Table of contents

The International Conference on Highly Frustrated Magnetism 2008 (HFM2008) took place on 7–12 September 2008 at the Technische Universität Carolo-Wilhelmina zu Braunschweig, Germany. This conference was the fourth event in a series of meetings, which started in Waterloo, Canada (HFM 2000), followed by the second one in Grenoble, France (HFM 2003), and the third meeting in Osaka, Japan (HFM 2006). HFM2008 attracted more than 220 participants from all over the world. The number of participants of the HFM conference series has been increasing steadily, from about 80 participants at HFM 2000, to 120 participants at HFM 2003, and 190 participants at HFM 2006, demonstrating that highly frustrated magnetism remains a rapidly growing area of research in condensed matter physics. At the end of HFM2008 it was decided that the next International Conference on Highly Frustrated Magnetism will be held in Baltimore, USA in 2010.

HFM2008 saw four plenary talks by R Moessner, S Nakatsuji, S-W Cheong, and S Sachdev, 18 invited presentations, 30 contributed talks and about 160 poster presentations from all areas of frustrated magnetism. The subjects covered by the conference included:

• Kagome systems

• Itinerant frustrated systems

• Spinels and pyrochlore materials

• Triangular systems

• Unconventional order and spin liquids

• Chain systems

• Chain systems

• Novel frustrated systems

Ilya EreminProceedings Editor

Wolfram Brenig, Reinhard Kremer, and Jochen LitterstCo-Editors

International Advisory Board L Balents (USA) F Becca (Italy) S Bramwell (UK) P Fulde (Germany) B D Gaulin (Canada) J E Greedan (Canada) A Harrison (France) Z Hiroi (Japan) H Kawamura (Japan) A Keren (Israel) C Lacroix (France) C Lhuillier (France) A Loidl (Germany) G Misguich (France) J Richter (Germany) A M Olés (Poland) P Schiffer (USA) R Stern (Estonia) O Tchernyshyov (USA) M R. Valenti (Germany) G Zwicknagl (Germany)

International Program Committee W Brenig (Germany) C Broholm (USA) M Gingras (Canada) K Ueda (Japan) P Mendels (France) F Mila (Switzerland) R Moessner (Germany)

On behalf of the HFM2008 Organizing Committee, I wish to express my sincere thanks to everyone who supported us in organizing and setting up HFM2008. Especially, I would like to thank the European Science Foundation and the Max-Planck-Institut für Festkörperforschung for the generous financial support, the Technische Universität Braunschweig and the City of Braunschweig for hosting the conference, all colleagues who served on the Advisory and Program Board, the Referees, and last but not least, the staff members from Stuttgart and Braunschweig, Mrs Gisela Siegle, Mrs Regine Noack and Mrs Katharina Schnettler, for their helpful and invaluable assistance.

Reinhard Kremer

This short review surveys phenomena observed when a magnetic field is applied to a system of localised spins on a lattice. Its focus is on frustrated magnets in dimension d ≥ 2. The interplay of field and entropy is illustrated in the context of their unusual magnetocaloric properties, where field-tuned degeneracies assert themselves. Magnetisation plateaux can reveal the physics of fluctuations, with unusual excitations (such as local modes, extended string defects or monopoles) involved in plateau termination. Field-tuning lattice geometry is the final topic, where mechanisms for dimensional reduction and conversion between different lattice types are discussed.

Two kagome compounds, volborthite Cu₃V₂O₇(OH)₂·2H₂O and herbertsmithite ZnCu₃(OH)₆Cl₂, are compared in order to derive information about the intrinsic properties of the spin-1/2 kagome antiferromagnet. Observed for volborthite are a broad maximum at T ∼ J/4 and a large finite value approached at T = 0 in bulk magnetic susceptibility χ_bulk as well as local one χ_local from the NMR measurements. These must be the intrinsic properties for the spin-1/2 kagome antiferromagnet, as similar behavior was also reported in χ_local for herbertsmithite [Olariu A et al. 2008 Phys. Rev. Lett., 100 087202]. Impurity effects that may influence seriously the bulk properties are discussed.

We discuss the results of several small perturbations to the thermodynamic properties of Kagome Lattice Heisenberg Model (KLHM) at high and intermediate temperatures, including Curie impurities, dilution, in-plane and out of plane Dzyaloshinski-Moria (DM) anisotropies and exchange anisotropy. We examine the combined role of Curie impurities and dilution in the behavior of uniform susceptibility. We also study the changes in specific heat and entropy with various anisotropies. Their relevance to newly discovered materials ZnCu₃(OH)₆Cl₂ is explored. We find that the magnetic susceptibility is well described by about 6 percent impurity and dilution. We also find that the entropy difference between the material and KLHM is well described by the DM parameter D_z/J ≈ 0:1.

The frustration of antiferromagnetic interactions on the kagome lattice of corner sharing triangles, associated to the enhancement of quantum fluctuations for S=1/2 spins, was acknowledged long ago as a keypoint to stabilize novel ground states of magnetic matter. Only very recently, the model compound Herbersmithite, ZnCu₃(OH)₆Cl₂, a structurally perfect kagome antiferromagnet could be synthesized and allows close comparison to theories. Muon spin resonance investigation has demonstrated the absence of any spin freezing at least down to 50 mK, an energy scale 4000 times smaller than the main antiferromagnetic interaction (J ≊ 180 K). The kagome plane susceptibility could be accurately measured from the ¹⁷O NMR lineshift. It goes through a broad maximum at T ≊ J/2 at variance with the diverging SQUID susceptibility which can be consistently interpreted as being dominated by a paramagnetic-like defect contribution arising from Zn/Cu intersite mixing. At lower temperatures (T ≊ J/100), the kagome susceptibility is found to saturate to a non zero value in agreement with the absence of a gap in relaxation measurements.

We synthesized single crystals of the new hexagonal compounds A₂Cu₃SnF₁₂ with A=Cs and Rb, and investigated their magnetic properties. These compounds are composed of Kagomé layers of corner-sharing CuF₆-octahedra. Cs₂Cu₃SnF₁₂ has the proper Kagomé layer at room temperature, and undergoes structural phase transition at T_t ≊ 185 K. The temperature dependence of the magnetic susceptibility in Cs₂Cu₃SnF₁₂ agrees well with the result of the numerical calculation for S = 1/2 two-dimensional Heisenberg Kagomé antiferromagnet down to T_t with the nearest exchange interaction J/k_B ≊ 240 K. Although the magnetic susceptibility deviates from the calculated result below T < T_t, the rounded maxima were observed at approximately T ≊ (1/6)J/k_B as predicted by the theory. Cs₂Cu₃SnF₁₂ undergoes three-dimensional magnetic ordering at T_N = 20 K. Rb₂Cu₃SnF₁₂ has the Kagomé layer, whose unit cell is enlarged by 2a × 2a as compared with the proper Kagomé layer even at room temperature. From the viewpoint of crystal structure, the exchange interactions between nearest neighbor Cu²⁺-ions are classified into four kinds. From the magnetic susceptibility and high-field magnetization measurements, it was found that the ground state is a disordered singlet with the spin gap, as predicted by recent theory. Exact diagonalization method with 12-site Kagomé cluster was performed to analyze the magnetic susceptibility. By comparing the calculated results with the experimental data, the individual exchange interactions were evaluated.

