Anomalous Excitation Spectra of Frustrated Quantum Antiferromagnets

We use series expansions to study the excitation spectra of spin-1/2 antiferromagnets on anisotropic triangular lattices. For the isotropic triangular lattice model (TLM), the high-energy spectra show several anomalous features that differ strongly from linear spin-wave theory (LSWT). Even in the Neel phase, the deviations from LSWT increase sharply with frustration, leading to rotonlike minima at special wave vectors. We argue that these results can be interpreted naturally in a spinon language and provide an explanation for the previously observed anomalous finite-temperature properties of the TLM. In the coupled-chains limit, quantum renormalizations strongly enhance the one-dimensionality of the spectra, in agreement with experiments on Cs2CuCl4.

The Heisenberg antiferromagnet on an anisotropic triangular lattice: linear spin-wave theory

We consider the effect of quantum spin fluctuations on the ground-state properties of the Heisenberg antiferromagnet on an anisotropic triangular lattice using linear spin-wave (LSW) theory. This model should describe the magnetic properties of the insulating phase of the kappa-(BEDT-TTF)(2)X family of superconducting molecular crystals. The ground-state energy, the staggered magnetization, magnon excitation spectra, and spin-wave velocities are computed as functions of the ratio of the antiferromagnetic exchange between the second and first neighbours, J(2)/J(1). We find that near J(2)/J(1) = 0.5, i.e., in the region where the classical spin configuration changes from a Neel-ordered phase to a spiral phase, the staggered magnetization vanishes, suggesting the possibility of a quantum disordered state. in this region, the quantum correction to the magnetization is large but finite. This is in contrast to the case for the frustrated Heisenberg model on a square lattice, for which the quantum correction diverges logarithmically at the transition from the Neel to the collinear phase. For large J(2)/J(1), the model becomes a set of chains with frustrated interchain coupling. For J(2) > 4J(1), the quantum correction to the magnetization, within LSW theory, becomes comparable to the classical magnetization, suggesting the possibility of a quantum disordered state. We show that, in this regime, the quantum fluctuations are much larger than for a set of weakly coupled chains with non-frustrated interchain coupling.

Phase diagram for a class of spin-1/2 Heisenberg models interpolating between the square-lattice, the triangular-lattice, and the linear-chain limits

We study the spin-1/2 Heisenberg models on an anisotropic two-dimensional lattice which interpolates between the square lattice at one end, a set of decoupled spin chains on the other end, and the triangular-lattice Heisenberg model in between. By series expansions around two different dimer ground states and around various commensurate and incommensurate magnetically ordered states, we establish the phase diagram for this model of a frustrated antiferromagnet. We find a particularly rich phase diagram due to the interplay of magnetic frustration, quantum fluctuations, and varying dimensionality. There is a large region of the usual two-sublattice Neel phase, a three-sublattice phase for the triangular-lattice model, a region of incommensurate magnetic order around the triangular-lattice model, and regions in parameter space where there is no magnetic order. We find that the incommensurate ordering wave vector is in general altered from its classical value by quantum fluctuations. The regime of weakly coupled chains is particularly interesting and appears to be nearly critical. [S0163-1829(99)10421-1].

Large-N solutions of the Heisenberg and Hubbard-Heisenberg models on the anisotropic triangular lattice: application to Cs2CuCl4 and to the layered organic superconductors kappa-(BEDT-TTF)(2)X (BEDT-TTF bis(ethylene-dithio)tetrathiafulvalene); X anion)

We solve the Sp(N) Heisenberg and SU(N) Hubbard-Heisenberg models on the anisotropic triangular lattice in the large-N limit. These two models may describe respectively the magnetic and electronic properties of the family of layered organic materials K-(BEDT-TTF)(2)X, The Heisenberg model is also relevant to the frustrated antiferromagnet, Cs2CuCl4. We find rich phase diagrams for each model. The Sp(N) :antiferromagnet is shown to have five different phases as a function of the size of the spin and the degree of anisotropy of the triangular lattice. The effects of fluctuations at finite N are also discussed. For parameters relevant to Cs2CuCl4 the ground state either exhibits incommensurate spin order, or is in a quantum disordered phase with deconfined spin-1/2 excitations and topological order. The SU(N) Hubbard-Heisenberg model exhibits an insulating dimer phase, an insulating box phase, a semi-metallic staggered flux phase (SFP), and a metallic uniform phase. The uniform and SFP phases exhibit a pseudogap, A metal-insulator transition occurs at intermediate values of the interaction strength.

