Site-selective oxygen isotope effect on the magnetic-field penetration depth in underdoped ${\mathrm{Y}}_{0.6}{\mathrm{Pr}}_{0.4}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$

We report site-selective oxygen isotope ${(}^{16}\mathrm{O}{/}^{18}\mathrm{O})$ effect (OIE) measurements on the in-plane penetration depth ${\lambda }_{\mathrm{ab}}$ in underdoped ${\mathrm{Y}}_{0.6}{\mathrm{Pr}}_{0.4}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta },$ using the muon-spin rotation technique. A pronounced OIE on the transition temperature $T_c$ as well as on ${\lambda }_{\mathrm{ab}}^{-2}\mathrm{}\left(0\right)\mathrm{}$ was observed, which mainly arises from the oxygen sites within the superconducting ${\mathrm{CuO}}_2$ planes (100% within error bar). The values of the corresponding relative isotope shifts were found to be $\Delta T_c{/T}_c=-3.7\left(4\right)\%$ and $\Delta {\lambda }_{\mathrm{ab}}^{-2}\mathrm{}\left(0\right)/{\lambda }_{\mathrm{ab}}^{-2}\mathrm{}\left(0\right)=-6.2\left(1.0\right)\%.\mathrm{}$ Our results imply that in this compound the phonon modes involving the movement of planar oxygen are dominantly coupled to the electrons.