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arXiv:0709.2863 · Physical Review B

Dynamics of a distorted diamond chain

H.-J. Mikeska, C. Luckmann

Published Feb 6, 2008• 30 citations
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Abstract

We present results on the dynamics of the distorted diamond chain, $S=1∕2$ dimers alternating with single spins $1∕2$ and exchange couplings ${J}_{1}$ and ${J}_{3}$ in between. The dynamics in the spin fluid (SF) and tetramer-dimer (TD) phases is investigated numerically by exact diagonalization for up to 24 spins. Representative excitation spectra are presented both for zero magnetic field and in the $1∕3$ plateau phase and the relevant parameters are determined across the phase diagram. The behavior across the SF-TD phase transition line is discussed for the specific heat and for excitation spectra. The relevance of the distorted diamond chain model for the ${\mathrm{Cu}}_{3}{(\mathrm{C}{\mathrm{O}}_{3})}_{2}{(\mathrm{O}\mathrm{H})}_{2}$ (azurite) material is discussed with particular emphasis on inelastic neutron scattering experiments; the recent suggestion of one possibly ferromagnetic coupling constant is not confirmed.

DOI
10.1103/physrevb.77.054405

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We investigate the ground state properties of an S=1/2 distorted diamond chain described by the Hamiltonian ${\cal H}=J_1\sum_\ell\bigl\{\bigl(\vecS_{3\ell-1}\cdot\vecS_{3\ell} +\vecS_{3\ell}\cdot\vecS_{3\ell+1}\bigr)+J_2\vecS_{3\ell-2}\cdot\vecS_{3\ell-1} +J_3\bigl(\vecS_{3\ell-2}\cdot\vecS_{3\ell}+\vecS_{3\ell}\cdot\vecS_{3\ ell+2}\bigr)-H S_{\ell}^z\bigr\}$ (J1, J2, J3≥0J_1,~J_2,~J_3\geq0J1​, J2​, J3​≥0), which models well a trimerized S=1/2 spin chain system Cu3_33​Cl6_66​(H2_22​O)2_22​$\cdot2H2H2H_8CCC_4SOSOSO_2$. Using an exact diagonalization method by means of the Lanczös technique, we determine the ground state phase diagram in the H=0 case, composed of the dimerized, spin fluid, and ferrimagnetic phases. Performing a degenerate perturbation calculation, we analyze the phase boundary line between the latter two phases in the $J_2,~J_3\llJ_1$ limit, the result of which is in good agreement with the numerical result. We calculate, by the use of the density matrix renormalization group method, the ground state magnetization curve for the case (a) where J1=1.0J_1=1.0J1​=1.0, J2=0.8J_2=0.8J2​=0.8, and J3=0.5J_3=0.5J3​=0.5, and the case (b) where J1=1.0J_1=1.0J1​=1.0, J2=0.8J_2=0.8J2​=0.8, and J3=0.3J_3=0.3J3​=0.3. We find that in the case (b) the 2/3-plateau appears in addition to the 1/3-plateau which also appears in the case (a). The translational symmetry of the Hamiltonian H\cal HH is spontaneously broken in the 2/3-plateau state as well as in the dimerized state.
Abstract. We study the ground state of the model Hamiltonian of the trimerized S = 1/2 quantum Heisenberg chain Cu3Cl6(H2O)2 · 2H8C4SO2 in which the non-magnetic ground state is observed recently. This model consists of stacked trimers and has three kinds of coupling constants between spins; the intra-trimer coupling constant J1 and the inter-trimer coupling constants J2 and J3. All of these constants are assumed to be antiferromagnetic. By use of the analytical method and physical considerations, we show that there are three phases on the ˜ J2 − ˜ J3 plane ( ˜ J2 ≡ J2/J1, ˜ J3 ≡ J3/J1), the dimer phase, the spin fluid phase and the ferrimagnetic phase. The dimer phase is caused by the frustration effect. In the dimer phase, there exists the excitation gap between the twofold degenerate ground state and the first excited state, which explains the non-magnetic ground state observed in Cu3Cl6(H2O)2 ·2H8C4SO2. We also obtain the phase diagram on the ˜ J2 − ˜ J3 plane from the numerical diagonalization data for finite systems. PACS numbers: 75.10.Jm, 75.40.Cx, 75.50.Ee, 75.50.GgGround state of an S = 1/2 distorted diamond chain 2 1.
By use of mainly the exact diagonalization and the level spectroscopy method, we investigate the ground-state phase diagrams of the S = 1/2 distorted diamond type quantum spin chain with the monomer-monomer interactions and/or ferromagnetic interactions for the zero magnetic field case, as well as the M = M s /3 case and the M = (2/3) M s case, where M is the total magnetization and M s is the saturation magnetization. The magnetization plateau at M = M s /3 vanishes in the region where the ferromagnetic interaction is rather strong. The monomer-monomer interaction remarkably stabilizes the magnetization plateau at M = (2/3) M s .
The S = 1/2 distorted diamond spin chain with the anisotropic ferromagnetic interaction is investigated using the numerical diagonalization and the level spectroscopy analysis. It is known that the system exhibits a plateau of the magnetization curve at the 1/3 of the saturation. The present study indicates that as the anisotropy is varied the quantum phase transition occurs between two different mechanisms of the 1/3 magnetization plateau. The phase diagram with respect to the anisotropy and the ferromagnetic coupling is also presented.
We study the phase diagram of a symmetric spin-1/2 Heisenberg diamond chain with additional cyclic four-spin exchange interactions. The presented analysis supplemented by numerical exact-diagonalization results for finite periodic clusters implies a rich phase diagram containing, apart from standard magnetic and spin-liquid phases, two different tetramer-dimer phases as well as an exotic fourfold degenerate dimerized phase. The characteristics of the established spin phases as well as the nature of quantum phase transitions are discussed as well.