀ (A = Rb, Li), in corresponding anhydrous molten salts. Powder x-ray diffraction patterns of the products are successfully indexed assuming tetragonal symmetry with cell dimensions a = 3.829 Å and c = 15.533 Å for Cu, and a = 3.822 Å and c = 15.672 Å for Fe. Being separated by the Ca₂Ta₃O₁₀ triple-layer perovskite slabs, the transition-metal chloride (MCl) network provides a two-dimensional magnetic lattice. Magnetic susceptibility measurements show that (CuCl)Ca₂Ta₃O₁₀ is in an antiferromagnetic state below 8 K, while (FeCl)Ca₂Ta₃O₁₀ has two anomalies at 91 and 125 K, suggesting successive phase transitions due to geometrical spin frustration.

We review a number of different approaches which have been used in order to explain the physical properties of some metallic spinels, in particular of magnetite Fe₃O₄ and LiV₂O₄. It is also pointed out that in geometrically frustrated lattices such as the pyrochlore structure one may have excitations with fractional charge.

Temperature and magnetic field dependences of the anomalous Hall effect have been investigated for single crystals of Mo-based ferromagnets with pyrochlore structure. The Hall resistivity of Nd₂Mo₂O₇ compound shows unconventional temperature dependence whereas Gd₂Mo₂O₇ exhibits rather normal behaviour. The Berry phase model can explain the difference well; it is attributed to the difference in nature of the anisotropy of the rare-earth moment and the resultant Mo spin state. The Hall resistivity of Nd₂Mo₂O₇ changes its sign with increasing field applied along the [111] direction, while it monotonically approaches zero with the field applied along the [100] or [110] direction. This behaviour is also in accord with the prediction of the Berry phase theory.

At low temperatures LiV₂O₄ exhibits short range paramagnetic correlations, peaked on momentum transfer . A marked evolution in the spectral intensity towards low Q values () and low energy transfers ω is observed as the temperature is increased above 2 K (to  K and higher). The form of the spectral response is rather complex, requiring at least two spectral components to describe the scattering over the relatively small energy range investigated. We show that the observed paramagnetic spin fluctuations in LiV₂O₄, i.e. the spin degrees of freedom, can account reasonably well for its large specific heat coefficient γ (= C/T).

The Knight shift K and the nuclear spin–lattice relaxation time T₁ of ⁷Li have been measured under high pressure up to 4.74 GPa. 1/T₁T becomes larger on applying higher pressure below 10 K and does not obey the T₁T = constant relation down to 1 K. Meanwhile, K is independent of pressure above 2 GPa, indicating that the uniform component of the susceptibility does not change under high pressure. These results indicate that some antiferromagnetic fluctuations with wavevector dominate the relaxation rate in LiV₂O₄ near the boundary of the pressure induced insulating phase. It is noted that the pressure dependence of T₁ for LiV₂O₄ is opposite to that of typical Ce HF compounds, such as CeCu_5.9Au_0.1 and CeCu₂Si₂. At the highest pressure of 4.74 GPa, we found that 1/T₁ obeys a power law dependence of T^2/3 over the wide T range between 60 mK and 10 K. The spin dynamics under high pressure will be discussed.

Motivated by recent inelastic neutron scattering experiments we examine the magnetic properties of LiV₂O₄. We consider a model which describes the half-filled localized A_1g spins interacting via frustrated antiferromagnetic Heisenberg exchange and coupled by local Hund's interactions with the 1/8-filled itinerant E_g band and study it within an exact diagonalization scheme. In the present study we limited the analysis to the case of the cluster of two isolated tetrahedrons. We found that both the ground state structure and low-lying excitations depend strongly on the value of Hund's coupling, which favours the triplet states. With increasing temperature the triplet states become more and more populated, which results in the formation of non-zero residual magnetic moment. We present the temperature dependence of the calculated magnetic moment and of the spin–spin correlation functions at different values of Hund's coupling and compare them with the experimental results.

In this work, we report on low-temperature x-ray diffraction, electron-spin-resonance and magnetic-susceptibility measurements performed on η-Na_1.286V₂O₅. We show that the low-temperature structure of this compound differs from that at room temperature mainly by the doubling of the unit cell in the b direction. The magnetic measurements give evidence for the opening of a spin gap which we discuss in conjunction with the low-temperature structure of this compound.

