Pressure dependence of the magnetization plateaus of ${\mathrm{SrCu}}_2{\left({\mathrm{BO}}_3\right)}_2$

We show that the critical fields of the magnetization plateaus of the Shastry-Sutherland model decrease significantly upon increasing the ratio of inter- to intradimer coupling and accordingly that the magnetization plateaus of ${\mathrm{SrCu}}_2{\left({\mathrm{BO}}_3\right)}_2$ shift to lower field under pressure, making the first two plateaus at $1/8$ and $2/15$ potentially accessible to neutron scattering experiments. These conclusions are based on the derivation of an effective classical model of interacting pinwheel-shaped spin-2 bound states using a combination of perturbative and graph-based continuous unitary transformations, showing that pinwheel crystals are indeed the lowest-energy plateau structures at low magnetization and that a simple model of intermediate-range two-body repulsion between pinwheels is able to account quantitatively for the plateau sequence.

Figure 1

Left: Illustration of the Shastry-Sutherland model. Solid (dashed) bonds denote intradimer (interdimer) couplings $J$ ($J^{\prime }$). Additionally, two pinwheels at distance $\delta =({\delta }_x,{\delta }_y)$ are shown as thicker red bonds. Right: The effective interaction $V_{\mathrm{pw}}\left(\delta \right)$ between two pinwheels located at sites $(0,0)$ and $\delta$ of the effective square lattice formed by the centers of the pinwheels for $J^{\prime }/J=0.63$. Note that the inner hardcore potential for small $\delta$ is not given (white area).

Figure 2

Upper panel: Phase diagram of the Shastry-Sutherland model as a function of $J^{\prime }/J$ and magnetic field $h/J$ obtained from the effective pinwheel model ${\mathcal{H}}_{\mathrm{pw}}$ in a self-consistent calculation. Lower panel: Local magnetization of the pinwheel crystals at densities 1/8 (left) and 2/15 (right). The area of the red (blue) circles is proportional to the positive (negative) magnetization along the $z$ direction orthogonal to the displayed plane.

Figure 3

Phase diagram of ${\mathrm{SrCu}}_2{\left({\mathrm{BO}}_3\right)}_2$ as a function of pressure $p$ and magnetic field $H$ obtained from the effective pinwheel model ${\mathcal{H}}_{\mathrm{pw}}$.