We report a comprehensive ²⁹Si NMR and ^69,71Ga NMR/NQR study of the large-spin magnetically anisotropic kagomé compound Nd₃Ga₅SiO₁₄. We find a sizable transferred hyperfine coupling between the nuclear and electron moments, proving that these nuclei can be utilized as local probes which provide useful information about the magnetic Nd³⁺ ions. Our results give evidence of unexpectedly broad distributions of local environments on all nuclear sites under investigation, implying also exchange disorder.

We study a model of strongly interacting spinless fermions and hard-core bosons on an anisotropic kagome lattice near 2/3-filling. Our main focus lies on the strongly anisotropic case in which the nearest–neighbor repulsions V and V' are large compared to the hopping amplitudes |t| and |t'|. When t = t' = 0, the system has a charge ordered insulating ground state where the charges align in striped configurations. Doping one electron or hole into the ground state yields an anisotropic metal at V' > V, where the particle fractionalizes along the V'-bonds while propagates along the V-bonds in a one–body like manner. The sixth order ring exchange processes around the hexagonal unit of the lattice play a crucial role in forming a bound state of fractional charges.

Spin-1/2 magnets with kagomé geometry, being for years a generic object of theoretical investigations, have few real material realizations. Recently, a DFT-based microscopic model for two such materials, kapellasite Cu₃Zn(OH)₆Cl₂ and haydeeite Cu₃Mg(OH)₆Cl₂, was presented [Janson O, Richter J and Rosner H arxiv:0806.1592]. Here, we focus on the intrinsic properties of real spin-1/2 kagomé materials having influence on the magnetic ground state and the low-temperature excitations. We find that the values of exchange integrals are strongly dependent on O—H distance inside the hydroxyl groups, present in most spin-1/2 kagomé compounds up to date. Besides the original kagomé model, considering only the nearest neighbour exchange, we emphasize the crucial role of the exchange along the diagonals of the kagomé lattice.

1H-NMR and magnetic susceptibility χ(T) are measured on Zn_xCu_4-x(OH)₆Cl₂ (0 ≤ x ≤ 1), whose end member at x = 0 is a distorted pyrochlore- and x = 1 is a kagomélattice spin frustrated antiferromagnet. For x = 0 compound, NMR spectra broaden abruptly at T_N = 18 K, and a spin - lattice relaxation rate shows large divergent behavior at T_C = 6 K. These anomalies indicate an onset of magnetic order at TN and TC. For x = 1 compound, no magnetic order is observed, which is consistent with the previously reported result. Determined values of T_N and T_C from anomalies in NMR and χ(T) results are summarized in a detailed x-T phase diagram.

X-band and high field electron spin resonance (ESR) measurements on S = 1/2 kagome lattice antiferromagnet Cu₃V₂O₇(OH)₂ · 2H²O (volborthite) have been performed. Although the kagome lattice is slightly deformed in the ab plane, no sign of magnetic order is observed down to 3.8 K, which is consistent with the magnetic susceptibility and the speciflc heat results, because the X-band ESR result shows no g-shift and the broadening of the linewidth down to 3.8 K. However, high field ESR results above 40 GHz show continuous g-shift below 20 K, which coincides with the broad maximum in the magnetic susceptibility. These results suggest the existence of the short range order and the field dependence in the system, and they are discussed in connection with the recent magnetization result.

We report the spin dynamics of the quantum kagome lattice ZnCu₃(OH)₆Cl₂ observed by our high field ESR. The spin susceptibility deduced from our ESR result follows the Curie-Weiss-dependence, which is identical with the magnetic susceptibility. No resonance shift is observed down to 1.8 K in our measurement. This means that the internal field does not develop down to very low temperature. Moreover, the linewidth turns out to take the constant value from room temperature to 1.8 K. It suggests that the spin-spin correlation does not develop down to very low temperature of 0.009J. Our results suggest that ZnCu₃(OH)₆Cl₂ looks like an ideal S = 1/2 kagome antiferromagnet from the ESR point of view.

The spin-1/2 Ising-Heisenberg model on the triangulated Kagomé (triangles-in-triangles) lattice is exactly solved by establishing a precise mapping correspondence to the simple spin-1/2 Ising model on Kagomé lattice. It is shown that the disordered spin liquid state, which otherwise occurs in the ground state of this frustrated spin system on assumption that there is a sufficiently strong antiferromagnetic intra-trimer interaction, is eliminated from the ground state by arbitrary but non-zero Dzyaloshinskii-Moriya anisotropy.

We study the Hubbard model on a geometrically-frustrated hyperkagome lattice by a cluster extension of the dynamical mean field theory. We calculate the temperature (T) dependences of the specific heat (C) and the spin-lattice relaxation time (T₁) in correlated metallic region. C/T shows a peak at T = T_p1 and rapidly decreases as T → 0. On the other hand, 1/T₁T has a peak at a higher temperature T_p2 than T_p1, and largely decreases below T_p2, followed by the Korringa law 1/T₁ ∝ T as T → 0. Both peak temperatures are suppressed and the peaks become sharper as electron correlation is increased. These behaviors originate from strong renormalization of the energy scales in the peculiar electronic structure in this frustrated system; a pseudo-gap like feature, the van-Hove singularity, and the flat band. The results are discussed in comparison with the experimental data in the hyperkagome material, Na₄Ir₃O₈.

We report a temperature and frequency dependent electron spin resonance (ESR) study of the kagomé spin-1/2 compound ZnCu₃(OH)₆Cl₂. Our results demonstrate that two spin species are simultaneously detected; copper spins on the intra-plane Cu²⁺ kagomé sites and those on the inter-plane Zn²⁺ sites, the latter resulting from the Cu²⁺/Zn²⁺ antisite disorder. We examine all the possible magnetic anisotropy terms, which could lead to the observed extremely broad ESR lines in this system. We argue that the line broadening is due to Dzyaloshinsky-Moriya interaction.

We review our two recent theoretical works on strongly correlated electrons on typical frustrated lattices. The first topic is about a Mott transition in the single-band Hubbard model on anisotropic triangular lattice, and we discuss a reentrant behaviour of metal-insulator transition, consistent with that in a κ-type BEDT-TTF salt. The second topic is about heavy fermion behaviour in the vanadium spinel LiV₂O₄. We study the 3-orbital t_2g Hubbard model on the pyrochlore lattice at quarter filling and derive its low-energy effective model. The correlations of spin and orbital degrees of freedom are discussed.

We study the phase diagram of the frustrated t-t' Hubbard model on the square lattice by using a novel variational wave function. Taking the clue from the backflow correlations that have been introduced long-time ago by Feynman and Cohen and have been used for describing various interacting systems on the continuum (like liquid ³He, the electron jellium, and metallic Hydrogen), we consider many-body correlations to construct a suitable approximation for the ground state of this correlated model on the lattice. In this way, a very accurate ansatz can be achieved both at weak and strong coupling. We present the evidence that an insulating and non-magnetic phase can be stabilized at strong coupling and sufficiently large frustrating ratio t' = t.

Spin glass properties of a novel ruthenate, Ca₂Ru₂O₇, were studied by precise magnetization measurements. The effective moment per Ru atom is only 0.25μ_B, which is one decade smaller than that expected from a localized spin model with S = 3/2 for Ru⁵⁺. In spite of the small moment, a spin glass transition occurs at T_g = 25.0 K, and the nonlinear susceptibility χ_nl(≈ χ²) diverges negatively at T_g. The value of the critical exponent δ can be estimated as δ = 3.7 from the magnetic field dependence of χ_nl at T_g, which is compared to those of other pyrochlore spin glasses and the canonical spin glasses.

