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arXiv:1903.07887 · Physical review. B./Physical review. B

Competition between intermediate plaquette phases in SrCu2 ( BO3)2 under pressure

C. Boos, S. P. G. Crone, Ido Niesen, Philippe Corboz, Kai Phillip Schmidt, Frédéric Mila

Published Oct 30, 2019• 60 citations
arXivHTMLPDF

Abstract

Building on the growing evidence based on NMR, magnetization, neutron scattering, electron spin resonance, and specific heat that, under pressure, ${\mathrm{SrCu}}_{2}{({\mathrm{BO}}_{3})}_{2}$ has an intermediate phase between the dimer and the N\'eel phase, we study the competition between two candidate phases in the context of a minimal model that includes two types of intra- and interdimer interactions without enlarging the unit cell. We show that the empty plaquette phase of the Shastry-Sutherland model is quickly replaced by a quasi-one-dimensional full plaquette phase when intra- and/or interdimer couplings take different values, and that this full plaquette phase is in much better agreement with available experimental data than the empty plaquette one.

DOI
10.1103/physrevb.100.140413

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Building on the growing evidence based on NMR, magnetization, neutron scattering, electron spin resonance, and specific heat that, under pressure, SrCu2(BO3)2{\mathrm{SrCu}}_{2}{({\mathrm{BO}}_{3})}_{2}SrCu2​(BO3​)2​ has an intermediate phase between the dimer and the N'eel phase, we study the competition between two candidate phases in the context of a minimal model that includes two types of intra- and interdimer interactions without enlarging the unit cell. We show that the empty plaquette phase of the Shastry-Sutherland model is quickly replaced by a quasi-one-dimensional full plaquette phase when intra- and/or interdimer couplings take different values, and that this full plaquette phase is in much better agreement with available experimental data than the empty plaquette one.
Abstract The 2-dimensional layered oxide material SrCu2(BO3)2, long studied as a realization of the Shastry-Sutherland spin topology, exhibits a range of intriguing physics as a function of both hydrostatic pressure and magnetic field, with a still debated intermediate plaquette phase appearing at approximately 20 kbar and a possible deconfined critical point at higher pressure. Here, we employ a tunnel diode oscillator (TDO) technique to probe the behavior in the combined extreme conditions of high pressure, high magnetic field, and low temperature. We reveal an extensive phase space consisting of multiple magnetic analogs of the elusive supersolid phase and a magnetization plateau. In particular, a 10 × 2 supersolid and a 1/5 plateau, identified by infinite Projected Entangled Pair States (iPEPS) calculations, are found to rely on the presence of both magnetic and non-magnetic particles in the sea of dimer singlets. These states are best understood as descendants of the full-plaquette phase, the leading candidate for the intermediate phase of SrCu2(BO3)2.
The deconfined quantum critical point (DQCP) has become a central open concept in the physics of quantum matter, and its proposed presence in the Shastry-Sutherland model was followed by the experimental observation of at least a minimal DQC scenario induced by an applied magnetic field in SrCu2_22​(BO3_33​)2_22​. However, the nature of the plaquette-singlet phase in SrCu2_22​(BO3_33​)2_22​ remains unresolved, and with it the identification of the DQCP symmetry from among several theoretical scenarios. Here we perform detailed high-pressure 11^{11}11B NMR studies to reveal the presence of both the full-plaquette (FP) and empty-plaquette (EP) phases in SrCu2_22​(BO3_33​)2_22​, phase-separated at a first-order, pressure-driven transition with a volume-fraction effect. The field-driven transition from the EP to the antiferromagnetic (AFM) phase complements our previous observations of the FP--AFM transition, with both showing deconfined quantum criticality, while the scaling of the spin-lattice relaxation rate near the EP--AFM transition, 1/T1∝T0.61/T_1 \propto T^{0.6}1/T1​∝T0.6, suggests a DQCP governed by a different universality class. We discuss possible extensions to the Shastry-Sutherland model that account for these pressure and field effects. The expanded phase space we discover mandates an SO(5) DQCP symmetry, and hence our results take an important step towards a complete understanding of deconfined quantum criticality in SrCu2_22​(BO3_33​)2_22​.
Motivated by the ongoing investigation of SrCu2{}_{2}2​(BO3{}_{3}3​)2{}_{2}2​ under pressure, we study a variant of the two-dimensional Shastry-Sutherland (SS) spin-1/21/21/2 model with two types of dimers. Combined with the frustration of the SS model, this modification induces, in a large parameter range, a dimensional reduction at low energies, with nearly decoupled effective S=1S=1S=1 Haldane chains forming along one of the diagonals of the lattice. We also present evidence that the intermediate plaquette solid phase of the undistorted SS model remains stable in a finite region of the phase diagram.
Recent experiments [Guo et al., Phys. Rev. Lett. 124 206602 (2020)] on thermodynamic properties of the frustrated layered quantum magnet SrCu2(BO3)2 — the Shastry–Sutherland material — have provided strong evidence for a low-temperature phase transition between plaquette-singlet and antiferromagnetic order as a function of pressure. Further motivated by the recently discovered unusual first-order quantum phase transition with an apparent emergent O(4) symmetry of the antiferromagnetic and plaquette-singlet order parameters in a two-dimensional “checkerboard J-Q” quantum spin model [Zhao et al., Nat. Phys. 15 678 (2019)], we here study the same model in the presence of weak inter-layer couplings. Our focus is on the evolution of the emergent symmetry as the system crosses over from two to three dimensions and the phase transition extends from strictly zero temperature in two dimensions up to finite temperature as expected in SrCu2(BO3)2. Using quantum Monte Carlo simulations, we map out the phase boundaries of the plaquette-singlet and antiferromagnetic phases, with particular focus on the triple point where these two ordered phases meet the paramagnetic phase for given strength of the inter-layer coupling. All transitions are first-order in the neighborhood of the triple point. We show that the emergent O(4) symmetry of the coexistence state breaks down clearly when the interlayer coupling becomes sufficiently large, but for a weak coupling, of the magnitude expected experimentally, the enlarged symmetry can still be observed at the triple point up to significant length scales. Thus, it is likely that the plaquette-singlet to antiferromagnetic transition in SrCu2(BO3)2 exhibits remnants of emergent O(4) symmetry, which should be observable due to additional weakly gapped Goldstone modes.
The layered material SrCu _2 2 (BO _3 3 ) _2 2 has long been studied because of its fascinating physics in a magnetic field and under pressure. Many of its properties are remarkably well described by the Shastry-Sutherland model (SSM) - a two-dimensional frustrated spin system. However, the extent of the intermediate plaquette phase discovered in SrCu _2 2 (BO _3 3 ) _2 2 under pressure is significantly smaller than predicted in theory, which is likely due to the weak interlayer coupling that is present in the material but neglected in the model. Using state-of-the-art tensor network methods we study the SSM with a weak interlayer coupling and show that the intermediate plaquette phase is destabilized already at a smaller value around J''/J\sim0.04-0.05 J ″ / J ∼ 0.04 − 0.05 than previously predicted from series expansion. Based on our phase diagram we estimate the effective interlayer coupling in SrCu _2 2 (BO _3 3 ) _2 2 to be around J''/J\sim 0.027 J ″ / J ∼ 0.027 at ambient pressure.
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.