Competition between intermediate plaquette phases in ${\mathrm{SrCu}}_2$(${\mathrm{BO}}_3{)}_2$ under pressure

Building on the growing evidence based on NMR, magnetization, neutron scattering, electron spin resonance, and specific heat that, under pressure, ${\mathrm{SrCu}}_2{\left({\mathrm{BO}}_3\right)}_2$ has an intermediate phase between the dimer and the Néel 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.

Figure 1

(a) Sketch of the distorted orthogonal dimer lattice. The unit cell is defined by the unit vectors ${\vec{e}}_x$ and ${\vec{e}}_y$. (b) Spin-spin correlations in the EPP and (c) in the FPP phase obtained with iPEPS for the parameters used in Figs. 3 and 3 and 3 and 3, respectively.

Figure 2

Ground-state phase diagrams of distorted Shastry-Sutherland models by iPEPS and SE. In (a) for identical nearest-neighbor couplings $J_1^{\prime }=J_2^{\prime }$, in (b) for identical diagonal couplings, and in (c) both asymmetries are included at the ratio $J_2^{\prime }/J_2=0.68$. The area based on the iPEPS results of the dimer singlet phase is colored in red, the EPP in yellow, the FPP/Haldane phase in white, and the Néel phase is shown in blue.

Figure 3

Magnetic excitations in the EPP (top) and FPP/Haldane (bottom). Panels (a) and (d): magnetic excitations along $k_x=k_y$; panels (b) and (e): static structure factors along $k_y=0$. The parameters are given inside the figures. Panels (c) and (f): pressure dependence of the gap (with couplings from magnetic susceptibility $\chi$ [13] and excitation energies $\mathrm{\Delta }$ measured by ESR [12]; see main text). All lines are guides to the eye.