Excitation spectra of the spin-1/2 triangular-lattice Heisenberg antiferromagnet

We use series expansion methods to calculate the dispersion relation of the one-magnon excitations for the spin-(1)/(2) triangular-lattice nearest-neighbor Heisenberg antiferromagnet above a three-sublattice ordered ground state. Several striking features are observed compared to the classical (large-S) spin-wave spectra. Whereas, at low energies the dispersion is only weakly renormalized by quantum fluctuations, significant anomalies are observed at high energies. In particular, we find rotonlike minima at special wave vectors and strong downward renormalization in large parts of the Brillouin zone, leading to very flat or dispersionless modes. We present detailed comparison of our calculated excitation energies in the Brillouin zone with the spin-wave dispersion to order 1/S calculated recently by Starykh, Chubukov, and Abanov [Phys. Rev. B74, 180403(R) (2006)]. We find many common features but also some quantitative and qualitative differences. We show that at temperatures as low as 0.1J the thermally excited rotons make a significant contribution to the entropy. Consequently, unlike for the square lattice model, a nonlinear sigma model description of the finite-temperature properties is only applicable at temperatures < 0.1J. Finally, we review recent NMR measurements on the organic compound kappa-(BEDT-TTF)(2)Cu-2(CN)(3). We argue that these are inconsistent with long-range order and a description of the low-energy excitations in terms of interacting magnons, and that therefore a Heisenberg model with only nearest-neighbor exchange does not offer an adequate description of this material.

Temperature dependence of the magnetic susceptibility for triangular-lattice antiferromagnets with spatially anisotropic exchange constants

We present the temperature dependence of the uniform susceptibility of spin-half quantum antiferromagnets on spatially anisotropic triangular lattices, using high-temperature series expansions. We consider a model with two exchange constants J1 and J2 on a lattice that interpolates between the limits of a square lattice (J1=0), a triangular lattice (J2=J1), and decoupled linear chains (J2=0). In all cases, the susceptibility, which has a Curie-Weiss behavior at high temperatures, rolls over and begins to decrease below a peak temperature Tp. Scaling the exchange constants to get the same peak temperature shows that the susceptibilities for the square lattice and linear chain limits have similar magnitudes near the peak. Maximum deviation arises near the triangular-lattice limit, where frustration leads to much smaller susceptibility and with a flatter temperature dependence. We compare our results to the inorganic materials Cs2CuCl4 and Cs2CuBr4 and to a number of organic molecular crystals. We find that the former (Cs2CuCl4 and Cs2CuBr4) are weakly frustrated and their exchange parameters determined through the temperature dependence of the susceptibility are in agreement with neutron-scattering measurements. In contrast, the organic materials considered are strongly frustrated with exchange parameters near the isotropic triangular-lattice limit.

Quantum-Critical Spin Dynamics in Quasi-One-Dimensional Antiferromagnets

By means of nuclear spin-lattice relaxation rate T-1(-1), we follow the spin dynamics as a function of the applied magnetic field in two gapped quasi-one-dimensional quantum antiferromagnets: the anisotropic spin-chain system NiCl2-4SC(NH2)(2) and the spin-ladder system (C5H12N)(2)CuBr4. In both systems, spin excitations are confirmed to evolve from magnons in the gapped state to spinons in the gapless Tomonaga-Luttinger-liquid state. In between, T-1(-1) exhibits a pronounced, continuous variation, which is shown to scale in accordance with quantum criticality. We extract the critical exponent for T-1(-1), compare it to the theory, and show that this behavior is identical in both studied systems, thus demonstrating the universality of quantum-critical behavior.

