Thermodynamics of the S=1 spin ladder as a composite S=2 chain model

A special class of S=1 spin ladder hamiltonians, with second- neighbor exchange interactions and with anisotropies in the $z$-direction, can be mapped onto one-dimensional composite S=2 (tetrahedral S=1) models. We calculate the high temperature expansion of the Helmoltz free energy for the latter class of models, and show that their magnetization behaves closely to that of standard XXZ models with a suitable effective spin $S_{eff}$, such that $S_{eff}(1+S_{eff})=$, where ${\bf S}_i$ refers to the components of spin in the composite model. It is also shown that the specific heat per site of the composite model, on the other hand, can be very different from that of the effective spin model, depending on the parameters of the hamiltonian.Comment: 17 pages, 4 figures. Submitted for publicatio

Series expansion analysis of a tetrahedral cluster spin chain

Using series expansion by continuous unitary transformations we study the magnetic properties of a frustrated tetrahedral spin-1/2 chain. Starting from the limit of isolated tetrahedra we analyze the evolution of the ground state energy and the elementary triplet dispersion as a function of the inter-tetrahedral coupling. The quantum phase diagram is evaluated and is shown to incorporate a singlet product, a dimer, and a Haldane phase. Comparison of our results with those from several other techniques, such as density matrix renormalization group, exact diagonalization and bond-operator theory are provided and convincing agreement is found.Comment: 6 pages, 5 figures, 1 tabl

Magnetization plateaus in weakly coupled dimer spin system

I study a spin system consisting of strongly coupled dimers which are in turn weakly coupled in a plane by zigzag interactions. The model can be viewed as the strong-coupling limit of a two-dimensional zigzag chain structure typical, e.g., for the $(ac)$-planes of KCuCl_3. It is shown that the magnetization curve in this model has plateaus at 1/3 and 2/3 of the saturation magnetization, and an additional plateau at 1/2 can appear in a certain range of the model parameters; the critical fields are calculated perturbatively. It is argued that for the three-dimensional lattice structure of the KCuCl_3 family the plateaus at 1/4 and 3/4 of the saturation can be favored in a similar way, which might be relevant to the recent experiments on NH_4CuCl_3 by Shiramura et al., J. Phys. Soc. Jpn. {\bf 67}, 1548 (1998).Comment: serious changes in Sect. II,III, final version to appear in PR

Low-lying excitations and magnetization process of coupled tetrahedral systems

We investigate low-lying singlet and triplet excitations and the magnetization process of quasi-1D spin systems composed of tetrahedral spin clusters. For a class of such models, we found various exact low-lying excitations; some of them are responsible for the first-order transition between two different ground states formed by local singlets. Moreover, we find that there are two different kinds of magnetization plateaus which are separated by a first-order transition.Comment: To appear in Phys.Rev.B (Issue 01 August 2002). A short comment is adde

Dynamical properties of S=1 bond-alternating Heisenberg chains at finite temperatures

Dynamical structure factors of the S=1 bond-alternating spin chains in the dimer phase are calculated at finite temperature, using the pair dynamical correlated-effective-field approximation. At T=0, the delta-function-type peak of the one-magnon mode appears. When temperature is increased, such a sharp peak is broadened and the additional weak peak caused by the excitation from the triplet state to the quintet state emerges in the higher energy region. The results are discussed in comparison with those obtained by the exact diagonalization method.Comment: 5 pages, 4 figure

Magnetization plateaus as insulator-superfluid transitions in quantum spin systems

We study the magnetization process in two-dimensional S=1/2 spin systems, to discuss the appearance of a plateau structure. The following three cases are considered: (1) the Heisenberg antiferromagnet and multiple-spin exchange model on the triangular lattice, (2) Shastry-Sutherland type lattice, [which is a possible model for SrCu2(BO3)2,] (3) 1/5-depleted lattice (for CaV4O9). We find in these systems that magnetization plateaus can appear owing to a transition from superfluid to a Mott insulator of magnetic excitations. The plateau states have CDW order of the excitations. The magnetizations of the plateaus depend on components of the magnetic excitations, range of the repulsive interaction, and the geometry of the lattice.Comment: 5 pages, RevTeX, 7 figures, note and reference adde

Ground State Properties of One Dimensional S=1/2 Heisenberg Model with Dimerization and Quadrumerization