¹H NMR measurements of 3d electron three-dimensional frustrated systems, Co₂(OH)₃Cl with s = 3/2 and Cu₂(OH)₃Cl with s = 1/2 have been performed. The relaxation rates T^-1₁ of both compounds suggest the development of spin correlations at much higher temperatures compared with the magnetic transition temperatures. The temperature dependence of T^-1₁ below 6 K of both compounds indicates the magnetic ordering and the existence of magnon excitations. The estimated magnon energy gaps are 13 K and 27 K for Cu₂(OH)₃Cl and Co₂(OH)₃Cl, respectively, which are consistent with the inelastic neutron experiments. The intermediate phase between T_N1 = 18.1 K and T_N2 = 6.4 K for Cu₂(OH)₃Cl shows the conflicting behaviors which are the coexistence of the freezing of the moments and the paramagnetic spin dynamics. The partial freezing and the time scale of spin dynamics should be crucial to understand these frustrated systems.

We have proposed the conduction mechanism of the hole-induced chiral-like spin solitons in the layered organic conductor with triangular lattice, and have discussed the pressure efiect of difiusivity of those hole-induced solitons.

We calculate the intrinsic Hall conductivity of conductions electrons coupled to a pyrochlore lattice of localized moments. In the presence of anisotropy the localized moments may order in a non-coplanar chiral structure, which can be at the origin of an intrinsic Hall effect. The sign and the value of the Hall conductance depend on the band filling factor and the local exchange coupling. Application of an external magnetic field induces a change in the magnetic structure of the localized spins which results in a change of the Hall conductance. In this framework, the temperature dependence of the Hall conductance may exhibit a nonmonotonical behavior. The results are in a qualitative agreement with experimental results on Mo pyrochlores.

We have studied the field induced magnetic structures (H//[110]) in Tb2Ti2O7 in a wide temperature (0.2<T<270 K) and field (0<H<7 T) range, by combining polarized and unpolarized neutron diffraction in a single crystal. Below 2 K and above 2 T, two structures with k = 0 and (0,0,1) propagation vectors are simultaneously observed. Their analysis yields a precise description of the field induced ground states. The k = 0 structure with net magnetization shows spin-ice like local order, but with Tb moments of very different magnitudes. The k = (0,0,1) AF-like structure is stabilized in a finite (H,T) range and attributed to magnetostriction.

I consider the class of 'depleted pyrochlore' lattices of corner-sharing triangles, made by removing spins from a pyrochlore lattice such that every tetrahedron loses exactly one. Previously known examples are the 'hyperkagome' and 'kagome staircase'. I give criteria in terms of loops for whether a given depleted lattice can order analogous to the kagome state, and also show how the pseudo-dipolar correlations (due to local constraints) generalize to even the random depleted case.

We conducted precise magneto-optical Faraday rotation measurements in CdCr₂O₄and ZnCr₂O₄up to ultra-high magnetic fields using methods of the single turn coil(up to 190 T) and also the electro-magnetic flux compression(up to 360 T). In CdCr₂O₄, we have succeeded in observation of the full magnetization process. In ZnCr₂O₄, we observed magnetization process up to 2.7 μ_B(the full moment is 3.0 μ_B). The magnetization processes of both materials were well described by a 4 sub-lattice Heisenberg-spin model including spin-lattice interactions.

We discuss the nearest neighbour spin ice model in the presence of a magnetic field placed along the cubic [100] direction. As recently shown in Phys. Rev. Lett. 100, 067207, 2008, the symmetry sustaining ordering transition observed at low temperature is a three dimensional Kasteleyn transition. We confirm this with numerical data using a non-local algorithm that conserves the topological constraints at low temperature and from analytic calculations from a Bethe lattice of corner sharing tetrahedra. We present a thermodynamic description of the Kasteleyn transition and discuss the relevance of our results to recent neutron scattering experiments on spin ice materials.

The ordering of the Ising model on a pyrochlore lattice interacting via the long- range RKKY interaction, which is intended to model a metallic pyrochlore magnet such as Pr₂Ir₂O₇, is studied by Monte Carlo simulations. Depending on the parameter k_F representing the Fermi wavevector, the model exhibits rich ordering behaviors. When the k_F -value is close to the experimental value, the model exhibits a '2-in 2-out' local spin structure reminiscent of the spin ice accompanied by the antiferromagnetic Curie-Weiss constant. This observation is consistent with experiment. The model exhibits a first-order transition into the magnetic long-range ordered state without showing a spin-liquid-like behavior.

Gd₃Ga₅O₁₂, (GGG), has an extraordinary magnetic phase diagram, where no long range order is found down to 25 mK despite Θ_CW ≈2 K. However, long range order is induced by an applied field of around 1 T. Motivated by recent theoretical developments and the experimental results for a closely related hyperkagome system, we have performed neutron diffraction measurements on a single crystal sample of GGG in an applied magnetic field. The measurements reveal that the H - T phase diagram of GGG is much more complicated than previously assumed. The application of an external field at low T results in an intensity change for most of the magnetic peaks which can be divided into three distinct sets: ferromagnetic, commensurate antiferromagnetic, and incommensurate antiferromagnetic. The ferromagnetic peaks (e.g. (112), (440) and (220)) have intensities that increase with the field and saturate at high field. The antiferromagnetic reflections have intensities that grow in low fields, reach a maximum at an intermediate field (apart from the (002) peak which shows two local maxima) and then decrease and disappear above 2 T. These AFM peaks appear, disappear and reach maxima in different fields. We conclude that the competition between magnetic interactions and alternative ground states prevents GGG from ordering in zero field. It is, however, on the verge of ordering and an applied magnetic field can be used to crystallise ordered components. The range of ferromagnetic (FM) and antiferromagnetic (AFM) propagation vectors found reflects the complex frustration in GGG.

Inelastic neutron spectra performed at 0.4 K in a single crystal of Tb₂Ti₂O₇, with a magnetic field applied along the [110] direction, confirm the presence of a tetragonal lattice distortion from the nominal cubic symmetry, previously evidenced below 20 K in high resolution x-ray experiments. The signature of the distortion is an inelastic line at very low energy (≈ 0.04 THz), which is also present in the powder inelastic neutron spectra of Tb₂Sn₂O₇.

Two different distributions for the octahedral-site cations in ZnFe₂O₄ and CdFe₂O₄ are investigated by the first-principles method of density functional theory. Both the local density approximation (LDA) and the generalized gradient approximation (GGA) as well as the inclusion of the one-site Coulomb interaction (LDA+U and GGA+U) are considered for the exchange-correlation energy functional. It is shown that a different octahedral-site distribution can lead to considerably different density of states as well as band gaps in both the normal and inverse spinel configurations of these two materials.

The zero-point entropy of a spin glass is a difficult property to experimentally determine and interpret. Spin glass theory provides various predictions, including unphysical ones, for the value of the zero-point entropy, however experimental results have been lacking. We have investigated the magnetic properties and zero-point entropy of two spinel Cu²⁺ based spin glasses, CuGa₂O₄ and CuAl₂O₄. Dc- and ac-susceptibility and specific heat measurements show many characteristic spin glass features for both materials. The spin glass freezing temperature is determined to be T_f = 2.89 ± 0.05 K for CuGa²O⁴ and T^f = 2.30 ± 0.05 K for CuAl²O⁴. By integrating the specific heat data we have found that CuGa₂O₄ and CuAl₂O₄ have zero-point entropies of S₀ = 4.96 JK^-1mol^-1 and S₀ = 4.76 JK^-1mol^-1 respectively. These values are closest to the prediction for a Sherrington-Kirkpatrick XY spin glass, however they are notably higher than all of the theoretical predictions. This indicates that CuGa₂O₄ and CuAl₂O₄ have a greater degeneracy in their ground states than any of the spin glass models.