Effet de la symétrie sur la supraconductivité de LaRhSi3 et la frustration magnétique du SrRE2O4 (RE = Dy ou Ho)

Dans la première partie, nous présentons les résultats de l'étude du supraconducteur sans inversion de symétrie LaRhSi3 par spectroscopie muonique. En champ nul, nous n'avons pas détecté de champ interne. Ceci indique que la fonction d'onde de l'état supraconducteur n'est pas dominée par l'état triplet. Les mesures en champ transverse de 35G présentent une transition en accord avec la transition de phase attendue sous le champ critique Hc1. Nous avons répété ces mesures pour un champ entre Hc1 et Hc2, 150G. Le spectre obtenu pour ces mesures conserve l'asymétrie et relaxe rapidement à basse température tel que prédit pour un supraconducteur dans la phase d'Abrikosov. Néanmoins, les relaxations produites par ce balayage en température présentent une transition à près de 2 fois la température critique attendue. Dans la deuxième partie de ce mémoire, nous donnons l'interprétation des résultats de la diffraction neutronique inélastique par l'étude des champs électriques cristallins. Ces mesures ont été effectuées sur des aimants frustrés SrHo2O4 et SrDy2O4 sous la forme de poudre. L'étude des niveaux produits par les champs cristallins par la méthode des opérateurs de Stevens indique une perte du moment cinétique dans les deux matériaux. Pour le SrDy2O4, l'état fondamental serait constitué de quatre états dégénérés quasi accidentellement qui portent un moment magnétique total non-nul. Toute fois, nos mesures de susceptibilité magnétique ne montrent aucun ordre au-dessus de 50mK. Pour le SrHo2O4, le fondamental est formé d'une paire accidentelle. Nous obtenons un moment magnétique de 6.94(8)$\mu_B$ ce qui s'accorde avec les données expérimentales.

Investigation of Frustrated Quasi-One-Dimensional Quantum Spin-Chain Materials

Copper arsenite CuAs2O4 and Copper antimonite CuSb2O4 are S=1/2 (Cu2+ 3d9 electronic configuration) quasi-one-dimensional quantum spin-chain compounds. Both compounds crystallize with tetragonal structures containing edge sharing CuO6 octahedra chains which experience Jahn-Teller distortions. The basal planes of the octahedra link together to form CuO2 ribbon-chains which harbor Cu2+ spin-chains. These compounds are magnetically frustrated with competing nearest-neighbour and next-nearest-neighbour intrachain spin-exchange interactions. Despite the similarities between CuAs2O4 and CuSb2O4, they exhibit very different magnetic properties. In this thesis work, the physical properties of CuAs2O4 and CuSb2O4 are investigated using a variety of experimental techniques which include x-ray diffraction, magnetic susceptibility measurements, heat capacity measurements, Raman spectroscopy, electron paramagnetic resonance, neutron diffraction, and dielectric capacitance measurements. CuAs2O4 exhibits dominant ferromagnetic nearest-neighbour and weaker antiferromagnetic next-nearest-neighbour intrachain spin-exchange interactions. The ratio of the intrachain interactions amounts to Jnn/Jnnn = -4.1. CuAs2O4 was found to order with a ferromagnetic groundstate below TC = 7.4 K. An extensive physical characterization of the magnetic and structural properties of CuAs2O4 was carried out. Under the effect of hydrostatic pressure, CuAs2O4 was found to undergo a structural phase transition at 9 GPa to a new spin-chain structure. The structural phase transition is accompanied by a severe alteration of the magnetic properties. The high-pressure phase exhibits dominant ferromagnetic next-nearest-neighbour spin-exchange interactions and weaker ferromagnetic nearest-neighbour interactions. The ratio of the intrachain interactions in the high-pressure phase was found to be Jnn/Jnnn = 0.3. Structural and magnetic characterizations under hydrostatic pressure are reported and a relationship between the structural and magnetic properties was established. CuSb2O4 orders antiferromagnetically below TN = 1.8 K with an incommensurate helicoidal magnetic structure. CuSb2O4 is characterized by ferromagnetic nearest-neighbour and antiferromagnetic next-nearest-neighbour spin-exchange interactions with Jnn/Jnnn = -1.8. A (H, T) magnetic phase diagram was constructed using low-temperature magnetization and heat capacity measurements. The resulting phase diagram contains multiple phases as a consequence of the strong intrachain magnetic frustration. Indications of ferroelectricity were observed in the incommensurate antiferromagnetic phase.

