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International Conference on Low Temperature Physics (LT)

Quantum Phase Transition of the Shastry–Sutherland System and ESR Forbidden Transition

Tôru Sakai, Rito Furuchi, Hiroki Nakano

Published May 22, 2023• 2 citations
Publisher

Abstract

The recent ESR measurement on the Shastry-Sutherland compound SrCu 2 (BO 3 ) 2 detected the pressure-induced phase transition that is expected to correspond to the quantum phase transition from the orthogonal dimer to the plaquette singlet phases.In this experiment the pressure dependence of the spin gap was observed by ESR.The ESR transition of the spin gap is forbidden due to the spin conservation law, but the Dzyaloshinsky-Moriya interaction of this compound enables the observation.Then the selection rule of the ESR transition of the spin gap in the presence ot the Dzyaloshinsky-Moriya interaction is investigated using the numerical diagonalization of the Shastry-Sutherland model.As a result, it is found that the selection rule changes at the quantum phase transition between the dimer and the plaquette singlet phases.

DOI
10.7566/jpscp.38.011155

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The recent ESR measurement on the Shastry-Sutherland compound SrCu 2 (BO 3 ) 2 detected the pressure-induced phase transition that is expected to correspond to the quantum phase transition from the orthogonal dimer to the plaquette singlet phases.In this experiment the pressure dependence of the spin gap was observed by ESR.The ESR transition of the spin gap is forbidden due to the spin conservation law, but the Dzyaloshinsky-Moriya interaction of this compound enables the observation.Then the selection rule of the ESR transition of the spin gap in the presence ot the Dzyaloshinsky-Moriya interaction is investigated using the numerical diagonalization of the Shastry-Sutherland model.As a result, it is found that the selection rule changes at the quantum phase transition between the dimer and the plaquette singlet phases.
High-pressure and high-field electron spin resonance (ESR) measurements have been performed on a single crystal of the orthogonal-dimer spin system SrCu2_{2}2​(BO3_{3}3​)2_{2}2​. With frequencies below 1 THz, ESR signals associated with transitions from the singlet ground state to the one-triplet excited states and the two-triplet bound state were observed at pressures up to 2.1 GPa. We obtained directly the pressure dependence of the gap energies, finding a clear first-order phase transition at Pc=1.85±0.05P_{c}=1.85\pm0.05Pc​=1.85±0.05 GPa. By comparing this pressure dependence with the calculated excitation energies obtained from an exact diagonalization, we determined the precise pressure dependence for inter- (J′J'J′) and intra-dimer (JJJ) exchange interactions considering the Dzyaloshinski-Moriya interaction. Thus this system undergoes a first-order quantum phase transition from the dimer singlet phase to a plaquette singlet phase above the ratio (J′/J)c=0.660±0.003(J'/J)_{c}=0.660\pm0.003(J′/J)c​=0.660±0.003.
Inspired by recent experimental measurements [Guo et al., Phys. Rev. Lett. 124, 206602 (2020PRLTAO0031-900710.1103/PhysRevLett.124.206602); Jiménez et al., Nature (London) 592, 370 (2021)NATUAS0028-083610.1038/s41586-021-03411-8] on frustrated quantum magnet SrCu_{2}(BO_{3})_{2} under combined pressure and magnetic fields, we study the related spin-1/2 Shastry-Sutherland model using state-of-the-art tensor network methods. By calculating thermodynamics, correlations, and susceptibilities, we find, in zero magnetic field, not only a line of first-order dimer-singlet to plaquette-singlet phase transition ending with a critical point, but also signatures of the ordered plaquette-singlet transition with its critical end point terminating on this first-order line. Moreover, we uncover prominent magnetic barocaloric responses, a novel type of quantum correlation induced cooling effect, in the strongly fluctuating supercritical regime. Under finite fields, we identify a quantum phase transition from the plaquette-singlet phase to the spin supersolid phase that breaks simultaneously lattice translational and spin rotational symmetries. The present findings on the Shastry-Sutherland model are accessible in current experiments and would shed new light on the critical and supercritical phenomena in the archetypal frustrated quantum magnet SrCu_{2}(BO_{3})_{2}.
We report heat capacity measurements of SrCu_{2}(BO_{3})_{2} under high pressure along with simulations of relevant quantum spin models and map out the (P,T) phase diagram of the material. We find a first-order quantum phase transition between the low-pressure quantum dimer paramagnet and a phase with signatures of a plaquette-singlet state below T=2 K. At higher pressures, we observe a transition into a previously unknown antiferromagnetic state below 4 K. Our findings can be explained within the two-dimensional Shastry-Sutherland quantum spin model supplemented by weak interlayer couplings. The possibility to tune SrCu_{2}(BO_{3})_{2} between the plaquette-singlet and antiferromagnetic states opens opportunities for experimental tests of quantum field theories and lattice models involving fractionalized excitations, emergent symmetries, and gauge fluctuations.
The orthogonal dimer structure of the SrCu2{}_{2}2​(BO3{}_{3}3​)2{}_{2}2​ spin-1/2 magnet provides a realization of the Shastry--Sutherland model. Using a dimer-product variational wave function, we map out the phase diagram of the Shastry--Sutherland model including anisotropies. Based on the variational solution, we construct a bond-wave approach to obtain the excitation spectra as a function of the magnetic field. The characteristic features of the experimentally measured neutron and ESR spectra are reproduced, like the anisotropy-induced zero-field splittings and the persistent gap at higher fields.
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​.
The field- and frequency-dependence of Electron Spin Resonance (ESR) in the Shastry–Sutherland lattice with small Dzyaloshinsky–Moriya (DM) interaction is studied by the direct numerical estimation of the Kubo formula. Beside the strong paramagnetic resonance, we find the resonance due to the transitions between the triplet and singlet levels which are prohibited in the case without the DM interaction. Furthermore, we find the resonance which is distributed in a wide range of the field for a specific frequency, which corresponds to the transition between the states with the same magnetization.