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

S. Kramer (1) , R. Stern (2) , M. Horvatic (1) , C. Berthier (1) , T. Kimura (3) , I.R. Fisher (4)

1 LCMI-GHMFL - Laboratoire des champs magnétiques intenses
2 Laboratory of Chemical Physics
3 MST-8 - Materials Science & Technology Division
4 Geballe Laboratory for Advanced Materials and Departement of Applied Physics

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 ($\Delta_{\rm{B}}/\Delta_{\rm{A}}$ = 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 $H_{\rm{c1}}$ = 23.35 T the average boson density $\overline{n}$ of the Bose-Einstein condensate is strongly modulated along the $c$-axis with a density ratio for every second plane $\overline{n}_{\rm{A}}/\overline{n}_{\rm{B}} \simeq 5$. An IC modulation of the local density is also present in each plane. This adds new constraints for the understanding of the 2D value $\phi$ = 1 of the critical exponent describing the phase boundary.

Mots clés: BEC; NMR; Han Purple; dimensionality; High Field

Domaines: Electrons fortement corrélés [cond-mat.str-el]

S. Kramer, R. Stern, M. Horvatic, C. Berthier, T. Kimura, et al.. NMR evidence for a strong modulation of the Bose-Einstein Condensate in BaCuSi$_2$O$_6$. Physical Review B: Condensed Matter and Materials Physics (1998-2015), 2007, 76 (10), pp.100406(R). ⟨10.1103/PhysRevB.76.100406⟩. ⟨hal-00140519⟩