Quasi-two-dimensional Bose-Einstein condensation of spin triplets in the dimerized quantum magnetBa2CuSi2O6Cl2

We synthesized single crystals of composition ${\mathrm{Ba}}₂{\mathrm{CuSi}}₂{\mathrm{O}}₆{\mathrm{Cl}}₂$ and investigated their quantum magnetic properties. The crystal structure is closely related to that of the quasi-two-dimensional (2D) dimerized magnet ${\mathrm{BaCuSi}}₂{\mathrm{O}}₆$ also known as Han purple. ${\mathrm{Ba}}₂{\mathrm{CuSi}}₂{\mathrm{O}}₆{\mathrm{Cl}}₂$ has a singlet ground state with an excitation gap of $\mathrm{\ensuremath{\Delta}}/{k}_{\mathrm{B}}=20.8$ K. The magnetization curves for two different field directions almost perfectly coincide when normalized by the $g$ factor except for a small jump anomaly for a magnetic field perpendicular to the $c$ axis. The magnetization curve with a nonlinear slope above the critical field is in excellent agreement with exact-diagonalization calculations based on a 2D coupled spin-dimer model. Individual exchange constants are also evaluated using density functional theory (DFT). The DFT results demonstrate a 2D exchange network and weak frustration between interdimer exchange interactions, supported by weak spin-lattice coupling implied from our magnetostriction data. The magnetic-field-induced spin ordering in ${\mathrm{Ba}}₂{\mathrm{CuSi}}₂{\mathrm{O}}₆{\mathrm{Cl}}₂$ is described as the quasi-2D Bose-Einstein condensation of triplets.