Orthogonal spin arrangement as possible ground state of three-dimensional Shastry-Sutherland network in Ba3Cu3In4O12

The Ba${}_{3}$Cu${}_{3}$In${}_{4}$O${}_{12}$ stands for unique topology of the magnetic subsystem. It consists of rotated by 90\ifmmode^\circ\else\textdegree\fi{} relative to each other ``paper-chain'' columns made of vertex-sharing Cu${}^{\mathrm{I}}$O${}_{4}$ and Cu${}^{\mathrm{II}}$O${}_{4}$ planar units. The overall pattern of the copper ions is that of a three-dimensional Shastry-Sutherland network. At high temperatures, the magnetic susceptibility follows the Curie-Weiss law with positive Weiss temperature indicating strong predominance of ferromagnetic coupling. At low temperatures, however, this compound exhibits a long-range antiferromagnetically ordered state that reaches saturation magnetization by a nontrivial succession of two spin-flop and two spin-flip transitions already in modest magnetic fields. We show that the ground state in Ba${}_{3}$Cu${}_{3}$In${}_{4}$O${}_{12}$ may be a three-dimensional orthogonal arrangement of the Cu${}^{2+}$ (S $=$ 1/2) magnetic moments forming three virtually independent antiferromagnetic subsystems. In this arrangement, favored by anisotropic exchange interactions, the quantum fluctuations provide the coupling between three mutually orthogonal magnetic subsystems resulting in an impressive ``order by disorder'' effect.