We present an elaborate electron-spin resonance study of the low-energy dynamics and magnetization in the ordered phase of the frustrated spinel ZnCr₂O₄. We observe several resonance modes corresponding to different structural domains and found that the number of domains can be easily reduced by field-cooling the sample through the transition point. To describe the observed antiferromagnetic resonance spectra it is necessary to take into account an orthorhombic lattice distortion in addition to the earlier reported tetragonal distortion which both appear at the antiferromagnetic phase transition.

We report on the low temperature magnetism of pyrochlore oxide Pr₂Zr₂O₇. The crystal electric field ground state in Pr³⁺ (4f², J = 4) ions has non-Kramers doublet with local <111> Ising magnetic anisotropy. The negative Curie-Weiss temperature below 10 K (-0.55 K) indicates an antiferromagnetic coupling between the spins. The AC magnetic susceptibility does not exhibit any long range ordering at least down to 76 mK. Instead, a frequency dependence of AC magnetic susceptibility is observed below 0.3 K, indicating a spin freezing behavior. Furthermore, recently we have succeeded for the first time in growing a single crystal of Pr₂Zr₂O₇ by the floating-zone method using an infrared furnace equipped with four Xe lamps. We will also comment on the crystal growth of Pr₂Zr₂O₇.

We consider the possibility that the discrete long-range ordered states of Er₂Ti₂O₇ are selected energetically at the mean field level as an alternative scenario that suggests selection via thermal fluctuations. We show that nearest neighbour exchange interactions alone are not sufficient for this purpose, but that anisotropies arising from excited single ion crystal field states in Er₂Ti₂O₇, together with appropriate anisotropic exchange interactions, can produce the required long range order. However, the effect of the single ion anisotropies is rather weak so we expect thermal or quantum fluctuations, in some guise, to be ultimately important in this material. We reproduce recent experimental results for the variation of magnetic Bragg peak intensities as a function of magnetic field.

A study of the modifications of the magnetic properties of Ho_2-YxSn₂O₇ upon varying the concentration of diamagnetic Y³⁺ ions is presented. Magnetization and specific heat measurements show that the Spin Ice ground-state is only weakly affected by doping for x ≤ 0.3, even if non-negligible changes in the crystal field at Ho³⁺ occur. In this low doping range μSR relaxation measurements evidence a modification in the low-temperature dynamics with respect to the one observed in the pure Spin Ice. For x → 2, or at high temperature, the dynamics involve fluctuations among Ho³⁺ crystal field levels which give rise to a characteristic peak in ¹¹⁹Sn nuclear spin-lattice relaxation rate. In this doping limit also the changes in Ho³⁺magnetic moment suggest a variation of the crystal field parameters.

Following the discovery of frustrated magnetism in deformed pyrochlore lattice Cu₂(OH)₃Cl and Co₂(OH)₃Cl we have extensively investigated the material series in the chemical formula of M₂(OH)₃X, with M = Cu, Co, Ni, Fe, Mn, and X = Cl, Br, or I. In atacamite-structure Ni₂(OH)₃Cl, strong geometric frustration and an exotic antiferromagnetic transition below 5 K was found. While neutron diffraction witnessed unambiguously an antiferromagnetic long-range order, the μSR method can't 'see' this order, instead, the detected local field behaved quite like a dynamically fluctuating one. For the system of Co₂(OH)₃Cl, the magnetic state is very sensitive to both the anion and cation substitution. While Co₂(OH)₃Cl behaves like a zero-field kagomé ice ferromagnet, a completely substituted version of Co₂(OH)₃Br becomes antiferromagnetic although there is little difference in the crystal structure. The antiferromagnetic Co₂(OH)₃Br showed complicated magnetic transitions. Meanwhile, partially substituted Co₂(OH)₃Cl_1-xBr_x transforms from ferromagnetic to antiferromagnetic with increasing the x ratio. The results suggest that the interaction on the kagome-lattice plane is antiferromagnetic while that on the triangular lattice plane is ferromagnetic. For the substituted series (Co_1-xFe_x)₂(OH)₃Cl a spin glass state is observed.

Multi-frequency ESR measurements of S = 1/2 phyrochlore system Zn_xCu_4-x(OH)₆Cl₂(x = 0 ∼ 0.5) have been performed using the pulse magnetic field up to 16 T and in the frequency region from 30 GHz to 360 GHz. Temperature dependence ESR measurement of the distorted pyrochlore system (x = 0) from 1.76 K to 265 K shows the linewidth broadening below 20 K, and the coexistence of AFMR modes and the peculiar mode is suggested below 6 K. Moreover, the x dependence measurements at 1.8 K suggest the existence of phase boundaries around x = 0.3 and 0.5. Possible model to interpret the result will be presented.

We investigate two-magnon Raman scattering from the S = 1/2 Heisenberg antiferromagnet on the triangular lattice (THAF), considering both isotropic and anisotropic exchange interactions. We find that the Raman intensity for the isotropic THAF is insensitive to the scattering geometry, while both the line profile and the intensity of the Raman response for the anisotropic THAF shows a strong dependence on the scattering geometry. For the isotropic case we present an analytical and numerical study of the Raman intensity including both the efiect of renormalization of the one-magnon spectrum by 1 = S corrections and final-state magnonmagnon interactions. The bare Raman intensity displays two peaks related to one-magnon van-Hove singularities. We find that 1 = S self-energy corrections to the one-magnon spectrum strongly modify this intensity profile. The central Raman-peak is significantly enhanced due to plateaus in the magnon dispersion, the high frequency peak is suppressed due to magnon damping, and the overall spectral support narrows considerably. Additionally we investigate final-state interactions by solving the Bethe-Salpeter equation to O(1 = S). In contrast to collinear antiferromagnets, the non-collinear nature of the magnetic ground state leads to an irreducible magnon scattering which is retarded and non-separable already to lowest order. We show that final-state interactions lead to a rather broad Raman-continuum centered around approximately twice the 'roton'-energy.

Ni₂SiO₄, Liebenbergite, is an example of a quasi-one-dimensional magnet made up of frustrated corner sharing triangles of Ni²⁺ (S = 1) ions that propagate parallel to the b axis. Ni₂SiO₄ is isostructural with olivine, a common mineral of varying composition Fe_2-xMg_xSiO₄, and is described in the orthorhombic space group Pnma. A synthetic polycrystalline sample of Ni₂SiO₄ was studied using powder neutron diffraction with spectra taken above and below the antiferromagnetic ordering transition (T_N ≈ 34 K). Analysis of the magnetic structure was carried out using the symmetry models of corepresentation theory. The refined spin structure evidences both ferromagnetic and antiferromagnetic inter-chain interactions, and ferromagnetic intra-chain coupling. The competition between the magnetic interactions can be seen in the canting of the moments away from a collinear arrangement.