Neutron scattering and ac-susceptibility techniques have been performed on the spin ice material Ho₂Ti₂O₇ to study the spin relaxation processes in the 'hot' paramagnetic phase (T>1 K). Neutron spin echo (NSE) proves that above  K the spin dynamics are governed by a thermally activated single-ion process. At lower temperatures (T<15 K) this cannot account for the spin dynamics found in ac-susceptibility measurements. It is inferred that a second, slower process, with a different thermal signature dominates. We suggest that this is a quantum-mechanical tunnelling process between different spin states separated by a large energy barrier.

We have studied the spin dynamics of several antiferromagnetic pyrochlore oxides. These magnets are geometrically frustrated and only reach their ground states at temperatures much lower than that expected from mean field theory. Here we present data on the magnetic nature, especially the spin dynamics of Tb₂Ti₂O₇, Gd₂Ti₂O₇ and Y₂Mo₂O₇. In these systems the ground states are found to be very different. Y₂Mo₂O₇ freezes completely into a spin glass-like state, Tb₂Ti₂O₇ is a cooperative paramagnetic and remains dynamic down to 15 mK and Gd₂Ti₂O₇ enters a unique partially ordered state at  K.

The rare earth titanates show unusual types of short range magnetic order, known as spin liquid and spin ice states, which arise from the geometrical frustration of the pyrochlore lattice. We have investigated the effect of applied pressures on these magnetic states by means of powder neutron diffraction, up to 8 GPa. In the spin liquid Tb₂Ti₂O₇, pressure induces a long range antiferromagnetic order, coexisting with the spin liquid state below the Néel temperature (T_N = 2.1 K). The onset of long range order coincides with a strong decrease of the diffuse intensity, due to a gradual transfer from the liquid to the ordered state as the temperature decreases. The short range correlations are also modified under pressure, even above T_N. In contrast, in Ho₂Ti₂O₇ the spin ice state remains stable under pressure, as was checked up to 6 GPa, and down to 1.4 K. The short range correlations are unaffected here. The possible origins of this behaviour are discussed.

Thermal fluctuations lift the high ground state degeneracy of the classical nearest neighbour pyrochlore antiferromagnet, with easy plane anisotropy, giving a first-order phase transition to a long range ordered state. We show, from spin wave analysis and numerical simulation, that even below this transition a continuous manifold of states, of dimension N^2/3, exist (N is the number of degrees of freedom). As the temperature goes to zero a further 'order by disorder' selection is made from this manifold. The pyrochlore antiferromagnet Er₂Ti₂O₇ is believed to have an easy plane anisotropy and is reported to have the same magnetic structure. This is perhaps surprising, given that the dipole interaction lifts the degeneracy of the classical model in favour of a different structure. We interpret our results in the light of these facts.

The pyrochlore antiferromagnet Tb₂Ti₂O₇ has proven to be an enigma to experimentalists and theorists working on frustrated magnetic systems. The experimentally determined energy level structure suggests a local Ising antiferromagnet at low temperatures,  K. An appropriate model then predicts a long-range ordered Q = 0 state below approximately 2 K. However, muon spin resonance (μSR) experiments reveal a paramagnetic structure down to tens of millikelvins. The importance of fluctuations out of the ground state effective Ising doublet has been recently understood, for the measured paramagnetic correlations cannot be described without including the higher crystal field states. However, these fluctuations treated within the random phase approximation (RPA) fail to account for the lack of ordering in this system below 2 K. In this work, we briefly review the experimental evidence for the collective paramagnetic state of Tb₂Ti₂O₇. The basic theoretical picture for this system is discussed, where results from classical spin models are used to motivate the investigation of quantum effects to lowest order via the RPA. Avenues for future experimental and theoretical work on Tb₂Ti₂O₇ are presented.

We report on the specific heat and the entropy of single crystals of the spin ice compound Dy₂Ti₂O₇ down to 100 mK under magnetic fields along the [111] direction in order to study detailed low temperature properties of the Kagome ice state. Previously, we reported anisotropic release of the residual entropy reflecting the Ising anisotropy. We pointed out that the anisotropic behaviour can be viewed as the difference in frustration dimensionality. In an intermediate field, the entropy for the [111] field direction is different from those of the other principal directions. This is because the frustration structure changes from that of a three-dimensional (3D) pyrochlore to that of a two-dimensional (2D) Kagome lattice with constraint from the ice rule, accompanied by a different zero-point entropy value. We call this state 'the Kagome ice state'. In the Kagome ice state, the value of the residual entropy, ΔS_Kagome, is estimated as 0.598 J K⁻¹/(mol Dy) by Pauling's method.

