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

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The oxygen-isotope (¹⁶O/¹⁸O) effect (OIE) on the in-plane magnetic penetration depth λab(0) in optimally-doped YBa₂Cu₃O₇₋δ and La₁.₈₅Sr₀.₁₅CuO₄, and in slightly underdoped YBa₂Cu₄O₈ and Y₀.₈Pr₀.₂Ba₂Cu₃O₇₋δ was studied by means of muon-spin rotation. A substantial OIE on λab(0) with an OIE exponent βₒ=-dλab(0)/d Mₒ≈ - 0.2 (Mₒ is the mass of the oxygen isotope), and a small OIE on the transition temperature Tc with an OIE exponent αₒ=-d Tc/d Mₒ≃0.02 to 0.1 were observed. The observation of a substantial isotope effect on λab(0), even in cuprates where the OIE on Tc is small, indicates that lattice effects play an important role in cuprate HTS.