We investigate the microscopic model for the frustrated layered antiferromagnets Cs₂CuCl₄ and Cs₂CuBr₄ by performing ab initio density functional theory (DFT) calculations and with the help of the tight-binding method. The combination of both methods provide the relevant interaction paths in these materials, and we estimate the corresponding exchange constants. We find for Cs₂CuCl₄ that the calculated ratio of the strongest in-plane exchange constants J'/J between the spin-1/2 Cu ions agrees well with neutron scattering experiments. The microscopic model based on the derived exchange constants is tested by comparing the magnetic susceptibilities obtained from exact diagonalization with experimental data. The electronic structure differences between Cs₂CuCl₄ and Cs₂CuBr₄ are also analyzed.

The family of layered organic salts X[Pd(dmit)₂]₂ are Mott insulators and form scalenetriangular spin-1/2 systems with antiferromagnetic exchange interactions J. Among them, EtMe₃Sb[Pd(dmit)₂]₂ has a nearly regular-triangular spin system with J = 220-250 K. Our previous study proposed that a quantum spin-liquid state is realized in this system because this system was revealed to have neither spin ordering/freezing nor an appreciable spin gap down to 1.37 K. In the present study, to confirm the absence of spin ordering/freezing in the low-temperature limit, we cooled this system down to 19.4 mK, which is 4 orders of magnitude smaller than J, and measured ¹³C-NMR spectra. The obtained spectra do not show any critical broadening. Therefore, it is concluded that the spin system of EtMe₃Sb[Pd(dmit)₂]₂ does not have spin ordering/freezing in the low-temperature limit; that is, the spin system is in a quantum-fluctuating spin state.

Longitudinal-field muon spin rotation (LF-μSR) experiments in the two-dimensional geometrically-frustrated antiferromagnet NiGa2S4 reveal a number of features of spin freezing and dynamics in this system. Long-lived (correlation time ⪆ 10^-6 s at 2 K) disordered Ni spin freezing sets in abruptly below T_f = 8.5±0.5 K. At low temperatures slow Ni spin fluctuations are found in low applied field HL that are rapidly suppressed for H_L ⪆ 0.04 T. Activated muon spin relaxation above T_f is strong evidence for 2D critical behaviour. The LF-μSR data indicate that NiGa₂S₄ is neither a conventional magnet nor a singlet spin liquid, and raise the question of how to reconcile the strongly field-dependent muon relaxation with the field-independent specific heat.

We study three-leg antiferromagnetic Heisenberg model with the periodic boundary conditions in the rung direction. Since the rungs form regular triangles, spin frustration is induced. We use the density-matrix renormalization group method to investigate the ground-state properties. We find that the spin excitations are always gapped to remove the spin frustration as long as the rung coupling is nonzero. We also demonstrate a direct observation of spin-Peierls dimerization order in the leg direction. Both the spin gap and the dimerization order are basically enhanced as the rung coupling increases.

NaCrO₂ has been shown to be a very good model compound for the study of triangular Heisenberg antiferromagnets with isotropic interactions [1]. We examine by NMR and μSR the effect of substitution of non magnetic Ga³⁺ ions at the Cr³⁺ sites (S = 3/2). The presence of non-magnetic defects is found to impact both the dynamics and the static properties of the triangular network.

We study a Berezinskii-Kosterlitz-Thouless-like phase transition in a triangular-lattice three-spin interaction model. The vector sine-Gordon field theory describes defects involved, and enables us to perform the renormalization-group analysis of the transition. Based on it, we discuss properties of the spin-spin correlation function, and also analyze the helicity modulus for the present model. To provide the data to support our analysis, we perform the Monte-Carlo simulations to calculate them. Further, we exhibit snapshots of some typical defect conflgurations, which are helpful to illustrate the defect-mediated phase transition.

¹¹B NMR and magnetic susceptibility measurements have been performed in order to investigate the spin dynamics of a triangular-lattice XY antiferromagnet UNi₄B. In this compound, the partially ordered state appears below T_N = 20 K with a peculiar vortex-like structure. Magnetic susceptibility shows that T_N is slightly lower than the round maximum of the magnetic susceptibility suggesting the two dimensional character of this compound. The temperature dependence of the relaxation rate T^-1₁ above T_N is well reproduced by the theoretical model that were discussed in the Kosterlitz-Thouless-Berezinskii transition. Thus the temperature dependence of T^-1₁ suggests that the spin dynamics in UNi₄B above T_N is dominated by the motion of the unbound vortices.

It has been shown in 2005 by neutron powder diffraction that the triangular layer Heisenberg compound NiGa₂S₄ is characterized by nano-scale magnetic correlations below ∼ 18 K. Using the muon-spin rotation and relaxation (μSR) techniques, we have evidenced that the compound displays a phase transition at T_c = 9.2 (2) K below which a coherent oscillation of the muon spins is detected. Remarkably, the magnetic specific heat C_m exhibits a rounded low- temperature maximum at ∼ 13 K, i.e. at a temperature above T^c. This is consistent with the theory of Kawamura and Miyashita which attributes the transition at T_c to the unbinding of Z₂ vortices. NiGa₂S₄ is characterized by a wide spectrum of magnetic fluctuations as inferred, for example, from the difference in the temperature scale deduced from μSR and neutron scattering.

We report a comparative study of the conductive oxides PdMO₂ (M = Cr, Co) consisting of a layered structure with a triangular lattice of M³⁺ ions: PdCrO₂ (S = 3 = 2) is magnetically active showing an antiferromagnetic (AF) transition at T_N' 37.5 K, whereas PdCoO₂ (S = 0) is not magnetically active. Both compounds exhibit metallic conductivity down to low temperatures, but the temperature dependence of the resistivity is quite different reflecting the difference in their magnetic properties. Especially, the resistivity of PdCrO₂ exhibits strong sub-linear temperature dependence in a wide temperature range above T_N. Such dependence is markedly different from that of ordinary magnetic metals with non-frustrated localized spin moments. The estimated entropy at T_N is substantially smaller than that expected for a system with S = 3/2, suggesting that the spin correlations still remain much above T_N. These facts indicate that it is the short-range correlations of frustrated spins that leads to the unusual sub-linear temperature dependence of the resistivity.

We study an extended two-dimensional Shastry-Sutherland model in a magnetic field where besides the usual Heisenberg exchanges of the Shastry-Sutherland model two additional SU(2) invariant couplings are included. Perturbative continous unitary transformations are used to determine the leading order effects of the additional couplings on the pure hopping and on the long-range interactions between the triplons which are the most relevant terms for small magnetization. We then compare the energy of various magnetization plateaux in the classical limit and we discuss the implications for the two-dimensional quantum magnet SrCu₂(BO₃)₂.

Phase diagram of the S = 1/2, J₁-J₂-J₃ Heisenberg model on the square lattice with ferromagnetic 1st neighbor and antiferromagnetic 2nd and 3rd neighbor interactions is studied by means of exact diagonalization and spin wave calculations. Quantum fluctuations are shown to induce phases that are not present classically and a shift in the wave vector of the spiral phases. Results are compared with recent experimental data.

Using the coupled-cluster method for infinite lattices and the exact diagonalization method for finite lattices, we study the influence of an exchange anisotropy Δ on the ground-state phase diagram of the spin-1/2 frustrated J₁-J₂ XXZ antiferromagnet on the square lattice. We find that increasing Δ > 1 (i.e. an Ising type easy-axis anisotropy) as well as decreasing Δ < 1 (i.e. an XY type easy-plane anisotropy) both lead to a monotonic shrinking of the parameter region of the magnetically disordered quantum phase. Finally, at Δ^c ≈ 1.9 this quantum phase disappears, whereas in the pure XY limit (Δ = 0) there is still a narrow region around J₂ = 0.5J₁ where the quantum paramagnetic ground-state phase exists.