Cubic interactions and quantum criticality in dimerized antiferromagnets

In certain Mott-insulating dimerized antiferromagnets, triplet excitations of the paramagnetic phase display both three-particle and four-particle interactions. When such a magnet undergoes a quantum phase transition into a magnetically ordered state, the three-particle interaction becomes part of the critical theory provided that the lattice ordering wave vector is zero. One microscopic example is the staggered-dimer antiferromagnet on the square lattice, for which deviations from O(3) universality have been reported in numerical studies. Using both symmetry arguments and microscopic calculations, we show that a nontrivial cubic term arises in the relevant order-parameter quantum field theory, and we assess its consequences using a combination of analytical and numerical methods. We also present finite-temperature quantum Monte Carlo data for the staggered-dimer antiferromagnet which complement recently published results. The data can be consistently interpreted in terms of critical exponents identical to that of the standard O(3) universality class, but with anomalously large corrections to scaling. We argue that the cubic interaction of critical triplons, although irrelevant in two spatial dimensions, is responsible for the leading corrections to scaling due to its small scaling dimension.

Bose-Einstein condensation in antiferromagnets close to the saturation field

At zero temperature and strong applied magnetic fields the ground state of an anisotropic antiferromagnet is a saturated paramagnet with fully aligned spins. We study the quantum phase transition as the field is reduced below an upper critical H(c2) and the system enters a XY-antiferromagnetic phase. Using a bond operator representation we consider a model spin-1 Heisenberg antiferromagnetic with single-ion anisotropy in hypercubic lattices under strong magnetic fields. We show that the transition at H(c2) can be interpreted as a Bose-Einstein condensation (BEC) of magnons. The theoretical results are used to analyze our magnetization versus field data in the organic compound NiCl(2)-4SC(NH(2))(2) (DTN) at very low temperatures. This is the ideal BEC system to study this transition since H(c2) is sufficiently low to be reached with static magnetic fields (as opposed to pulsed fields). The scaling of the magnetization as a function of field and temperature close to H(c2) shows excellent agreement with the theoretical predictions. It allows us to obtain the quantum critical exponents and confirm the BEC nature of the transition at H(c2).

Phase diagram of a Heisenberg spin-Peierls model with quantum phonons

Using a new version of the density-matrix renormalization group we determine the phase diagram of a model of an antiferromagnetic Heisenberg spin chain where the spins interact with quantum phonons. A quantum phase transition from a gapless spin-fluid state to a gapped dimerized phase occurs at a nonzero value of the spin-phonon coupling. The transition is in the same universality class as that of a frustrated spin chain, to which the model maps in the diabatic limit. We argue that realistic modeling of known spin-Peierls materials should include the effects of quantum phonons.

Energy as an entanglement witness for quantum many-body systems

We investigate quantum many-body systems where all low-energy states are entangled. As a tool for quantifying such systems, we introduce the concept of the entanglement gap, which is the difference in energy between the ground-state energy and the minimum energy that a separable (unentangled) state may attain. If the energy of the system lies within the entanglement gap, the state of the system is guaranteed to be entangled. We find Hamiltonians that have the largest possible entanglement gap; for a system consisting of two interacting spin-1/2 subsystems, the Heisenberg antiferromagnet is one such example. We also introduce a related concept, the entanglement-gap temperature: the temperature below which the thermal state is certainly entangled, as witnessed by its energy. We give an example of a bipartite Hamiltonian with an arbitrarily high entanglement-gap temperature for fixed total energy range. For bipartite spin lattices we prove a theorem demonstrating that the entanglement gap necessarily decreases as the coordination number is increased. We investigate frustrated lattices and quantum phase transitions as physical phenomena that affect the entanglement gap.