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Journal of the Physical Society of Japan

Spin-1/2 Triangular-Lattice Heisenberg Antiferromagnet with \(\sqrt{3} \times \sqrt{3} \)-Type Distortion — Behavior around the Boundaries of the Intermediate Phase

Alisa Shimada, Hiroki Nakano, Tôru Sakai, Kazuyoshi Yoshimura

Published Feb 15, 2018• 10 citations
Publisher

Abstract

The S = 1/2 triangular-lattice Heisenberg antiferromagnet with distortion is investigated by the numerical-diagonalization method. The examined distortion type is \(\sqrt{3} \times \sqrt{3} \). We study the case when the distortion connects the undistorted triangular lattice and the dice lattice. For the intermediate phase reported previously in this system, we obtain results of the boundaries of the intermediate phase for a larger system than those in the previous report and examine the system size dependence of the boundaries in detail. We also report the specific heat of this system, which shows a marked peak structure related to the appearance of the intermediate state.

DOI
10.7566/jpsj.87.034706

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Spin-1/2 Triangular-Lattice Heisenberg Antiferromagnet with 3×3\sqrt{3} \times \sqrt{3} 3​×3​-Type Distortion — Behavior around the Boundaries of the Intermediate Phase
The S = 1/2 triangular-lattice Heisenberg antiferromagnet with distortion is investigated by the numerical-diagonalization method. The examined distortion type is (\sqrt{3} \times \sqrt{3} ). We study the case when the distortion connects the undistorted triangular lattice and the dice lattice. For the intermediate phase reported previously in this system, we obtain results of the boundaries of the intermediate phase for a larger system than those in the previous report and examine the system size dependence of the boundaries in detail. We also report the specific heat of this system, which shows a marked peak structure related to the appearance of the intermediate state.
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The spin-1/21/21/2 anisotropic triangular model, which is believed to describe the materials Cs2CuCl4{\mathrm{Cs}}_{2}{\mathrm{CuCl}}_{4}Cs2​CuCl4​ and Cs2CuBr4{\mathrm{Cs}}_{2}{\mathrm{CuBr}}_{4}Cs2​CuBr4​, among others, is dominated by incommensurate spiral physics and is thus extremely resistant to numerical analysis on small system sizes. In this paper, we use twisted boundary conditions and exact diagonalization techniques to study the ground state of this model as a function of exchange parameter strength. With these boundary conditions we are able to extract the inter- and intrachain ordering qqq vectors for the $\frac{{J}^{\ensuremath{'}}}{J}<1$ region finding very close agreement with recent DMRG results on much larger systems. Our results suggest a phase transition between a long-range incommensurate spiral ordered phase, and a more subtle phase with short-range spiral correlations with the qqq vector describing the incommensurate correlations varying smoothly through the transition. In the latter phase correlations between next-nearest chains exhibit an extremely close competition between predominantly antiferromagnetic and ferromagnetic correlations. Further analysis suggests that the antiferromagnetic next-nearest chain correlations may be slightly stronger than the ferromagnetic ones. This difference is found to be slight but in line with previous renormalization group predictions of a collinear antiferromagnetic ordering in this region.
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Quantum paramagnetic states in the spin-1/2 distorted honeycomb-lattice Heisenberg antiferromagnet -- application to Cu2_22​(pymca)3_33​(ClO4_44​)
We investigate the ground-state phase diagram of a spin-1/2 honeycomb-lattice antiferromagnetic (AF) Heisenberg model with three exchange interactions, JAJ_{\rm A}JA​, JBJ_{\rm B}JB​, and JCJ_{\rm C}JC​ that is realized in a distorted honeycomb-lattice antiferromagnet Cu2(pymca)3(ClO4){\rm Cu_2 (pymca)_3 (ClO_4)}Cu2​(pymca)3​(ClO4​). We remeasured the magnetic susceptibility of its polycrystalline sample with special care, and determined the exchange parameters of this material through the comparison with numerical results based on a quantum Monte Carlo (QMC) method. The QMC method also provides a ground-state phase diagram in the JA/JCJ_{\rm A}/J_{\rm C}JA​/JC​-JB/JCJ_{\rm B}/J_{\rm C}JB​/JC​ plane. The phase diagram consists of a small Neˊ{\rm \acute{e}}eˊel phase and a gapped quantum paramagnetic phase surrounding the Neˊ{\rm \acute{e}}eˊel phase. The latter includes six regimes of hexagonal-singlet-type states and dimer-singlet-type states alternatingly without boundaries closing the spin gap. We further calculate the equal-time spin structure factor in each phase using the QMC method. The computed spin dynamics by the exact diagonalization method exhibits continuums near and in the AF phase. Characteristic four energy band structures in the state with strong hexagonal-singlet-type correlations are informative to clarify the ground-state of Cu2(pymca)3(ClO4){\rm Cu_2 (pymca)_3 (ClO_4)}Cu2​(pymca)3​(ClO4​) by future neutron scattering measurements.
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