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Journal of Physics Condensed Matter

The spin- S Heisenberg antiferromagnet on the Shastry–Sutherland lattice

Hiroki Nakano, Yuko Hosokoshi, Tôru Sakai

Published Oct 7, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1361-648x/ae8e18

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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.
The magnetic properties of SrCu 2 (BO 3 ) 2 are reviewed from a theoretical point of view. SrCu 2 (BO 3 ) 2 is a new two-dimensional spin gap system and its magnetic properties are well described by a spin-1/2 antiferromagnetic Heisenberg model of the orthogonal dimer lattice. The model has a dimer singlet ground state whose exactness was proven by Shastry and Sutherland for a topologically equivalent model more than 20 years ago. The exactness of the ground state is maintained even if interlayer couplings are introduced for SrCu 2 (BO 3 ) 2 . In the two-dimensional model, quantum phase transitions take place between different ground states for which three phases are expected: a gapped dimer singlet state, a plaquette resonating valence bond state and a gapless magnetic ordered state. Analysis of the experimental data shows that the dimer singlet ground state is realized in SrCu 2 (BO 3 ) 2 . The orthogonality of the dimer bonds, which is the underlying symmetry of the exactness of the ground state, also leads to an unusual property of elementary excitations, namely the almost localized nature of the triplet excitations. Application of an external magnetic field changes the density of the triplet excitations. In general, there is competition between kinetic energies and interaction energies between triplets. The almost localized nature of the triplets makes it easy to form regular lattices. In fact, at certain densities, where the commensurability energy is significant, the triplet excitations form superstructures and plateaux appear at 1/2, 1/3, 1/4 and 1/8 in the magnetization curve. In high-magnetic-field experiments, magnetic plateaux at magnetizations of 1/3, 1/4 and 1/8 have been observed. Translational symmetry of the lattice is spontaneously broken at the plateaux, except for the 1/2 plateau. The 1/3 and 1/4 plateaux are expected to have magnetic superstructures of stripe form while the 1/2 plateau has a square unit cell and the 1/8 plateau a rhomboid cell. Especially at the 1/8 plateau, nuclear magnetic resonance experiments indicate the presence of at least 11 distinct Cu sites with different spin polarizations, which is the first evidence of breaking of the translational symmetry at the plateau phase. The spin texture calculated on the basis of a Heisenberg model with adiabatic spin–phonon coupling is consistent with the experimental results.
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.
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 Shastry-Sutherland lattice, one of the simplest systems with geometrical frustration, which has an exact eigenstate by putting singlets on diagonal bonds, can be realized in a group of layered compounds and raises both theoretical and experimental interest. Most of the previous studies on the Shastry-Sutherland lattice are focusing on the Heisenberg model. Here we opt for the Hubbard model to calculate phase diagrams over a wide range of interaction parameters, and show the competing effects of interaction, frustration and temperature. At low temperature, frustration is shown to favor a paramagnetic metallic ground state, while interaction drives the system to an antiferromagnetic insulator phase. Between these two phases, there are an antiferromagnetic metal phase and a paramagnetic insulator phase (which should consist of a small plaquette phase and a dimer phase) resulting from the competition of the frustration and the interaction. Our results may shed light on more exhaustive studies about quantum phase transitions in geometrically frustrated systems.
The two-dimensional quantum spin model proposed by Shastry and Sutherland more than four decades ago is notable for its realization in SrCu2{}_{2}2​(BO3{}_{3}3​)2{}_{2}2​. Here, the authors present numerical evidence of a gapless spin liquid phase in the model and discuss its connection to a deconfined quantum critical point. The new phase exists in a parameter regime where recent high-pressure heat capacity measurements on SrCu2{}_{2}2​(BO3{}_{3}3​)2{}_{2}2​ did not detect any low-temperature order, in contrast to the antiferromagnetic and plaquette-singlet phases existing at higher and lower pressures, respectively. Thus, the elusive spin liquid may exist in SrCu2{}_{2}2​(BO3{}_{3}3​)2{}_{2}2​.
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.