In the present experiment, we observed that the specific heat at 1 T exhibits a sharp peak at 400 mK and an anomalous upturn at lower temperature. This peak indicates the entropy release from a 1-in 3-out state with no residual entropy to a 1-in 3-free state.

The heat capacity c_p(T,H) in magnetic fields up to 14 T for polycrystalline samples of Gd₂Mo₂O₇ and Sm₂Mo₂O₇ pyrochlore compounds is presented. In contrast to previous work, for both compounds well defined peaks in c_p(T,H = 0) at 73 K (Gd) and 70 K (Sm) mark the onset of ferromagnetic order in the Mo subsystem. For Gd₂Mo₂O₇ a small step-like anomaly at 11.3 K on top of a large Schottky-like anomaly indicates partial magnetic ordering in the Gd subsystem. The magnetic contributions to c_p(T) are estimated by comparing with a proper lattice reference and the evolution of magnetic entropies with temperature and external field is analysed.

Multiple spin exchange processes lead to strong quantum frustration in low density solid phases of ³He. It has been predicted theoretically that the 4/7 phase of the second layer of ³He adsorbed on graphite is a two-dimensional RVB magnet with a spin-liquid ground state. We have measured the nuclear magnetization of the second layer of ³He adsorbed on a Papyex substrate preplated by a monolayer of ⁴He, using cw-NMR techniques, for a large temperature range (0.1–400 mK). Special attention has been devoted to carefully eliminating from our sample spurious phases and paramagnetic defects. The analysis of the data provides us with information on the presence of a spin gap in the excitation spectrum and on the density of states of the magnetic excitations of this phase.

The low temperature properties of fermionic solids are governed by spin exchanges. Near the melting transition, the spin-exchange energy increases as well as the relative contribution of large loops. In this paper, we check the convergence of the multi-spin exchange model and the validity of the Thouless theory near the melting of the Wigner crystal in two dimensions. Exchange energies are computed using a path integral Monte Carlo for loop sizes up to 8, at r_s = 40, 50 and 75. The data are then fitted to a geometric model. Then the exchange energies are extrapolated to larger sizes in order to evaluate their contributions to the leading term of the magnetic susceptibility and the specific heat. These results are used to check the convergence of the multi-spin exchange model.

This paper explores the large-S route to quantum disorder in the Heisenberg antiferromagnet on the pyrochlore lattice and its homologues in lower dimensions. It is shown that zero-point fluctuations of spins shape up a valence-bond solid at low temperatures for one two-dimensional lattice and a liquid with very short-range valence-bond correlations for another. A one-dimensional model demonstrates potential significance of quantum interference effects (as in Haldane's gap): the quantum melting of a valence-bond order yields different valence-bond liquids for integer and half-integer values of S.

Spin glasses are frustrated magnetic systems due to a random distribution of ferro- and antiferromagnetic interactions. An experimental three dimensional (3d) spin glass exhibits a second order phase transition to a low temperature spin glass phase regardless of the spin dimensionality. In addition, the low temperature phase of Ising and Heisenberg spin glasses exhibits similar non-equilibrium dynamics and an infinitely slow approach towards a thermodynamic equilibrium state. There are, however, significant differences in the detailed character of the dynamics as to memory and rejuvenation phenomena, and the influence of critical dynamics on the behaviour. In this paper some aspects of the non-equilibrium dynamics of an Ising and a Heisenberg spin glass are briefly reviewed and some comparisons are made to other glassy systems that exhibit magnetic non-equilibrium dynamics.

We solve the SU(N) Heisenberg spin-glass model in the limit of large N focusing on the small temperature behaviour of the specific heat C_V within the spin-glass phase. We consider the influence of the quantum fluctuations and observe that when they are strong the low T behaviour is quadratic. As quantum fluctuations decrease for large values of S, a broad maximum appears in the C_V(T)/T curve.

We discuss the slow, nonequilibrium, dynamics of spin glasses in their glassy phase. We briefly review the present theoretical understanding of the spectacular phenomena observed in experiments and describe new numerical results obtained in the first large-scale simulation of the nonequilibrium dynamics of the three-dimensional Heisenberg spin glass.