I consider the ground state of quantum spins interacting via Heisenberg antiferromagnetic exchange, in lattices having several types of local environment. In unfrustrated cases, when a Néel type order exists, it is known that quantum fluctuations are site-dependent, and lead to an inhomogeneous local staggered order parameter. This paper discusses some effects of adding frustration to such a system, by including next nearest neighbor antiferromagnetic interactions. Within linear spinwave theory, it is found that as the frustration parameter increases, the local order parameters decrease at a rate that depends on the type of sites involved in the frustrated loops. The cases of a decorated square lattice system, and of a quasiperiodic tiling are considered to study difierent ways in which antiferromagnetism is suppressed in these inhomogeneous systems.

We use improved Monte-Carlo algorithms to study the antiferromagnetic 2D-Ising model with competing interactions J₁ on nearest neighbour and J₂ on next-nearest neighbour bonds. The finite-temperature phase diagram is divided by a critical point at J₂ = J₁/2 where the groundstate is highly degenerate. To analyse the phase boundaries we look at the speciflc heat and the energy distribution for various ratios of J₂/₁. We find a first order transition for small J₂ > J₁/2 and the transition temperature suppressed to T_C = 0 at the critical point.

A spin-1/2 frustrated two-leg ladder with four-spin exchange interaction is studied by quantized Berry phases. We found that the Berry phase successfully characterizes the Haldane phase in addition to the rung-singlet phase, and the dominant vector-chirality phase. The Hamiltonian of the Haldane phase is topologically identical to the S = 1 antiferromagnetic Heisenberg chain. Decoupled models connected to the dominant vector-chirality phase revealed that the local object identified by the non-trivial (π) Berry phase is the direct product of two diagonal singlets.

We investigated the classical Shastry-Sutherland lattice under an external magnetic field in order to understand the recently discovered magnetization plateaux in the rare-earth tetraborides compounds RB4. A detailed study of the role of thermal fluctuations was carried out by mean of classical spin waves theory and Monte-Carlo simulations. Magnetization quasi-plateaux were observed at 1/3 of the saturation magnetization at non zero temperature. We showed that the existence of these quasi-plateaux is due to an entropic selection of a particular collinear state. We also obtained a phase diagram that shows the domains of existence of different spin configurations in the magnetic field versus temperature plane.

We discuss the two-dimensional S = 1/2 J₁-J₂ frustrated Heisenberg model on a square lattice. This model provides a good description of two classes of quasi-two-dimensional vanadates, namely the Li₂VOXO₄ (X = Si,Ge) and AA'VO(PO₄)₂ (A,A' = Pb, Zn, Sr,Ba,Cd) compounds. We use the finite-temperature Lanczos method and spin wave analysis to study the high-field properties of this model in the whole J₁-J₂ plane.

Of particular interest is the saturation field of the low-temperature magnetization. Together with the estimates for the average effective exchange constant from the zero-field heat capacity and Θ_CW = (J₁ + J₂)/k_B from the uniform magnetic susceptibility, the saturation field determines the position of a particular compound in the phase diagram uniquely.

We give a summary of the results for the experimentally known compounds and show that our numerical findings agree very well with the experimental data for the magnetic susceptibility and the field dependence of the magnetization of the new compound BaCdVO(PO₄)₂. This compound is close to the quantum-critical point of the spin-nematic and collinear antiferromagnetic phase of the J₁-J₂ model as witnessed by a pronounced nonlinear magnetization curve.

We report our Monte Carlo results on the critical and multicritical behavior of the ±J Ising model [with a random-exchange probability P(J_xy) = pδ(J_xy -J)+(1-p)δ(J_xy +J)], in two and three dimensions. We study the transition line between the paramagnetic and ferromagnetic phase, which extends from p = 1 to a multicritical (Nishimori) point. By a finite-size scaling analysis, we provide strong numerical evidence that in three dimensions the critical behavior along this line belongs to the same universality class as that of the critical transition in the randomly dilute Ising model. In two dimensions we confirm that the critical behavior is controlled by the pure Ising fixed point and that disorder is marginally irrelevant, giving rise to universal logarithmic corrections. In both two and three dimensions, we also determine the location of the multicritical Nishimori point, as well as the renormalization-group dimensions of the operators that control the renormalization-group flow close to it.

The frustrated magnet clinoatacamite, γ-Cu₂(OH)₃Cl, is attracting a lot of interest after suggestions that at low temperature it forms an exotic quantum state termed a Valence Bond Solid (VBS) made from dimerised Cu²⁺ (S = ½) spins.[12] Key to the arguments surrounding this proposal were suggestions that the kagomé planes in the magnetic pyrochlore lattice of clinoatacamite are only weakly coupled, causing the system to behave as a quasi-2-dimensional magnet. This was reasoned from the near 95° angles made at the bridging oxygens that mediate exchange between the Cu ions that link the kagomé planes.

Recent work pointed out that this exchange model is inappropriate for γ-Cu₂(OH)₃Cl, where the oxygen is present as a μ₃-OH.[11] Further, it used symmetry calculations and neutron powder diffraction to show that the low temperature magnetic structure (T < 6 K) was canted and involved significant spin ordering on all the Cu²⁺ spins, which is incompatible with the interpretation of simultaneous VBS and Néel ordering. Correspondingly, clinoatacamite is best considered a distorted pyrochlore magnet. In this report we show detailed inelastic neutron scattering spectra and revisit the responses of this frustrated quantum magnet.

We present the phase diagram of the frustrated ferromagnetic S = 1/2 Heisenberg J₁-J₂ chain in a magnetic field, obtained by large scale exact diagonalizations and densitymatrix-renormalization-group simulations. A vector chirally ordered state, metamagnetic behavior and a sequence of spin multipolar Luttinger liquid phases up to hexadecupolar order are found. Starting from classical considerations, we point out that various multipolar correlations are imprinted in a magnetic state and that they can survive the onset of frustration and quantum fluctuations which destroy the conventional magnetic order. Our results also shed new light on previously discovered spin multipolar phases in two-dimensional S = 1/2 quantum magnets in a magnetic field.

Magnetization process of the mixed spin-1/2 and spin-3/2 Ising-Heisenberg diamond chain is examined by combining three exact analytical techniques: Kambe projection method, decoration-iteration transformation and transfer-matrix method. Multiple frustration-induced plateaus in a magnetization process of this geometrically frustrated system are found provided that a relative ratio between the antiferromagnetic Heisenberg- and Ising-type interactions exceeds some particular value. By contrast, there is just a single magnetization plateau if the frustrating Heisenberg interaction is sufficiently small compared to the Ising one.

We consider the antiferromagnetic Heisenberg model and the repulsive Hubbard model for a class of frustrated lattices with a completely dispersionless (flat) lowest one-particle (either one-magnon or one-electron) band. We construct exact many-particle ground states for a wide range of particle densities, calculate their degeneracy, and, as a result, obtain closed-form expressions for the low-temperature thermodynamic quantities around a particular value of the magnetic field h_sat or the chemical potential μ₀. We confirm our analytic findings by numerical data for finite lattices.

The optical conductivity σ(ω) is calculated at finite temperature T for CuO₂ chain clusters within a pd-Hubbard model. Data at T = 300 K for Li₂CuO₂ are reanalyzed within this approach. The relative weights of Zhang-Rice singlet and triplet charge excitations near 2.5 and 4 eV, respectively, depend strongly on T, and a dramatic dependence of σ(ω) on the ratio of the 1st to 2nd neighbor exchange integrals is predicted. Information about exchange interactions for edge-shared cuprates can be obtained from T-dependent optical spectra. A reduced intensity of the ZRS-transition with increasing T is also relevant for unfrustrated cuprates in general.

