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arXiv:cond-mat/9910165 · Physical Review Letters

Exact Demonstration of Magnetization Plateaus and First-Order Dimer-Néel Phase Transitions in a Modified Shastry-Sutherland Model for SrCu2(BO3)2

E. Müller‐Hartmann, Rajiv R. P. Singh, Christian Knetter, Götz Silvester Uhrig

Published Feb 21, 2000• 108 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.84.1808

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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.
The two dimensional Heisenberg model for SrCu2(BO3)2{\mathrm{SrCu}}_{2}({\mathrm{BO}}_{3}{)}_{2}SrCu2​(BO3​)2​ has an exact dimer ground state which was proven by Shastry and Sutherland almost twenty years ago. The critical value of the quantum phase transition from the dimer state to the N\'eel ordered state is determined. Analysis of the experimental data shows that SrCu2(BO3)2\mathrm{SrCu}{}_{2}(\mathrm{BO}{}_{3}{)}_{2}SrCu2​(BO3​)2​ has the dimer ground state but its coupling constants are close to the transition point, which leads to an unusual temperature dependence of the susceptibility. The almost localized nature of the triplet excitations explains the plateaus observed in the magnetization curve.
We investigate quantum phase transitions in the frustrated antiferromagnetic Heisenberg model for SrCu2(BO3)2\mathrm{Sr}{\mathrm{Cu}}_{2}({\mathrm{BO}}_{3}{)}_{2}SrCu2​(BO3​)2​ by using the series expansion method. It is found that a novel spin-gap phase, adiabatically connected to the plaquette-singlet phase, exists between the dimer and the magnetically ordered phases known thus far. When the ratio of the competing exchange couplings $\ensuremath{\alpha}({\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}J}^{\ensuremath{'}}/J)$ is varied, this spin-gap phase exhibits a first- (second-) order quantum phase transition to the dimer (the magnetically ordered) phase at the critical point ${\ensuremath{\alpha}}_{c1}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.677(2)$ [ ${\ensuremath{\alpha}}_{c2}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.86(1)$]. Our results shed light on some controversial arguments about the nature of quantum phase transitions in this model.
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 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.
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.
Abstract Under magnetic fields, quantum magnets often undergo exotic phase transitions with various kinds of order. The discovery of a sequence of fractional magnetization plateaus in the Shastry-Sutherland compound SrCu 2 (BO 3 ) 2 has played a central role in the high-field research on quantum materials, but so far this system could only be probed up to half the saturation value of the magnetization. Here, we report the first experimental and theoretical investigation of this compound up to the saturation magnetic field of 140 T and beyond. Using ultrasound and magnetostriction techniques combined with extensive tensor-network calculations (iPEPS), several spin-supersolid phases are revealed between the 1/2 plateau and saturation (1/1 plateau). Quite remarkably, the sound velocity of the 1/2 plateau exhibits a drastic decrease of -50%, related to the tetragonal-to-orthorhombic instability of the checkerboard-type magnon crystal. The unveiled nature of this paradigmatic quantum system is a new milestone for exploring exotic quantum states of matter emerging in extreme conditions.