The magnetization relaxations of three different types of geometrically frustrated magnetic systems have been studied with the same experimental procedures as previously used in spin glasses. The materials investigated are Y₂Mo₂O₇ (pyrochlore system), SrCr_8.6Ga_3.4O₁₉ (piled pairs of Kagomé layers) and (H₃O)Fe₃(SO₄)₂(OH)₆ (jarosite compound). Despite a very small amount of disorder, all the samples exhibit many characteristic features of spin glass dynamics below a freezing temperature T_g, much smaller than their Curie–Weiss temperature θ. The ageing properties of their thermoremanent magnetization can be well accounted for by the same scaling law as in spin glasses, and the values of the scaling exponents are very close. The effects of temperature variations during ageing have been specifically investigated. In the pyrochlore and the bi-Kagomé compounds, a decrease of temperature after some waiting period at a certain temperature T_p reinitializes ageing, and the evolution at the new temperature is the same as if the system were just quenched from above T_g. However, as the temperature is raised back to T_p, the sample recovers the state it had previously reached at that temperature. These features are known in spin glasses as rejuvenation and memory effects. They are clear signatures of the spin glass dynamics. In the Kagomé compound, there is also some rejuvenation and memory, but much larger temperature changes are needed to observe the effects. In that sense, the behaviour of this compound is quantitatively different from that of spin glasses.

The AC susceptibility of a novel rare-earth boron-cluster-containing spin glass was measured. REB₁₇CN, REB₂₂C₂N, and REB_28.5C₄ (RE = Er,Ho) are a newly discovered class of crystalline, non-doped spin glass system in which the rare-earth atoms have a two-dimensional configuration. Well defined maxima in the in-phase linear AC susceptibility of HoB₂₂C₂N were observed with corresponding behaviour of the out-of-phase susceptibility as expected for a spin glass. It was found that the dynamical scaling theory of a 3D system, τ/τ₀ = [(T−T₀)/T]^−zν, could not describe the data well. More reasonable parameters could be extracted in terms of a generalized Arrhenius law which describes 2D spin glass systems. This result is in agreement with the previous studies which indicate the two-dimensionality of this system.

Plateaus can be observed in the zero-temperature magnetization curve of quantum spin systems at rational values of the magnetization. In one dimension, the appearance of a plateau is controlled by a quantization condition for the magnetization which involves the length of the local spin and the volume of a translational unit cell of the ground state. We discuss examples of geometrically frustrated quantum spin systems with large (in general unbounded) periodicities of spontaneous breaking of translational symmetry in the ground state.

In two dimensions, we discuss the square, triangular and Kagomé lattices using exact diagonalization (ED) for up to N = 40 sites. For the spin-1/2 XXZ model on the triangular lattice we study the nature and stability region of a plateau at one third of the saturation magnetization. The Kagomé lattice gives rise to particularly rich behaviour with several plateaus in the magnetization curve and a jump due to local magnon excitations just below saturation.

Ordering by thermal fluctuations is studied for the classical XY antiferromagnet on a checkerboard lattice in zero and finite magnetic fields by means of analytical and Monte Carlo methods. The model exhibits a variety of novel broken symmetries including states with nematic ordering in zero field and with triatic order parameter at high fields.

The magnetization process of an Ising-type S = 1 spin chain with nearest-neighbour interaction (J₁), next-nearest-neighbour interaction (J₂) and single-ion anisotropy (D) is investigated on the basis of the ground state phase diagram of the chain in a magnetic field (). The 49 possible spin structures for the ground state are obtained using Morita's theorem. The magnetization process is obtained from the ground state phase diagram, giving J₂/J₁ versus H/J₁, determined by comparing the energies of the 49 spin structures. It is shown that (1) among the 49 spin structures, 14 structures with unit cells of , , , , , , , , , , , , and appear in the phase diagram; (2) the magnetization process is equivalent to that of the usual Ising model for ; (3) a long period spin structure, , is realized for the intermediate ranges of J₂/J₁ and D/J₁ due to the frustration of the system.

The field induced magnetic phase transitions of Cs₂CuBr₄ were investigated by means of a magnetization process and neutron scattering experiments. This system undergoes a magnetic phase transition at Néel temperature T_N = 1.4 K at zero field, and exhibits a magnetization plateau at approximately one third of the saturation magnetization for the field directions and . In the present study, an additional symptom of the two-third magnetization plateau was found in the field derivative of the magnetization process. The magnetic structure was found to be incommensurate with the ordering vector Q = (0,0.575,0) at zero field. With increasing magnetic field parallel to the c-axis, the ordering vector increases continuously and is locked at Q = (0,0.662,0) in the plateau field range 13.1 T< H<14.4 T. This indicates that the collinear up–up–down spin structure is stabilized by quantum fluctuation at the magnetization plateau.

