Correlation between oxygen isotope effects on the transition temperature and the magnetic penetration depth in high-temperature superconductors close to optimal doping

The oxygen-isotope (^{16}O/^{18}O) effect (OIE) on the in-plane magnetic penetration depth \lambda_{ab}(0) in optimally-doped YBa_2Cu_3O_{7-\delta} and La_{1.85}Sr_{0.15}CuO_4, and in slightly underdoped YBa_2Cu_4O_8 and Y_{0.8}Pr_{0.2}Ba_2Cu_3O_{7-\delta} was studied by means of muon-spin rotation. A substantial OIE on \lambda_{ab}(0) with an OIE exponent \beta_O=-d\ln\lambda_{ab}(0)/d\ln M_O\approx - 0.2 (M_O is the mass of the oxygen isotope), and a small OIE on the transition temperature T_c with an OIE exponent \alpha_O=-d\ln T_{c}/d \ln M_O\simeq0.02 to 0.1 were observed. The observation of a substantial isotope effect on \lambda_{ab}(0), even in cuprates where the OIE on T_c is small, indicates that lattice effects play an important role in cuprate HTS.