NMR evidence for a strong modulation of the Bose-Einstein Condensate in BaCuSi${}_2$O${}_6$

Abstract

We present a ${}^{63,65}$Cu and ${}^{29}$Si NMR study of the quasi-2D coupled spin 1/2 dimer compound BaCuSi${}_2$O${}_6$ in the magnetic field range 13-26 T and at temperatures as low as 50 mK. NMR data in the gapped phase reveal that below 90 K different intra-dimer exchange couplings and different gaps ($\hat{I}{”}_{\mathrm{B}}/\hat{I}{”}_{\mathrm{A}}$ = 1.16) exist in every second plane along the c-axis, in addition to a planar incommensurate (IC) modulation. ${}^{29}$Si spectra in the field induced magnetic ordered phase reveal that close to the quantum critical point at $H_{c1}$ = 23.35 T the average boson density $\bar{n}$ of the Bose-Einstein condensate is strongly modulated along the c-axis with a density ratio for every second plane ${\bar{n}}_{\mathrm{A}}/{\bar{n}}_{\mathrm{B}}\simeq 5$. An IC modulation of the local density is also present in each plane. This adds new constraints for the understanding of the 2D value $\ddot{I}•$ = 1 of the critical exponent describing the phase boundary.