For a class of frustrated spin lattices including for example the 1D sawtooth chain, the 2D Kagomé and checkerboard, as well as the 3D pyrochlore lattices, we construct exact product eigenstates consisting of several independent, localized one-magnon states in a ferromagnetic background. Important geometrical elements of the relevant lattices are triangles being attached to polygons or lines. Then the magnons can be trapped on these polygons/lines. If the concentration of localized magnons is small, they can be distributed randomly over the lattice. On increasing the number of localized magnons, their distribution over the lattice becomes more and more regular, and finally the magnons condense in a crystal-like state.

The physical relevance of these eigenstates emerges in high magnetic fields where they become groundstates of the system. As a result a macroscopic magnetization jump appears in the zero-temperature magnetization curve just below the saturation field. The height of the jump decreases with increasing spin quantum number and vanishes in the classical limit. Thus it is a true macroscopic quantum effect.

We study, at T = 0, the anomalies in the magnetization curve of the S = 1 two-leg ladder with frustrated interactions. We focus mainly on the existence of the M = M_s/2 plateau, where M_s is the saturation magnetization. We report the results using the degenerate perturbation theory and the density matrix renormalization group, which lead to consistent conclusion with each other. We also touch on the M = M_s/4 and (3/4)M_s plateaux and cusps.

On the basis of the recently determined crystallographic structure of the delafossite Y CuO_2.5, we argue that the Cu–O network has nearly independent Δ chains, with however different interactions between the s = 1/2 spins, owing to the different angles, distances and coordinations of the Cu ions. Although band-structure calculations are still lacking, motivated by this observation we study here the sawtooth lattice for different ratios of the base–base and base–vertex interactions, J_bb/J_bv. By exact diagonalization and extrapolation to the infinite-size limit, we show that the elementary excitation spectrum is the same for total spins S_tot = 0 and 1, but not for S_tot = 2, and has a gap only in the interval . The gap, dispersionless for J_bb = J_bv, acquires increasing k-dependence as the ratio J_bb/J_bv moves away from unity, with the minimum energy excitations for k = 0 (k = π) when J_bb/J_bv< 1 (J_bb/J_bv> 1). Finally, we show that the gap closure is related to the instability of the dimers in the ground state as the difference between the interactions increases.

We present a µSR study of oxygen-doped delafossites RCuO_2+δ (δ = 0.5, 0.66; R³⁺ = La³⁺, Y³⁺) which present triangular based lattices of Cu²⁺, S = 1/2 spins. A slowing down of the spin dynamics without onset of a magnetic static freezing down to 1.6 K is found for Y CuO_2.5, which is believed to be an example of a Δ-chain. In contrast, Y CuO_2.66 and LaCuO_2.66 clearly order, probably into an antiferromagnetic state, which was rather unexpected.

The oxygen doping of delafossite compounds MCuO_2+δ allows the production of various networks of spins 1/2 (Cu²⁺) by the insertion of additional O atoms in the Cu layers that increase the valence of the Cu atoms. For instance, Δ-chains of spins 1/2 can be stabilized in Y CuO_2.5. In this compound, some glassiness is revealed in magnetostatic measurements while a strongly correlated quasielastic magnetic signal, observed at high temperatures in neutron scattering experiments, decreases in intensity with decreasing T, reflecting a freezing process.

New oxidized delafossite compounds of composition InCuO_2.5 and ScCuO_2.5 are synthesized and their structures are characterized by means of x-ray and neutron powder diffraction. Oxygen intake is accompanied by a small increase of the unit cell, and a complex superstructure attributed to oxygen ordering appears. Average structure refinements show the presence of additional oxygen close to the centres of Cu triangles, and an average copper valence of +2. The two compounds appear to be isostructural. Magnetic measurements show a non-linear thermal increase of the inverse magnetic susceptibility up to some maximum, soon followed by a minimum around 280 K.

