No abstract

The natural mineral azurite Cu(3)(CO(3))(2)(OH)(2) is a frustrated magnet displaying unusual and controversially discussed magnetic behavior. Motivated by the lack of a unified description for this system, we perform a theoretical study based on density functional theory as well as state-of-the-art numerical many-body calculations. We propose an effective generalized spin-1/2 diamond chain model which provides a consistent description of experiments: low-temperature magnetization, inelastic neutron scattering, nuclear magnetic resonance measurements, magnetic susceptibility as well as new specific heat measurements. With this study we demonstrate that the balanced combination of first principles with powerful many-body methods successfully describes the behavior of this frustrated material.

We present a specific heat and inelastic neutron scattering study in magnetic fields up into the 1/3 magnetization plateau phase of the diamond chain compound azurite Cu3(CO3)2(OH)2. We establish that the magnetization plateau is a dimer-monomer state, i.e., consisting of a chain of S = 1/2 monomers, which are separated by S = 0 dimers on the diamond chain backbone. The effective spin couplings Jmono/kB = 10.1(2) K and J dimer /kB = 1.8(1) K are derived from the monomer and dimer dispersions. They are associated to microscopic couplings J1/kB = 1(2) K, J2/kB = 55(5) K and a ferromagnetic J3/kB = −20(5) K, possibly as result of d z 2 orbitals in the Cu-O bonds providing the superexchange pathways.PACS numbers: 75.30. Et, 75.10.Pq, 75.45.+j Great interest has surrounded the observation of a 1/3 magnetization plateau in azurite CuThis material, famous as a painting pigment of deepblue colour, has been proposed as a realisation of the exotic diamond-chain Hamiltonian of coupled spin-1/2 moments, written aŝHere, J 2 is the magnetic coupling of the diamond backbone, while J 1 and J 3 represent the coupling of the monomers along the chain [3, 4, 5] (Fig. 3). Depending on the relative coupling strengths J 1 , J 2 , J 3 , this model affords a host of exotic phases and quantum phase transitions, including possibly M = 1/3 fractionalisation [6] or exotic dimer phases [4]. However, determining the magnetic exchange couplings in azurite has proved difficult, yielding controversial results. While a susceptibility χ study claims, subsequent numerical studies of χ dispute this claim, proposing a ferromagnetic (FM) J 3 , and thus a non-frustrated scenario [2]. The general issue underlying these starkly contrasting interpretations of the same experimental data is that of the nature of magnetic coupling in low-dimensional (low-D) quantum magnets. In azurite Cu 3 (CO 3 ) 2 (OH) 2 , the Cu 2+ ions (S = 1/2) are in a square-planar coordination on two inequivalent sites [7]. The system has a monoclinic crystal structure (space group P2 1 /c, lattice parameters a = 5.

The spin-liquid candidate kappa-(BEDT-TTF)2Cu2(CN)3 has been studied by measuring the uniaxial expansion coefficients alpha(i), the specific heat, and magnetic susceptibility. Special emphasis was placed on the mysterious anomaly around 6 K--a potential spin-liquid instability. Distinct and strongly anisotropic lattice effects have been observed at 6 K, clearly identifying this feature as a second-order phase transition. Owing to the large anomalies in alpha(i), the application of Grüneisen scaling has enabled us to determine the corresponding specific heat contribution and the entropy release. Comparison of the latter with available spin models suggests that spin degrees of freedom alone cannot account for the phase transition. Scenarios involving charge degrees of freedom are discussed.

Discontinuous changes of the lattice parameters at the Mott metal-insulator transition are detected by high-resolution dilatometry on deuterated crystals of the layered organic conductor kappa-(BEDT-TTF)(2)Cu[N(CN)(2)]Br. The uniaxial expansivities uncover a striking and unexpected anisotropy, notably a zero effect along the in-plane c axis along which the electronic interactions are relatively strong. A huge thermal expansion anomaly is observed near the end point of the first-order transition line enabling us to explore the critical behavior with very high sensitivity. The analysis yields critical fluctuations with an exponent alpha approximately 0.8+/-0.15 at odds with the novel criticality recently proposed for these materials [Kagawa et al., Nature (London) 436, 534 (2005)]. Our data suggest an intricate role of the lattice degrees of freedom in the Mott transition for the present materials.