The Magnetic phase diagram of the spin-chain system Ca$_{2+x}$Y$_{2-x}$Cu$_5$O$_{10-\delta}$ : Oxygen hole-doping

Recently, K. Kudo et al.\footnote{K. Kudo, S. Kurogi, and Y.Koike, Physical Review B \textbf{71}, 104413 (2005)} studied the magnetic ground state in the edge-sharing CuO$_2$ chains in the spin- chain system Ca$_{2+x}$Y$_{2-x}$Cu$_5$O$_{10-\delta}$. In that study, the antiferromagnetic transition temperature decreases with increasing \emph{x} and disappears around \emph{x}=1.4 followed by the appearance of a spin-glass phase at \emph{x}=1.5. We propose that the oxygen content should be included in the hole doping effect by $p=1/5(x-2\delta)$ in the spin-chain system. We present x-ray diffraction, magnetic susceptibility, specific heat and iodometric titration measurements\footnote{This work is supported by the Robert A. Welch Foundation grant No.F-1191 and the National Science Foundation grant No. DMR-0210383} which indicate that an oxygen deficiency shifts the magnetic features toward higher \emph{x}. For example, for $x=1$ samples, the single crystals of Ref.1 are equivalent to our oxygen deficient polycrystalline sample with $\delta \approx 0.5$. Such a composition has an only slightly suppressed N\'eel temperature, while for nearly fully oxygenated $x=1$ samples, the antiferromagnetic transition is completely suppressed.\footnote{M. D. Chabot, and J. T. Markert, Physical Review Letters \textbf{86}, 163 (2001)}