Theory of the Raman spectra of the Shastry-Sutherland antiferromagnet ${\text{SrCu}}_2{\left({\text{BO}}_3\right)}_2$ doped with nonmagnetic impurities

Controlled doping of ${\text{SrCu}}_2{\left({\text{BO}}_3\right)}_2$, a faithful realization of the Heisenberg spin-1/2 antiferromagnet on the Shastry-Sutherland lattice, with nonmagnetic impurities generates bound states below the spin gap. These bound states and their symmetry properties are investigated by exact diagonalization of small clusters and within a simple effective model describing a spinon submitted to an attractive extended potential. It is shown that Raman spectroscopy is a unique technique to probe these bound states. Quantitative theoretical Raman spectra are numerically obtained.

Figure 1

(Color online) Shastry-Sutherland lattice. $\pm$ signs correspond to Raman coupling in the $\left(a^{\prime }{b}^{\prime }\right)$ polarization case.

Figure 2

(Color online) Raman spectra for pure SSL for various $\alpha$ on $N=16$ and 32 clusters. The spin gap ${\Delta }_{01}$ [$\sim 0.95$, $0.80$, $0.50J$ in (a), (b), and (c), respectively] is used as a unit of frequency. An artificial width $\epsilon =0.01$ has been given to the delta peaks.

Figure 3

(Color online) Magnetization pattern around the impurity (marked as x) on $N=32$ SSL for $\alpha =0.6$ $\left(S_z^{tot}=1/2\right)$. Periodic boundary conditions are used. Since the reflection around the $b^{\prime }$ axis is still a good symmetry, we observe identical values on both sides.

Figure 4

(Color online) Raman spectra for SSL doped with a single nonmagnetic impurity for various $\alpha$ on $N=16$ and 32 clusters. The spin gap ${\Delta }_{01}$ [$\sim 0.95$, $0.80$, $0.50J$ in (a), (b), and (c), respectively] is used as a unit of frequency. An artificial width $\epsilon =0.01$ has been given to the delta peaks.

Figure 5

(Color online) Low-energy $S=1/2$ excitations vs $\alpha$. The dashed line indicates the perturbative estimation of the spin gap (see text). [(a)–(b)] Microscopic model on $N=16$ and 32 SSL. The states are classified according to their reflection symmetry. The two lowest $S=3/2$ states also shown give the onset of the continuum. (c) Effective model (see inset for a schematic plot of the effective potential) on a $N=625$ square lattice of dimers for which finite-size effects are not visible.