Bose-Einstein Condensation in Han Purple - a NMR Study

NMR study of the two quasi-2D coupled spin-1/2 dimer compound, BaCuSi$_2$O$_6$ (Han Purple) [1], is presented. $T_{\rm{BEC}}$ varies as $(H-H_{c1})^{2/d}$, where $d$ is the dimensionality of the system, and $H_{c1}$ the critical field which closes the gap. BaCuSi$_2$O$_6$ was claimed to exhibit an reduction of d from 3D to 2D at low T [2]. However, due to a structural transformation at 90 K, different intradimer exchange couplings and different gaps ($\Delta_{\rm{B}}$/$\Delta_{\rm{A}}$=1.16) exist in every second plane along the c axis [3]. In our first NMR experiments [3], we have shown that the population of bosons in the B planes $n_{\rm{B}}$ was much smaller than $n_{\rm{A}}$, but finite in the field range $\Delta_{\rm{A}}/g\mu_{\rm{B}} < H < \Delta_{\rm{B}}/g\mu_{\rm{B}}$ where $n_{\rm{B}}$ = 0 is expected in a naive model of uncoupled planes. Recently, a new model has been presented [4] which takes into account both frustration and quantum fluctuations. This leads to a non-zero population $n_{\rm{B}}$ of \emph{uncondensed} bosons in the $B$ plane, increasing quadratically with $(H-H_{c1})$, as compared to the linear dependence of $n_{\rm{A}}$. We compare our new NMR results to these predictions. $[$1$]$ M. Jaime \textit{et al.}, PRL \textbf{93},087203 (2004). $[$2$]$ S. E. Sebastian \textit{et al.}, Nature \textbf{441}, 617 (2006). $[$3$]$ S. Kr\"{a}mer \textit{et al.}, PRB \textbf{76}, 100406(R) (2007). $[$4$]$ N. Laflorencie and F. Mila, PRL \textbf{102}, 060602 (2009).