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arXiv:1401.3778 · Physical Review Letters

Crystals of Bound States in the Magnetization Plateaus of the Shastry-Sutherland Model

Philippe Corboz, Frédéric Mila

Published Apr 10, 2014• 165 citations
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Abstract

Using infinite projected entangled-pair states, we show that the Shastry-Sutherland model in an external magnetic field has low-magnetization plateaus which, in contrast to previous predictions, correspond to crystals of bound states of triplets, and not to crystals of triplets. The first sizable plateaus appear at magnetization 1/8, 2/15 and 1/6, in agreement with experiments on the orthogonal-dimer antiferromagnet SrCu2(BO3)2, and they can be naturally understood as regular patterns of bound states, including the intriguing 2/15 one. We also show that, even in a confined geometry, two triplets bind into a localized bound state with Sz=2. Finally, we discuss the role of competing domain-wall and supersolid phases, as well as that of additional anisotropic interactions.

DOI
10.1103/physrevlett.112.147203

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Using infinite projected entangled-pair states, we show that the Shastry-Sutherland model in an external magnetic field has low-magnetization plateaus which, in contrast to previous predictions, correspond to crystals of bound states of triplets, and not to crystals of triplets. The first sizable plateaus appear at magnetization 1/8, 2/15 and 1/6, in agreement with experiments on the orthogonal-dimer antiferromagnet SrCu2(BO3)2, and they can be naturally understood as regular patterns of bound states, including the intriguing 2/15 one. We also show that, even in a confined geometry, two triplets bind into a localized bound state with Sz=2. Finally, we discuss the role of competing domain-wall and supersolid phases, as well as that of additional anisotropic interactions.
Magnetization plateaus in the Shastry-Sutherland model for SrCu2(BO3)2{\rm SrCu_2(BO_3)_2}SrCu2​(BO3​)2​ are studied by the perturbation expansion method. The fourth-order effective Hamiltonian which describes the dynamics of triplet dimers (TD's) with Sztot=1S^{\rm tot}_z=1Sztot​=1 in the singlet sea is derived and then partially diagonalized for the space that consists of the TD configurations with the lowest second-order energy. The fourth-order terms are treated within a low-density approximation. Our procedure makes clear how TD interactions are responsible for the formation of magnetization plateaus. Particularly, the 1/4-plateau is obtained by the fourth-neighbor TD repulsion in the fourth-order perturbation, and a diagonal stripe arrangement of TD's appears at this plateau.
Using density matrix renormalization group (DMRG) and perturbative continuous unitary transformations (PCUTs), we study the magnetization process in a magnetic field for all coupling strengths of a quasi-1D version of the 2D Shastry-Sutherland lattice, a frustrated spin tube made of two orthogonal dimer chains. At small inter-dimer coupling, plateaus in the magnetization appear at 1/6, 1/4, 1/3, 3/8, and 1/2. As in 2D, they correspond to a Wigner crystal of triplons. However, close to the boundary of the product singlet phase, plateaus of a new type appear at 1/5 and 3/4. They are stabilized by the localization of bound states of triplons. Their magnetization profile differs significantly from that of single-triplon plateaus and leads to specific NMR signatures. We address the possibility to stabilize such plateaus in further geometries by analyzing small finite clusters using exact diagonalizations and the PCUTs.
In this paper, we briefly review our recent studies of the Heisenberg anti-ferromagnet on the Shastry–Sutherland lattice for SrCu2(BO3)2 under magnetic fields. Treating magnetic excitations promoted by the field as Bose particles and using a strong-coupling expansion, we derived an effective Hamiltonian for the magnetic particles. Anisotropic repulsive interactions between particles induce "insulating" states with a stripe spin-density wave structure at magnetization m/msat = 1/3 and with a checkerboard structure at 1/2, and thereby form magnetization plateaux. We also demonstrated how the unique geometry of the Shastry–Sutherland lattice affects dynamical properties and makes a novel type of quintuplet (S = 2) bound states condense for very small magnetization. PACS Nos.: 75.50-y, 75.60Ej, 75.10Jm
We study a generalized Shastry-Sutherland model for the material SrCu2(BO3)(2). Along a line in the parameter space, we show rigorously that the model has a first-order phase transition between dimerized and Neel-ordered ground states. Furthermore, when a magnetic field is applied in the dimerized phase, magnetization plateaus develop at commensurate values of the magnetization. We also discuss various aspects of the phase diagram and properties of this model away from this exactly soluble line, which include gap-closing continuous transitions between dimerized and magnetically ordered phases.
We examine ground-state properties of the spin-1/2 easy-axis Heisenberg model on the Shastry-Sutherland lattice with ferromagnetic transverse spin exchange using quantum Monte Carlo and degenerate perturbation theory. For vanishing transverse exchange, the model reduces to an antiferromagnetic Ising model that, besides N\'eel order, harbors regions of extensive ground-state degeneracy. In the quantum regime, we find a dimerized phase of triplet states separated from the N\'eel ordered phase by a superfluid. The quantum phase transitions between these phases are characterized. The magnetization process shows a magnetization plateau at 1/3 of the saturation value, which persists down to the Ising limit, and a further plateau at 1/2 only in the quantum regime. For both plateaus, we determine the crystalline patterns of the localized triplet excitations. No further plateaus or supersolid phases are found in this model.
Motivated by the remarkable properties of SrCu2(BO3) 2 in a magnetic field, we use perturbative continuous unitary transformations to determine the magnetization plateaux of the Shastry-Sutherland model, unveiling an unexpected sequence of plateaux progressively appearing at 2/9, 1/6, 1/9, and 2/15 upon increasing the interdimer coupling. We predict that a 1/6 plateau should be present in SrCu2(BO3)2, even if residual interactions beyond the Shastry-Sutherland are strong enough to modify the other plateaux below 1/3. The method is extended to calculate the magnetization profile within the plateaux, leading to a local structure around triplons that agrees with NMR results on SrCu2(BO3) 2.