Competition between intermediate plaquette phases in SrCu$_2$(BO$_3$)$_2$ under pressure

Building on the growing evidence based on NMR, magnetization, neutron scattering, ESR, and specific heat that, under pressure, SrCu$_2$(BO$_3$)$_2$ has an intermediate phase between the dimer and the Neel phase, we study the competition between two candidate phases in the context of a minimal model that includes two types of intra- and inter-dimer interactions without enlarging the unit cell. We show that the empty plaquette phase of the Shastry-Sutherland model is quickly replaced by a quasi-1D full plaquette phase when intra- and/or inter-dimer couplings take different values, and that this full plaquette phase is in much better agreement with available experimental data than the empty plaquette one.