Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1801.08242 · Journal of the Physical Society of Japan

Direct Observation of the Quantum Phase Transition of SrCu 2 (BO 3 ) 2 by High-Pressure and Terahertz Electron Spin Resonance

Takahiro Sakurai, Yuki Hirao, Keigo Hijii, Susumu Okubo, Hitoshi Ohta, Yoshiya Uwatoko, Kazutaka Kudo, Yoji Koike

Published Jan 31, 2018• 55 citations
arXivHTMLPDF

Abstract

High-pressure and high-field electron spin resonance (ESR) measurements have been performed on a single crystal of the orthogonal-dimer spin system SrCu$_{2}$(BO$_{3}$)$_{2}$. 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 $P_{c}=1.85\pm0.05$ GPa. By comparing this pressure dependence with the calculated excitation energies obtained from an exact diagonalization, we determined the precise pressure dependence for inter- ($J'$) and intra-dimer ($J$) 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 $(J'/J)_{c}=0.660\pm0.003$.

DOI
10.7566/jpsj.87.033701

Related papers

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

Tôru Sakai, Rito Furuchi, Hiroki Nakano

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.

International Conference on Low Temperature Physics (LT)•May 22, 2023•2 citations

Quantum Phases of SrCu 2 ( BO 3 ) 2 from High-Pressure Thermodynamics

Jing Guo, Guang-Yu Sun, Bowen Zhao +9 more

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.

arXiv:1904.09927•Physical Review Letters•May 20, 2020•106 citations

Theory of the orthogonal dimer Heisenberg spin model for SrCu 2 (BO 3 ) 2

Shin Miyahara, Kazuo Ueda

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.

Journal of Physics Condensed Matter•Feb 24, 2003•248 citations

Electron spin resonance of SrCu2(BO3)2 at high magnetic fields

Samir El Shawish, J. Bonča, Cristian D. Batista +1 more

We calculate the electron spin resonance (ESR) spectra of the quasi-two-dimensional dimer spin liquid $\mathrm{Sr}{\mathrm{Cu}}_{2}{(\mathrm{B}{\mathrm{O}}_{3})}_{2}$ as a function of magnetic field $B$. Using the standard Lanczos method, we solve a Shastry-Sutherland Hamiltonian with additional Dzyaloshinsky-Moriya (DM) terms which are crucial to explain different qualitative aspects of the ESR spectra. In particular, a nearest-neighbor DM interaction with a nonzero ${D}_{z}$ component is required to explain the low frequency ESR lines for $B\ensuremath{\Vert}c$. This suggests that crystal symmetry is lowered at low temperatures due to a structural phase transition.

arXiv:cond-mat/0407632•Physical Review B•Jan 12, 2005•10 citations

Two Plaquette-Singlet Phases and Emergent SO(5) Deconfined Quantum Criticality in SrCu2(BO3)2

Cui, Yi, Kefan Du, Zhanlong Wu +15 more

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 SrCu$_2$(BO$_3$)$_2$. However, the nature of the plaquette-singlet phase in SrCu$_2$(BO$_3$)$_2$ remains unresolved, and with it the identification of the DQCP symmetry from among several theoretical scenarios. Here we perform detailed high-pressure $^{11}$B NMR studies to reveal the presence of both the full-plaquette (FP) and empty-plaquette (EP) phases in SrCu$_2$(BO$_3$)$_2$, 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, $1/T_1 \propto T^{0.6}$, 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 SrCu$_2$(BO$_3$)$_2$.

arXiv:2411.00302•Nov 1, 2024•0 citations

Effect of Dzyaloshinskii-Moriya interactions on the phase diagram and magnetic excitations of SrCu 2 (BO 3 ) 2

Judit Romhányi, Keisuke Totsuka, Karlo Penc

The orthogonal dimer structure of the SrCu${}_{2}$(BO${}_{3}$)${}_{2}$ 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.

arXiv:1010.4476•Physical Review B•Jan 26, 2011•47 citations
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.
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.
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 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.
We calculate the electron spin resonance (ESR) spectra of the quasi-two-dimensional dimer spin liquid SrCu2(BO3)2\mathrm{Sr}{\mathrm{Cu}}_{2}{(\mathrm{B}{\mathrm{O}}_{3})}_{2}SrCu2​(BO3​)2​ as a function of magnetic field BBB. Using the standard Lanczos method, we solve a Shastry-Sutherland Hamiltonian with additional Dzyaloshinsky-Moriya (DM) terms which are crucial to explain different qualitative aspects of the ESR spectra. In particular, a nearest-neighbor DM interaction with a nonzero Dz{D}_{z}Dz​ component is required to explain the low frequency ESR lines for $B\ensuremath{\Vert}c$. This suggests that crystal symmetry is lowered at low temperatures due to a structural phase transition.
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​.
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.