It has been suggested that the nearest-neighbor antiferromagnetic Heisenberg model on the Kagome lattice may be a good starting point for understanding the spin-liquid behavior discovered in Herbertsmithite. In this work, we investigate possible quantum spin liquid phases in the presence of spin-rotation symmetry-breaking perturbations such as Dzyaloshinskii-Moriya (DM) and Ising interactions, as well as second-neighbor antiferromagnetic Heisenberg interactions. Experiments suggest that such perturbations are likely to be present in Herbertsmithite. We use the projective symmetry group (PSG) analysis within the framework of the slave-fermion construction of quantum spin liquid phases and systematically classify possible spin liquid phases in the presence of perturbations mentioned above. The dynamical spin-structure factor for relevant spin liquid phases is computed and the effect of those perturbations are studied. Our calculations reveal dispersive features in the spin structure factor embedded in a generally diffuse background due to the existence of fractionalized spin-1/2 excitations called spinons. For two of the previously proposed Z2 states, the dispersive features are almost absent, and diffuse scattering dominates over a large energy window throughout the Brillouin zone. This resembles the structure factor observed in recent inelastic neutron scattering experiments on singlet crystals of Herbertsmithite. Furthermore, one of the Z2 states with the spin structure factor with mostly diffuse scattering is gapped, and it may be adiabatically connected to the gapped spin liquid state observed in recent Density Matrix Renormalization Group calculations for the nearest neighbor antiferromagnetic Heisenberg model. The perturbations mentioned above are found to enhance the diffuse nature of the spin structure factor and reduce the momentum dependencies of the spin gap. We also calculate the electron spin resonance (ESR) absorption spectra that further characterize the role of spin-rotation symmetry breaking perturbations in these states. We suggest that the measurement of ESR spectra can shed more light into the nature of the ground state in Herbertsmithite.

We develop anisotropic pseudo-spin antiferromagnetic Heisenberg models for monoclinically distorted double perovskites. We focus on these A2BB ′ O6 materials that have magnetic moments on the 4d or 5d transition metal B ′ ions, which form a face-centered cubic lattice. In these models, we consider local z-axis distortion of B ′ -O octahedra, affecting relative occupancy of t2g orbitals, along with geometric effects of the monoclinic distortion and spin-orbit coupling. The resulting pseudo-spin-1/2 models are solved in the saddle-point limit of the Sp(N ) generalization of the Heisenberg model. The spin S in the SU(2) case generalizes as a parameter κ controlling quantum fluctuation in the Sp(N ) case. We consider two different models that may be appropriate for these systems. In particular, using Heisenberg exchange parameters for La2LiMoO6 from a spin-dimer calculation, we conclude that this pseudo-spin-1/2 system may order, but will be very close to a disordered spin liquid state.

Motivated by recent experiments on Ba 3 Cr 2 O 8 , a new spin-dimer compound with spin-1/2 moments of Cr 5+ ions, we theoretically investigate the field-induced magnetic ordering in this material in view of the BoseEinstein condensation ͑BEC͒ of triplet excitations ͑triplons͒. We apply the self-consistent Hartree-Fock-Popov ͑HFP͒ approach to a microscopic Hamiltonian, using the realistic triplon dispersion measured in an inelastic neutron-scattering experiment. In particular, we ask to what extent the BEC of dilute triplons near the critical field can explain the magnetic ordering in this material. For example, we investigate the temperature range where the BEC picture of triplons can be applied via the HFP approach. We also determine the temperature regime where a quadratic approximation of the triplon dispersion works. It is found that the strength of the effective repulsive interaction between triplons is much weaker in Ba 3 Cr 2 O 8 than in the canonical spin-dimer compound TlCuCl 3 . Small effective repulsive interaction in combination with the narrow band of triplons leads to higher density of triplons n cr at the critical point. The combined effect points to a bigger HFP correction Un cr in Ba 3 Cr 2 O 8 than in TlCuCl 3 . Nonetheless, the HFP approach provides a reasonable explanation of the transverse magnetization and the specific-heat data of Ba 3 Cr 2 O 8 .

A recent study [Tassel et al., Phys. Rev. Lett. 105, 167205 (2010)] has proposed a remarkable spin model for (CuCl)LaNb 2 O 7 , in which dimers are ferromagnetically coupled to each other on the distorted Shastry-Sutherland lattice. In this model, the intradimer exchange coupling J > 0 is antiferromagnetic, while the interdimer exchange couplings are ferromagnetic and take different values, J x ,J y < 0, in the two bond directions. Anticipating that the highly frustrated character of this model may lead to a wide range of behaviors in (CuCl)LaNb 2 O 7 and related compounds, we theoretically investigate the ground-state phase diagram of this model in detail using the following three approaches: a strong-coupling expansion for small J x and J y , exact diagonalization for finite clusters, and a Schwinger boson mean-field theory. When |J x |,|J y | J , the system stays in a dimer singlet phase with a finite spin gap. This state is adiabatically connected to the decoupled-dimer limit J x = J y = 0. We show that the magnetization process of this phase depends crucially on the spatial anisotropy of the interdimer couplings. The magnetization shows a jump or a smooth increase for weak and strong anisotropy, respectively, after the spin gap closes at a certain magnetic field. When |J x | or |J y | J , quantum phase transitions to various magnetically ordered phases (ferromagnetic, collinear stripe, and spiral) occur. The Schwinger boson analysis demonstrates that quantum fluctuations split the classical degeneracy of different spiral ground states. Implications for (CuCl)LaNb 2 O 7 and related compounds are discussed in light of our theoretical results and existing experimental data.

Recently, a number of experiments indicate the possible presence of spin liquid phases in quantum magnets with spin-1/2 and spin-1 moments sitting on triangular-lattice-based structures in Ba3CuSb2O9 and Ba3NiSb2O9 respectively. In relation to these experiments, several theoretical proposals have been made for spin liquid phases and spin-liquid-like behaviours on the stacked triangular lattice. While the crystal structures of these materials are currently under debate, it is nonetheless interesting to understand possible spin liquid phases on such frustrated lattices. In this work, we apply Schwinger boson mean-field theory and projective symmetry group (PSG) analysis to investigate spin liquid phases on the fully three-dimensional 6H-B structure, in contrast to previous works that considered two-dimensional systems. We find that a nematic Z2 spin liquid phase, where the lattice-rotational symmetry is spontaneously broken, is the most promising spin liquid phase that is consistent with spiral magnetic ordering in the classical limit. We discuss the implications of our results to future theoretical and experimental works.