The Antiferromagnetic Sawtooth Lattice - the study of a two spin variant

Generalising recent studies on the sawtooth lattice, a two-spin variant of the model is considered. Numerical studies of the energy spectra and the relevant spin correlations in the problem are presented. Perturbation theory analysis of the model explaining some of the features of the numerical data is put forward and the spin wave spectra of the model corresponding to different phases are investigated.Comment: Latex, 37 pages including 14 figures; M. S. project report, Indian Institute of Science (March, 2003); this is one of the references of cond-mat/030749

Gapless points of dimerized quantum spin chains: analytical and numerical studies

We study the locations of the gapless points which occur for quantum spin chains of finite length (with a twisted boundary condition) at particular values of the nearest neighbor dimerization, as a function of the spin S and the number of sites. For strong dimerization and large values of S, a tunneling calculation reproduces the same results as those obtained from more involved field theoretic methods using the non-linear sigma-model approach. A different analytical calculation of the matrix element between the two Neel states gives a set of gapless points; for strong dimerization, these differ significantly from the tunneling values. Finally, the exact diagonalization method for a finite number of sites yields a set of gapless points which are in good agreement with the Neel state calculations for all values of the dimerization, but the agreement with the tunneling values is not very good even for large S. This raises questions about possible corrections to the tunneling results.Comment: Revtex4, 10 pages including 5 figure

Frustrated spin ladder with alternating spin-1 and spin-1/2 rungs

We study the impact of the diagonal frustrating couplings on the quantum phase diagram of a two-leg ladder composed of alternating spin-1 and spin-1/2 rungs. As the coupling strength is increased the system successively exhibits two gapped paramagnetic phases (a rung-singlet and a Haldane-like non-degenerate states) and two ferrimagnetic phases with different ferromagnetic moments per rung. The first two states are similar to the phases studied in the frustrated spin-1/2 ladder, whereas the magnetic phases appear as a result of the mixed-spin structure of the model. A detailed characterization of these phases is presented using density-matrix renormalization-group calculations, exact diagonalizations of periodic clusters, and an effective Hamiltonian approach inspired by the analysis of numerical data. The present theoretical study was motivated by the recent synthesis of the quasi-one-dimensional ferrimagnetic material Fe$^{II}$Fe$^{III}$ (trans-1,4-cyclohexanedicarboxylate) exhibiting a similar ladder structure.Comment: 10 pages, 8 figure

p6 - Chiral Resonating Valence Bonds in the Kagome Antiferromagnet

The Kagome Heisenberg antiferromagnet is mapped onto an effective Hamiltonian on the star superlattice by Contractor Renormalization. Comparison of ground state energies on large lattices to Density Matrix Renormalization Group justifies truncation of effective interactions at range 3. Within our accuracy, magnetic and translational symmetries are not broken (i.e. a spin liquid ground state). However, we discover doublet spectral degeneracies which signal the onset of p6 - chirality symmetry breaking. This is understood by simple mean field analysis. Experimentally, the p6 chiral order parameter should split the optical phonons degeneracy near the zone center. Addition of weak next to nearest neighbor coupling is discussed.Comment: 7 pages, 5 figures including supplementary materia

Magnetic properties of a helical spin chain with alternating isotropic and anisotropic spins: magnetization plateaus and finite entropy

We study a model which could explain some of the unusual magnetic properties observed for the one-dimensional helical spin system Co(hfac)_2 NITPhOMe. One of the properties observed is that the magnetization shows plateaus near zero and near one-third of the saturation value if a magnetic field is applied along the helical axis, but not if the field is applied in the plane perpendicular to that axis. The system consists of a spin-1/2 chain in which cobalt ions (which are highly anisotropic with an easy axis e_i) and organic radicals (which are isotropic) alternate with each other. The easy axis of the cobalts e_i lie at an angle theta_i with respect to the helical axis, while the projection of e_{i+1} - e_i on the plane perpendicular to the helical axis is given by 2 pi /3. For temperatures and magnetic fields which are much smaller than the coupling between the nearest-neighbor cobalts and radicals, one can integrate out the radicals to obtain an Ising model for the cobalts; this enables one to compute the thermodynamic properties of the system using the transfer matrix approach. We consider a model in which the tilt angles theta_i are allowed to vary with i with period three; we find that for certain patterns of theta_i, the system shows the magnetization plateaus mentioned above. At the ends of the plateaus, the entropy is finite even at very low temperatures, while the magnetic susceptibility and specific heat also show some interesting features.Comment: Revtex, 7 pages including 7 figure