The one dimensional S=1/2 Heisenberg model with dimerization and quadrumerization is studied by means of the numerical exact diagonalization of finite size systems. Using the phenomenological renormalization group and finite size scaling law, the ground state phase diagram is obtained in the isotropic case. It exhibits a variety of the ground states which contains the S=1 Haldane state, S=1 dimer state and S=1/2 dimer state as limiting cases. The gap exponent $\nu$ is also calculated which coincides with the value for the dimerization transition of the isotropic Heisenberg chain. In the XY limit, the phase diagram is obtained analytically and the comparison is made with the isotropic case.Comment: 4 pages, 7 figure

Magnetization plateaux in dimerized spin ladder arrays

We investigate the ground state magnetization plateaux appearing in spin 1/2 two-leg ladders built up from dimerized antiferromagnetic Heisenberg chains and dimerized zig-zag interchain couplings. Using both Abelian bosonization and Lanczos methods we find that the system yields rather unusual plateaux and exhibits massive and massless phases for specific choices or ``tuning'' of exchange interactions. The relevance of this behavior in the study of NH_4CuCl_3 is discussed.Comment: 9 pages, RevTeX, 11 postscript figure

Field-Induced Magnetic Ordering in the Quantum Spin System KCuCl3_3

KCuCl$_3$ is a three-dimensional coupled spin-dimer system and has a singlet ground state with an excitation gap ${\Delta}/k_{\rm B}=31$ K. High-field magnetization measurements for KCuCl$_3$ have been performed in static magnetic fields of up to 30 T and in pulsed magnetic fields of up to 60 T. The entire magnetization curve including the saturation region was obtained at $T=1.3$ K. From the analysis of the magnetization curve, it was found that the exchange parameters determined from the dispersion relations of the magnetic excitations should be reduced, which suggests the importance of the renormalization effect in the magnetic excitations. The field-induced magnetic ordering accompanied by the cusplike minimum of the magnetization was observed as in the isomorphous compound TlCuCl$_3$. The phase boundary was almost independent of the field direction, and is represented by the power law. These results are consistent with the magnon Bose-Einstein condensation picture for field-induced magnetic ordering.Comment: 9 pages, 7 figures, 9 eps files, revtex styl

A comparative study of the phase diagrams of spin-121 \over 2 and spin-11 antiferromagnetic chains with dimerization and frustration

We use the density matrix renormalization group method to study the ground state `phase' diagram and some low-energy properties of isotropic antiferromagnetic spin-$1 \over 2$ and spin-$1$ chains with a next-nearest neighbor exchange $J_2 ~$ and an alternation $\delta$ of the nearest neighbor exchanges. In the spin-$1 \over 2$ chain, the system is gapless for $\delta=0$ and $J_2 < J_{2c} =0.241$, and is gapped everywhere else in the $J_2 - \delta$ plane. At $J_{2c}$, for small $\delta$, the gap increases as $\delta^{\alpha}$, where $\alpha = 0.667 \pm 0.001$. $2J_2 + \delta = 1$ is a disorder line. To the left of this line, the structure factor $S(q)$ peaks at $q_{max} = \pi$ (Neel `phase'), while to the right, $q_{max}$ decreases from $\pi$ to $\pi/2$ (spiral `phase') as $J_2$ increases. There is also a `$\uparrow \uparrow \downarrow \downarrow$ phase' for large values of both $J_2$ and $\delta$. In the spin-$1$ case, we find a line running from a gapless point at $(J_2 , \delta) = (0,0.25 \pm 0.01)$ upto a `gapless' point at $(0.73 \pm 0.005,0)$ such that the open chain ground state is four-fold degenerate below the line and is unique above it. There is a disorder line in this case also and it has the same equation as in the spin-$1 \over 2$ case, but the line ends at about $\delta =0.136$. Similar to the spin-$1 \over 2$ case, to the left of this line, the peak in the structure factor is at $\pi$ (Neel `phase'), while to the right of the line, it is at less than $\pi$ (spiral `phase'). For $\delta =1$, the system corresponds to a spin ladder and the system is gapped for all values of the interchain coupling for both spin-$1 \over 2$ and spin-$1$ ladders.Comment: 16 pages in latex; 9 figures available on reques