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Journal of Physics Condensed Matter

The spin-S Heisenberg antiferromagnet on the orthogonal-dimer lattice

Hiroki Nakano, Tôru Sakai

Published Aug 13, 2024• 3 citations
Publisher

Abstract

Abstract The spin-S Heisenberg antiferromagnet on the orthogonal-dimer lattice is studied. In most of the investigations of the antiferromagnet on this lattice beginning with the study by Shastry and Sutherland, the S = 1 / 2 case has intensively been treated. In the present study, the cases of S = 1 and 3/2 are particularly treated by the numerical-diagonalization method based on the Lanczos algorithm applied to finite-size clusters. We successfully capture the edge of the exact-dimer phase and that of the Néel-ordered phase. A significant finding is the existence of an intermediate phase between both the edges irrespective of spin-S.

DOI
10.1088/1361-648x/ad6522

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Magnetization dependence on the external magnetic field was studied in a system with the Shastry–Sutherland lattice using exact diagonalization method at zero temperature within the xxz-model with spin S = 1/2. It was found that contrary to the classical Heisenberg model, the magnetization plateaus corresponding to m* = m/msat = 1/4, 1/3, and 1/2 (here msat is the saturation magnetization) exist even in the case of isotropic exchange interactions. The effect of exchange interaction on the width of the plateaus was studied. It was shown that depending on the ratio of exchange constants, there exist three regions corresponding to different types of the behavior of the system: the regions of a Neel-like antiferromagnet, a “dimer” antiferromagnet, and an intermediate region where the unique properties of Shastry–Sutherland lattices are most pronounced. The boundaries of these regions were also determined.

Low Temperature Physics•Nov 1, 2014•2 citations
Abstract The spin-S Heisenberg antiferromagnet on the orthogonal-dimer lattice is studied. In most of the investigations of the antiferromagnet on this lattice beginning with the study by Shastry and Sutherland, the S = 1 / 2 case has intensively been treated. In the present study, the cases of S = 1 and 3/2 are particularly treated by the numerical-diagonalization method based on the Lanczos algorithm applied to finite-size clusters. We successfully capture the edge of the exact-dimer phase and that of the Néel-ordered phase. A significant finding is the existence of an intermediate phase between both the edges irrespective of spin-S.
The S = 1/2 Heisenberg antiferromagnet on the orthogonal-dimer lattice (Shastry-Sutherland model) is studied by the Lanczos diagonalization method.The properties of this model are determined by the ratio of two interactions, namely, r = J 2 /J 1 , where J 1 denotes the amplitude of spin interactions at orthogonal dimers and the interactions represented by J 2 form the square lattice.We focus our attention on the edge of the phase in which the dimer state is realized as the exact ground state.Our large-scale calculations of diagonalizations treating finite-size clusters including 44 and 48 spin sites successfully detect the target edge.Our conclusion is that the ratio for the edge is r = 0.6754(2).This estimate is compared with an experimental result from electron spin resonance measurements.
The Shastry-Sutherland model --- the S=1/2S=1/2S=1/2 Heisenberg antiferromagnet on the square lattice accompanied by orthogonal dimerized interactions --- is studied by the numerical-diagonalization method. Large-scale calculations provide results for larger clusters that have not been reported yet. The present study successfully captures the phase boundary between the dimer and plaquette-singlet phases and clarifies that the spin gap increases once when the interaction forming the square lattice is increased from the boundary. Our calculations strongly suggest that in addition to the edge of the dimer phase given by J2/J1∼0.675J_{2}/J_{1}\sim 0.675J2​/J1​∼0.675 and the edge of the Neˊ\acute{\rm e}eˊel-ordered phase given by J2/J1∼0.76J_{2}/J_{1}\sim 0.76J2​/J1​∼0.76, there exists a third boundary ratio J2/J1∼0.70J_{2}/J_{1}\sim 0.70J2​/J1​∼0.70 that divides the intermediate region into two parts, where J1J_{1}J1​ and J2J_{2}J2​ denote dimer and square-lattice interactions, respectively.
Abstract The spin- S Heisenberg antiferromagnet on the two-dimensional lattice is investigated for S = 1/2 and S = 1. We consider interaction at isolated dimers ( J d ) and interaction bonds that form the bounce lattice ( J b ). For J d = J b , the system is reduced to the maple-leaf-lattice antiferromagnet. We primarily conduct highly parallelized numerical diagonalization to examine the spin excitation gap above the ground state for various J b / J d cases. For S = 1/2, we report calculations for a 42-site cluster that has not been previously treated. The S = 1 case is examined for the first time for clusters up to 24 sites. Regardless of whether S = 1/2 or 1, we find that the system has a gapped nature for small J d / J b and becomes gapless at J d / J b ∼ 1.4. For S = 1, we also find that another gapped region appears between the gapless case at J d / J b ∼ 1.4 and the boundary of the exact-dimer phase.
Recent advances in the orthogonal-dimer spin-Heisenberg antiferromagnet are reviewed. This model has been examined for more than 40 years since it was originally studied by Shastry and Sutherland. The discovery of SrCu(BO)as a good candidate material for thesystem led to a considerable advancement in subsequent research. In the case whenis larger than 1/2, however, the elucidation of the properties of the system was relatively delayed. In the ground state of general-systems, interesting quantum phase transitions occur not only for. In this article, the systematic behavior depending onwhich has been recently clarified by unbiased and numerical computational calculations is reviewed. The effects due to spin anisotropy as determined from experimental and theoretical results are also overviewed. We also mention recent developments for thesystem.
Magnetization dependence on the external magnetic field was studied in a system with the Shastry–Sutherland lattice using exact diagonalization method at zero temperature within the xxz-model with spin S = 1/2. It was found that contrary to the classical Heisenberg model, the magnetization plateaus corresponding to m* = m/msat = 1/4, 1/3, and 1/2 (here msat is the saturation magnetization) exist even in the case of isotropic exchange interactions. The effect of exchange interaction on the width of the plateaus was studied. It was shown that depending on the ratio of exchange constants, there exist three regions corresponding to different types of the behavior of the system: the regions of a Neel-like antiferromagnet, a “dimer” antiferromagnet, and an intermediate region where the unique properties of Shastry–Sutherland lattices are most pronounced. The boundaries of these regions were also determined.