Strong anharmonicity and spin-phonon coupling in the quasi-two-dimensional quantum spin system ${\mathrm{Sr}}_{1-x}{\mathrm{Ba}}_x{\mathrm{Cu}}_2({\mathrm{BO}}_3{)}_2$

We report Raman-scattering measurements on the quasi-two-dimensional quantum spin system ${\mathrm{Sr}}_{1-x}{\mathrm{Ba}}_x{\mathrm{Cu}}_2({\mathrm{BO}}_3{)}_2$ $(x=0\mathrm{}$ and 0.1) in interlayer polarizations and temperatures between 5 K and 450 K. Upon approaching the structural phase transition at $T_s=395\mathrm{}\mathrm{K},$ a strong anharmonic softening of an interlayer mode at $62{\mathrm{cm}}^{-1}$ is observed together with overtone features and a broadening of its linewidth. Moreover, an additional 3% softening toward low temperatures points to strong spin-phonon coupling of exchange origin. Our results suggest a significance of spin-phonon interactions, interlayer lattice dynamics, and Dzyaloshinskii-Moriya interactions to understand the magnetic behavior in this compound that has earlier been discussed in the framework of the two-dimensional Shastry-Sutherland spin system.