¹H-NMR study of a spin-1/2 triple-chain system Cu₃(OH)₄SO₄, in which the realization of an `idle-spin' state has been suggested recently from neutron experiments, were carried out in the temperature range down to 1.4 K. In the experiments under about 1 T, we found a clear anomaly of the nuclear magnetic relaxation rate and drastic change of the spectrum at around T_N = 5.4 K. NMR spectrum below T_N has a characteristic shape of an antiferromagnetic ordered state. This low-temperature spectrum is consistently reproduced by the calculation of local fields at proton sites on the basis of the idel-spin state. Further, T_N decreased as the applied field is increased up to 6.9 T.

We investigate spectral features of spatially anisotropic spin-1/2 frustrated antiferromagnets in a magnetic field by a weak-coupling approach from the one-dimensional (1D) limit. Using exact results of the Heisenberg chain, we calculate dynamical structure factors of spatially anisotropic frustrated antiferromagnets in two dimensions. We obtain rich peak structures depending on the momentum and the strength of magnetic fields. We identify the sharp peaks as bound and antibound states between particles carrying fractional S^z in 1D in a magnetic field, psinons and antipsinons, and those originating from 2-string solutions. We compare these spectral features with available experimental results on Cs₂CuCl₄, and suggest that the dynamical properties of Cs₂CuCl₄ in a magnetic field can be interpreted in terms of particles in 1D in a magnetic field.

For the 1D spin-1/2 Heisenberg model with ferromagnetic nearest-neighbor interaction and antiferromagnetic next-nearest neighbor one we present the phase diagram at T = 0 as obtained by DMRG analysis. The interplay of interactions generates two massless and two massive phases in the range of parameters considered. We discuss the properties of the correlations in these phases.

We studied the thermodynamics of the one-dimensional J₁-J₂ spin-1/2 Heisenberg chain for ferromagnetic nearest-neighbor bonds J₁ < 0 and frustrating antiferromagnetic next- nearest-neighbor bonds J₂ > 0 using full diagonalization of finite rings and a second-order Green-function formalism. Thereby we focus on J₂ < |J₁|/4 where the ground state is still ferromagnetic, but the frustration influences the thermodynamic properties. We found that their critical indices are not changed by J₂. The analysis of the low-temperature behavior of the susceptibility χ leads to the conclusion that this behavior changes from χ ∝ T^-2 at J₂ < |J₁|/4 to χ ∝ T^-3/2 at the quantum-critical point J₂ = |J₁|/4. Another effect of the frustration is the appearance of an extra low-T maximum in the specific heat C_v(T) for J₂ & |J₁|/8, indicating its strong influence on the low-energy spectrum.

The magnetization process of the distorted diamond chain is theoretically investigated using the numerical exact diagonalization and the density matrix renormalization group calculation. It is found that for some specified parameters the ground-state critical behavior is dominated by the incommensurate spin correlation parallel to the external magnetic field, around the 2/3 magnetization plateau. In the presence of interchain interaction it should be an incommensurate long-range order which possibly leads to a supersolid if coexisting with the usual transverse antiferromagnetic long-range order.

Employing various numerical methods, we determine the ground-state phase diagram of an (S, S') = (1, 2) spin-alternating chain with antiferromagnetic nearest-neighboring exchange interactions and uniaxial single-ion anisotropies. The resulting phase diagram consists of eight kinds of phases including two phases which accompany the spontaneous breaking of the translational symmetry and a ferrimagnetic phase in which the ground-state magnetization varies continuously with the uniaxial single-ion anisotropy constants for the S=1 and S =2 spins. The appearance of these three phases is attributed to the competition between the uniaxial single-ion anisotropies of both spins.

We report on high-field magnetic properties of the silver vanadium phosphate Ag₂VOP₂O₇. This compound has a layered crystal structure, but the specific topology of the V-P-O framework gives rise to a one-dimensional spin system, a frustrated alternating chain. Low-field magnetization measurements and band structure calculations show that Ag₂VOP₂O₇ is close to the dimer limit with the largest nearest-neighbor interaction of about 30 K. High- field magnetization data reveal the critical fields μ₀H_c1 ≊ 23 T (closing of the spin gap) and μ₀H_c2 ≊ 30 T (saturation by full alignment of the magnetic moments). From H_c1 to H_c2 the magnetization increases sharply similar to the system of isolated dimers. Thus, the magnetic frustration in Ag₂VOP₂O₇ bears little influence on the high-field properties of this compound.

We present our theoretical results on the Kondo necklace model, which is known to give a good description of the half-filled state of the Kondo lattice model, on geometrically frustrated lattices. We employ the Lanczos exact diagonalization method as well as the bond-operator mean-field approximation to clarify the magnetic state at zero temperature. We examine a possibility of relieving severe frustration by making a spatially-periodic arrangement of magnetic ordered sites and nonmagnetic ones, i.e., the magnetic moments vanish periodically due to the Kondo singlet formation. We call the composite of magnetic and Kondo-singlet subsystems 'partial Kondo-singlet state', by analogy with the partial order in frustrated spin systems. We demonstrate that small clusters of 1D and 2D frustrated models show a tendency to exhibit the partial Kondo-singlet formation, and compare the results with those by the bond-operator mean-field approximation.

We report results of sound-velocity and sound-attenuation measurements in the quantum S = 1 spin-chain magnet NiCl₂-4SC(NH₂)₂ that shows a field-induced antiferromagnetic (AF) ordering and two corresponding quantum critical points at H_c ∼ 2.1 T and H_s ∼ 12.6 T. The longitudinal acoustic c₃₃ mode modulates the in-chain exchange interaction and shows a softening in the vicinity of the quantum critical points, accompanied by energy dissipation in the acoustic wave. We discuss our results with a model where the main contribution to the spin-lattice interaction arises from the exchange-striction coupling within one-dimensional spin-chains.

Ultrasonic velocity data obtained on CuFeO₂ are re-analyzed in the context of a Landau free energy which includes spin-lattice coupling. This comprehensive model simultaneously accounts for the elastic and magnetic properties of CuFeO₂ at zero field. Softening of the elastic constants C₁₁, C₄₄, and especially C₆₆, ineluctably indicates that the R3_m → C₂/m structural transition at T_N1 = 13.7 K is primarily pseudoproper ferroelastic. The present analysis also suggests that the elastic anomalies observed at T_N2 are dominated by magnetoelastic coupling and strengthens the conclusion that the unusual properties of CuFeO₂ are a consequence of the interplay between its magnetism and elastic deformations.

We report magnetic susceptibility measurements on nonmagnetic impurity-doped multiferroic CuFe_1-yGa_yO₂ with 0 ≤ y ≤ 0:08. The temperature versus Ga concentration magnetic phase diagram was obtained. Comparing the presently obtained phase diagram of CuFe_1-yGa_yO₂ with that of CuFe_1-xAl_xO₂, we find that the stability of 4SL ground state for substitution of nonmagnetic ions does not depend on the nonmagnetic ionic radius significantly. On the other hand, the FEIC phase in CuFe_1-yGa_yO₂ exists in a wider region of 0:02 ≤ y ≤ 0:05 than CuFe_1-xAl_xO₂. We thus find that the local lattice distortion caused by large difference in ionic radii between Al3⁺ and Fe3⁺ affects the stability of the FEIC phase for nonmagnetic ion substitution significantly.