We present a survey of an NMR and μSR magnetic study of the so called 'QS ferrite' frustrated antiferromagnet Ba₂Sn₂ZnCr_6.8Ga_3.2O₂₂ (BSZCGO(0.97)). We compare our results to the archetype of highly frustrated magnets, SrCr_8.6Ga_3.4O₁₉ (SCGO(0.95)), which has a very similar Kagomé bilayer structure. These two compounds show a spin glass like transition at a temperature T_g, much lower than the Curie–Weiss temperature, despite a strong frustration of the Cr³⁺ (S = 3/2) Kagomé bilayer lattice. Although there is a large difference between these transition temperatures, , the evolution of the dynamics of the Cr³⁺ spins around T_g, as probed by μSR, is very similar in both samples, with a persistent dynamical magnetic ground state under . This suggests that the spin glass like state and the dynamical properties are closely linked. A brief report of our NMR results is also given, where a maximum in the Cr bilayer susceptibility is observed around 45 K, similar to SCGO (p), and the existence of new dilution independent defects is evidenced.

A quantum dimer model (QDM) on the kagome lattice with an extensive ground-state entropy was recently introduced (Misguich et al 2003 Phys. Rev. B 67 214413). The ground-state energy of this QDM in the presence of one and two static holes is investigated by means of exact diagonalizations on lattices containing up to 144 kagome sites. The interaction energy between the holes (at distances up to seven lattice spacings) is evaluated and the results show no indication of confinement at large hole separations.

Volborthite, Cu₃V₂O₇(OH)₂·2H₂O, is a natural frustrated antiferromagnet ( K) with S = 1/2 spins (Cu²⁺) sitting at the vertices of a Kagomé-like lattice built on isosceles triangles. We report on the static (SQUID, ⁵¹V NMR) magnetic properties of the pure and 5% Zn/Cu substituted compounds and on an extensive μSR study of the dilution effect (up to 15% Zn substitutions) on the spin dynamics. Although volborthite shares most of the unusual features already exhibited in Kagomé bilayer compounds, namely a dynamical state as and a low temperature maximum in the local susceptibility, we found some surprising specificities. The dynamical state is less robust against dilution and the low temperature local susceptibility studied by means of NMR also strongly depends on dilution. Such a sensitivity to dilution questions the role of the asymmetry of the exchange constants.

The low-temperature properties of a diluted antiferromagnetic pyrochlore slab of S = 3/2 spins are investigated through a study of the frustrated oxides Ba₂Sn₂Ga_10−7pZnCr_7pO₂₂ (p>0.85). Powder neutron diffraction and ¹¹⁹Sn Mössbauer absorption show no evidence of long-range magnetic order above 1.5 K. As in SrCr_9qGa_12−9qO₁₉, diffuse magnetic scattering, indicative of short range spin–spin correlations, is observed at low temperature. The dependence of the low-temperature sub-Curie bulk susceptibility to weak site depletion is the inverse of that observed in SrCr_9qGa_12−9qO₁₉.

We suggest a new approach for describing the low-energy sector of spin- Kagomé Heisenberg antiferromagnets (KAFs). The Kagomé lattice is represented as a set of blocks (stars) arranged in a triangular lattice. Each of these stars has two degenerate singlet ground states. It is shown using symmetry considerations that the KAF lower singlet band is made by inter-star interaction from these degenerate states. The general form of the effective Hamiltonian describing this band is established. Low-T peculiarities in the specific heat of Kagomé clusters are also discussed.

An overview of the basic magnetic properties of vanadates which represent prototypes of frustrated two-dimensional S = 1/2 antiferromagnets on a square lattice is presented. It will be shown how information on the ground state sublattice magnetization, on the static uniform susceptibility and on the frustration driven lattice distortions can be achieved by means of NMR spectroscopy and magnetization measurements. The low-energy spin excitations, investigated by means of NMR and μSR relaxation measurements, will be analysed and the anomalous very-low-frequency dynamics, originating from the degeneracy of the ground state, discussed. Finally the effects of hydrostatic pressure on the degree of frustration of the vanadates will be addressed.

We report on a Raman scattering study of the superconducting cobaltite Na_xCoO₂·yH₂O as function of Na content and hydration (, 3/4 and , 2/3, 4/3). The observed scattering intensity is analysed in terms of lattice strain, structural misfit and disorder. Hydration, due to the intercalation of one or two H₂O layers, releases a part of this strain. Our Raman data suggest a connection between disorder on the partly occupied Na sites and the narrow phase space of superconductivity.

