  We report on muon spin rotation measurements of the internal magnetic field
distribution n(B) in the vortex solid phase of YBa2Cu3Oy (YBCO) single
crystals, from which we have simultaneously determined the hole doping
dependences of the in-plane Ginzburg-Landau (GL) length scales in the
underdoped regime. We find that Tc has a sublinear dependence on
1/lambda_{ab}^2, where lambda_{ab} is the in-plane magnetic penetration depth
in the extrapolated limits T -> 0 and H -> 0. The power coefficient of the
sublinear dependence is close to that determined in severely underdoped YBCO
thin films, indicating that the same relationship between Tc and the superfluid
density is maintained throughout the underdoped regime. The in-plane GL
coherence length (vortex core size) is found to increase with decreasing hole
doping concentration, and exhibit a field dependence that is explained by
proximity-induced superconductivity on the CuO chains. Both the magnetic
penetration depth and the vortex core size are enhanced near 1/8 hole doping,
supporting the belief by some that stripe correlations are a universal property
of high-Tc cuprates.