For the new class of multi-ferroics, in which inversion symmetry is broken by magnetic ordering, a number of models have been developed to describe the exchange interactions that might give rise to net polarisation. We explore the importance of phase factors in these theories and how this concept brings together existing ideas within a common motif. Phase differences appear ubiquitous within the subject and they are fixed or free dependent upon the symmetry of the magnetic atoms. Further, we state restrictions upon which representations and co-representations a system displaying electric polarisation can order under.

Electronic, dielectric and magnetic properties in exotic dielectrics, RFe₂O₄ (R: rare-earth metal ion), are investigated. By analyzing the effective Hamiltonian for Fe 3d electrons, spin and charge correlation functions and electric polarization are calculated by the Monte-Carlo technique. Electric polarization is strongly reinforced below magnetic ordering temperature and is controlled by applying magnetic field. Observed unique magneto-dielectric phenomena are attributed to frustration in a spin-charge coupled system.

The electric-field dependence of the magnetic structure of multiferroic MnWO4 has been directly investigated using spherical neutron polarimetry as a function of temperature. The application of an electric field is shown to drive the magnetic structure to a single `chiral' domain. The magnitude of the electric field required to do this is shown to increase upon cooling. The coupling between the magnetic order and electric polarization is further demonstrated.

Frustrated magnets in high magnetic field have a long history of offering beautiful surprises to the patient investigator. Here we present the results of extensive classical Monte Carlo simulations of a variety of models of two dimensional magnets in magnetic field, together with complementary spin wave analysis. Striking results include (i) a massively enhanced magnetocaloric effect in antiferromagnets bordering on ferromagnetic order, (ii) a route to an m = 1/3 magnetization plateau on a square lattice, and (iii) a cascade of phase transitions in a simple model of AgNiO₂.

The spin correlations in a series of cobaltate polycrystalline samples with Swedenborgite structure, ABaCo₃BO₇ (A = Y, Ca, and B = Co, Fe, Al, Zn), were studied by means of diffuse polarized neutron scattering. The alternate stacking of kagome and triangular Co layers forms a tetrahedral Co-network with geometrical frustration of antiferromagnetically (AF) coupled spins, which typically suppresses long-range order even at low temperatures (~1K) despite Curie-Weiss temperatures in the order of 1000 K. The generic diffuse magnetic scattering as found in Y_0.5Ca_0.5BaCo₄O₇ reveals two dimensional (2D) spin correlations on the kagome sublattices towards the entropically favoured × structure and suggests a decoupling of layers by low spin states S = 0 on triangular sites. Co-substitution by Al and Zn yields similar diffuse magnetic scattering, however, spin dilution results in even more disordered spin liquid or spin glass states. With B = Fe or Co, differences in the magnetic scattering evolve, indicating the onset of spin correlations perpendicular to the kagome layers and non-vanishing spin states on the triangular sites. Geometrical frustration prohibits any 3D long-range order when the characteristic 2D spin correlations with the × motif is present. We observe long-range order only in YBaCo₄O₇ and CaBaCo₃FeO₇ showing rather distinct ordering wave-vectors.

The magnetization process of single crystalline GaV4S8 including tetrahedral magnetic clusters was measured in the magnetically ordered state below T_C ≊ 13 K. Just below TC, steps were observed at very low fields of the order of 100 Oe, suggesting the competition of several intra- and inter-cluster interactions in a low energy range.

We report on neutron scattering studies of a rare earth intermetallic compound ErNi₂Ge₂. Polarized neutron scattering experiments revealed that the magnetic ordered moment m lies in ab-plane. Taking account of a lack of the third higher harmonic reflection, ErNi₂Ge₂ is considered to have a helical magnetic structure. The magnetic scattering profiles along the [100]*- and the [110]*-directions are well described by the sum of Gaussian and modified-Lorentzian terms, even far below TN, indicating that short-range orders coexist with a long-range order. Interestingly, the modified-Lorentzian-type diffuse scattering is not present in the profiles along the [001]*-direction. The anisotropy of the diffuse scattering suggests that the short-range-order consists of one dimensional long-range helices along the c-axis.

Anodic oxidation allows the preparation of aluminum oxide (AAO) templates with self-organized, ordered pores and diameters ranging from 10 nm to 200 nm. Electrochemical deposition of metals, semiconductors and oxides has been demonstrated. As a case study, we investigated the growth of Fe/Ni nanowires in the AAO templates. Transmission and scanning electron microscopy are used to optimize growth parameters and to demonstrate that length scales and periodicities of the templates can be transferred to the wire arrays. This paves the way for the preparation and investigation of tailored matter on nanoscales with emerging applications in photonics, sensorics and information technology.

A percolated-induced ferromagnetic moment in KNi_xZn_1−xF³ for x = 0:57, which is Heisenberg-type diluted three-dimensional magnet, is studied by electron spin resonance. Below T_C ' 24 K, ferrimagnetic resonance spectra appeared as expected. On the other hand, in KCo_xZn_1−xF³ for 0.49 ≥ x < 1, which are Ising-type diluted three-dimensional magnets, a percolated-induced ferromagnetic moment did not appear. This difierence may play an important key role in Coulomb repulsion between Zn²⁺ ions because KNi_xZn_1−xF³ consists of simple cubic lattice, on the other hand tetragonal distortion exists in KCo_xZn_1−xF³.

We study a spin-1/2 frustrated magnetic cluster Mo₇₅V₂₀, whose possible Hamiltonian is _SD = JΣ¹⁰_i=1S_2i-1 · S_2i+1J'JΣ²⁰_i=1S_i · S_i+1 + J"Σ¹⁰_i=1S_2i · S_2i+4. The J- and J"-bonds, respectively, form a ten-spin ring and two five-spin rings, and the five-spin rings are coupled to the ten-spin ring by the J'-bonds so as to form isosceles triangles of one J-bond and two J'-bonds. It is shown that experimental susceptibility, accompanied by low-temperature Curie law, is well reproduced by J = 388 K, J' = 163 K and J" = 81 K. We develop a perturbation theory to understand why the stronger J'-bonds does not wash out the low-temperature Curie law due to the doublet behavior of five-spin rings constructed by the weaker J"-bonds. Calculated results of temperature dependence of specific heat under small magnetic fields are also presented.

We use the example of the cuboctahedron, a highly frustrated molecule with 12 sites, to study the approach to the classical limit. We compute magnetic susceptibility, specific heat, and magnetic cooling rate at high magnetic fields and low temperatures for different spin quantum numbers s. Remarkably big deviations of these quantities from their classical counterparts are observed even for values of s which are usually considered to be almost classical.

We study integrated density of states (DOS) and thermodynamic properties for the S = 1=2 quantum spin icosidodecahedron, using a numerical method for calculating an eigenvalue distribution function. For the ideal quantum spin icosidodecahedron with next-nearest neighbor interactions, we find that there exist many singlet states before the first triplet state, which is an evidence of the resonating valence bond (RVB) state, and the experimental susceptibilities of Mo₇₂V₃₀ measured by Müller et al. and Botar et al. cannot be reproduced within the ideal model. Because V⁴⁺ ions are on vertices of a slightly distorted icosidodecahedron in Mo₇₂V₃₀, we study the distorted version of the model and find that agreement between theoretical and experimental susceptibilities is improved. For this distorted model, there exist about ten singlet states before the first triplet state.