Spontaneous structural distortion of the metallic Shastry-Sutherland system DyB4 by quadrupole-spin-lattice coupling

$\mathrm{Dy}{\mathrm{B}}₄$ has a two-dimensional Shastry-Sutherland (Sh-S) lattice with strong Ising character of the Dy ions. Despite the intrinsic frustrations, it undergoes two successive transitions: a magnetic ordering at ${T}_{\mathrm{N}}=\phantom{\rule{0.16em}{0ex}}20\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ and a quadrupole ordering at ${T}_Q=\phantom{\rule{0.16em}{0ex}}12.5\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. From high-resolution neutron and synchrotron x-ray powder diffraction studies, we have obtained full structural information on this material in all phases and demonstrate that structural modifications occurring at quadrupolar transition lead to the lifting of frustrations inherent in the Sh-S model. Our paper thus provides a complete experimental picture of how the intrinsic frustration of the Sh-S lattice can be lifted by the coupling to quadrupole moments. We show that two other factors, i.e., strong spin-orbit coupling and long-range Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in metallic $\mathrm{Dy}{\mathrm{B}}₄$, play an important role in this behavior.