NMR studies of quantum spin liquids using high magnetic fields: SrCu$_{2}$(BO$_{3})_{2}$ and BaCuSi$_{2}$O$_{6}$

We present the results of Nuclear Magnetic Resonance (NMR) experiments on the quasi-2D spin gap systems SrCu$_{2}$(BO$_{3})_{2}$ and BaCuSi$_{2}$O$_{6}$ in continuous magnetic fields H of up to 44 T. Using $^{11}$B spectra and spin-lattice relaxation times T$_{1}$ we explore the spin structure on the so-called 1/3 magnetization plateau of the Shastry-Sutherland model material SrCu$_{2}$(BO$_{3})_{2}$. In ancient Han purple - BaCuSi$_{2}$O$_{6}$ -- we observe with help of $^{29}$Si and $^{63,65}$Cu T$_{1}$ the closure of the singlet gap at H$_{c1}$ = 23.4 T down to temperatures T $\sim $ 40 mK. While entering the suggested Bose-Einstein Condensate phase for higher fields [M. Jaime \textit{et al}., Phys. Rev. Lett, \textbf{93}, 087203 (2004)] we discover dramatic changes in $^{29}$Si line shape suggesting incommensurate (and complicated) spin modulation in the ordered phase.