TlCuCl₃ is a quantum spin liquid of S = 1/2 Cu²⁺ dimers. Interdimer superexchange interactions give a three-dimensional magnon dispersion and a spin gap significantly smaller than the dimer coupling, which is closed by an applied hydrostatic pressure of approximately 2.5 kbar or by a magnetic field of 5.6 T, offering a unique opportunity to explore both the pressure- and field-induced quantum phase transitions and their associated critical phenomena.

Powder neutron diffraction on Tb₂C₂I₂ reveals strong resolution-limited magnetic Bragg reflections below 60 K due to commensurate antiferromagnetic (afm) long range ordering. Between 60 and 85 K the magnetic reflections broaden beyond instrumental resolution and the propagation vector becomes incommensurate. Above  K magnetic scattering is only seen as a diffuse ridge which we ascribe to short-range correlations within the triangular Tb atom planes. With decreasing temperature an additional Lorentzian shaped reflection grows on top of the decaying edge of this diffuse ridge. We analyse the diffuse scattering by fitting a Warren-type lineshape and a Lorentzian shaped Bragg reflection. The results of the fits indicate that, with diverging intra-plane correlations, significant inter-plane afm correlations build up close to 85 K. Above 95 K inter-plane correlations are essentially limited to nearest-neighbour Tb atom double layers only.

Frustrated magnets exhibit unusual critical behaviours: they display scaling laws accompanied by nonuniversal critical exponents. This suggests that these systems generically undergo very weak first-order phase transitions. Moreover, the different perturbative approaches used to investigate them are in conflict and fail to correctly reproduce their behaviour. Using a nonperturbative approach we explain the mismatch between the different perturbative approaches and account for the nonuniversal scaling observed.

For any classical statistical-mechanics model with a discrete state space, and endowed with a dynamics satisfying detailed balance, it is possible to generalize the Rokhsar–Kivelson point for the quantum dimer model. That is, a quantum Hamiltonian can be constructed (on the same state space) such that the ground state wavefunction coincides with the classical equilibrium distribution. Furthermore the excited eigenstates correspond to classical relaxation modes, which (in cases with a symmetry or conserved quantity) permits extraction of the dispersion law of long-wavelength excitations. The mapping is natural mainly when the states have equal weight, as is typical of a highly frustrated model. Quantum and classical correlation functions are related by analytic continuation to the imaginary time axis.

A general theoretical approach to polarized neutron chiral scattering is described. It is shown that using polarized neutrons one can study the projection of the spin chirality on the axial-vector interactions and investigate critical chiral fluctuations. Applications of this method to the triangular lattice antiferromagnets, helimagnets and spin glasses are discussed.

The phases of a system of weakly coupled tetrahedra (S = 1/2), in the presence of both Heisenberg and antisymmetric Dzyaloshinsky–Moriya interactions, are discussed. While non-magnetic dimer order is dominant for the specific interactions considered, we find that Dzyaloshinsky–Moriya induced magnetic long-range order can also emerge. The presence of antisymmetric interactions also leads to non-trivial effects (e.g. ordering) in an external magnetic field.

The two-dimensional spin-gap system SrCu₂(BO₃)₂ shows unique physical properties due to the strong quantum fluctuations that follow from its low-dimensionality and its very special topology. The magnetic properties of this material, e.g. dimer singlet ground state, an almost localized triplet and magnetization plateaux, are well described by a spin-1/2 antiferromagnetic Heisenberg model on the orthogonal dimer lattice. Recently, an unusual angular dependence of the shifts at the B sites with the external magnetic field rotated in the (110) plane, which indicates the presence of a field-induced staggered moment, has been observed by nuclear magnetic resonance. Such a behaviour cannot be explained by the Heisenberg model alone. We include an intra-dimer Dzyaloshinsky–Moriya interaction as well as an anisotropic gyromagnetic tensor in the orthogonal dimer model, and we show that the observed field-induced staggered moment can be very well described with physically reasonable values of the parameters.

We investigate the effects of Dzyaloshinsky–Moriya interactions (DMI) on the magnetic properties of the pyrochlore antiferromagnet. The relevance of this interaction for such a system is shown and we describe how to take it into account in accordance with the symmetries of the pyrochlore lattice. A phase transition from a high temperature paramagnetic phase to a low temperature long range ordered state takes place as soon as DMI are present. We describe the different magnetic structures obtained depending on the geometry of the DMI and special attention is given to the compound Cu₄O₃ for which a possible explanation of the experimentally observed ordering is given.