Spin pseudogap and interplane coupling in ${\mathrm{Y}}_2$${\mathrm{Ba}}_4$${\mathrm{Cu}}_7$${\mathrm{O}}_{15}$: A ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}$ nuclear spin-spin relaxation study

We report measurements of the Gaussian contribution ${\mathit{T}}_{2\mathit{G}}$ to the plane ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}$ nuclear spin-spin relaxation time in the ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ and ${\mathrm{YBa}}_2$${\mathrm{Cu}}_4$${\mathrm{O}}_8$ blocks of normal and superconducting ${\mathrm{Y}}_2$${\mathrm{Ba}}_4$${\mathrm{Cu}}_7$${\mathrm{O}}_{15}$. The data confirm our previous results that adjacent ${\mathrm{CuO}}_2$ planes have different doping levels and that these planes are strongly coupled. The static spin susceptibility at the antiferromagnetic wave vector exhibits a Curie-Weiss-like temperature dependence in the normal state. The ${\mathrm{Y}}_2$${\mathrm{Ba}}_4$${\mathrm{Cu}}_7$${\mathrm{O}}_{15}$ data are incompatible with a phase diagram based on a single ${\mathrm{CuO}}_2$ plane theory but point to the importance of the interplane coupling in the spin-gap formation. Additional data for ${\mathrm{YBa}}_2$${\mathrm{Cu}}_4$${\mathrm{O}}_8$ and ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6.982}$ are in acord with the single-plane theory. The temperature dependence of ${\mathit{T}}_{2\mathit{G},\mathrm{i}\mathrm{n}\mathrm{d}}$ below ${\mathit{T}}_{\mathit{c}}$ excludes isotropic s-wave superconductivity in all three compounds.