4-spin plaquette singlet state in the Shastry–Sutherland compound SrCu2(BO3)2

Abstract

The study of interacting spin systems is of fundamental importance for modern condensed matter physics. On frustrated lattices, magnetic exchange interactions cannot be simultaneously satisfied, and often give rise to competing exotic ground states 1 . The frustrated 2D ShastrySutherland lattice 2 realized by SrCu 2 (BO 3 ) 2 3 is an important test to our understanding of quantum magnetism. It was constructed to have an exactly solvable 2-spin dimer singlet ground state within a certain range of exchange parameters and frustration. While the exact dimer state and the antiferromagnetic order at both ends of the phase diagram are well known, the ground state and spin correlations in the intermediate frustration range have been widely debated 2-12 . We report here the first experimental identification of the conjectured plaquette singlet intermediate phase in SrCu 2 (BO 3 ) 2 . It is observed by inelastic neutron scattering after pressure tuning at 21.5 kbar. This gapped plaquette singlet state with strong 4-spin correlations leads to a transition to an ordered Néel state above 40 kbar, which can realize a deconfined quantum critical point.In the field of quantum magnetism, geometrically frustrated lattices generally imply major difficulties in analytical and numerical studies. For very few particular topologies however, it has been shown that the ground state, at least, can be calculated exactly as for the Majumdar-Gosh model 13 that solves the J 1 -J 2 zigzag chain when J 1 = 2J 2 . In 2D, the Shastry-Sutherland model 2 consisting of an orthogonal dimer network of spin S=1/2 was developed in order to be exactly solvable. For an inter-dimer J to intra-dimer J exchange ratio α ≡ J /J ≤ 0.5 the ground state is a product of singlets on the strong bond J. Numerical calculations have further shown that this remains valid up to α ≤∼ 0.7 and for small values of 3D couplings J between dimer layers. At the other end, for ∼ 0.9 ≤ α ≤ ∞ the system approaches the well known 2D square lattice, which is antiferromagnetically (AFM) ordered, albeit with significant quantum fluctuations that are believed to include resonating singlet correlations resulting in fractional excitations 14 . The phase diagram of the Shastry-Sutherland model, both with and without applied magnetic field, has been intensively studied by numerous theoretical and numerical approaches 3 . In the presence of magnetic field, magnetization plateaus at fractional values of the saturation magnetization corresponding to Mott insulator phases of dimer states, as well as possible superfluid and supersolid phases have been extensively studied 6,15,16 . At zero field, the main unsolved issue is the existence and nature arXiv:1603.02039v1 [cond-mat.str-el]

Triplon mean-field analysis of an antiferromagnet with degenerate Shastry–Sutherland ground states

“…Stabilities of the chosen spin-gapped states are searched by solving the self-consistent equations of the triplon mean-field theory. Recent experiments show that the plaquette state exits in the material SrCu 2 (BO 3 ) 2 in which the SS model is realized [18]. Remarkably, our results also predict a stable plaquette state even though our considered model has degenerate SS states unlike the SS model.…”

“…Here we work out triplon mean-field theory for Hamiltonian equation (1) with respect to a nonmagnetic plaquette state shown in figure 6. This state is chosen for two reasons: it is known to be exist as the ground state in a small region of J 1 -J 2 model [42,46,47] and also in the SS model as revealed by theoretical and experimental results [15][16][17][18]. A plaquette state is a quantum paramagnetic state in which two spin-singlet dimers resonate on a four-spin block, and therefore it is also known as the plaquette resonating valence bond (pRVB) state.…”

Crystallization of spin superlattices with pressure and field in the layered magnet SrCu2(BO3)2

“…calculated from fits to a thermally activated model24. Linear mapping between x and P is x= 0.63 for P= 0 and x= 0.69 for P= 2 GPa, determined from ambient pressure measurements of x and the critical pressure required to suppress the singlet–triplet gap and induce phase transition242526273132. (Right axis) Red circles show the singlet–triplet gap energy calculated at zero field as a function of x .…”

“…Hydrostatic pressure tunes x across the phase diagram, with a continuous quantum-phase transition into the plaquette state at P ∼2 GPa (refs 24, 25, 26, 27), followed by long-range antiferromagnetic order and an associated symmetry-breaking structural transition at P∼ 4.5 GPa (refs 28, 29). SCBO remains effectively 2D for pressures below this structural transition, at which point the Cu–Cu dimers tilt out of the plane28.…”

Design and experimental performance of local entanglement witness operators

“…From a fundamental viewpoint, the presence of entanglement allows one to rule out certain local realistic descriptions of Nature [5,6]. Recently, entanglement has also moved into the focus of other research areas beyond the field of quantum information science: examples include studies about the role of entanglement in quantum phase transitions [7][8][9][10], the presence of long-ranged quantum correlations as a signature of topologically ordered states in condensed matter systems [11][12][13][14][15], or in the AdS/CFT correspondence, where the entanglement entropy in a conformal field theory contains information about the spacetime geometry of the anti-de Sitter space [16][17][18][19].…”