Magnetic penetration depth in Ni- and Zn-doped ${\mathrm{YBa}}_2$(${\mathrm{Cu}}_{1\mathrm{-}\mathit{x}}$${\mathit{M}}_{\mathit{x}}$${)}_3$${\mathrm{O}}_7$ films

The penetration depth λ(T) in ${\mathrm{YBa}}_2$(${\mathrm{Cu}}_{1\mathrm{-}\mathit{x}}$ ${\mathit{M}}_{\mathit{x}}$ ${)}_3$ ${\mathrm{O}}_7$ films, with M=Ni or Zn and nominal concentrations, 0.02≤x≤0.06, is obtained from the mutual inductance of coaxial coils on opposite sides of the films. Both Ni and Zn increase λ(0) very rapidly, such that the superfluid density, ${\mathit{n}}_{\mathit{s}}$(0)∝${\lambda }^{\mathrm{-}2}$(0), decreases by a factor of 2 for each percent of dopant. The rapid increase in λ(0) implies that disorder fills in the superconducting density of states at low energy, so that ${\mathit{N}}_{\mathit{S}}$(0) is roughly 80–95 % of the normal-state density of states. An analytic d-wave theory, valid at T=0, finds that λ(0) increases rapidly with disorder, but not as rapidly as observed. It is striking that the dependence of λ(T/${\mathit{T}}_{\mathit{c}}$) on T/${\mathit{T}}_{\mathit{c}}$ does not change significantly as x increases from 2% to 6%, although it is different from undoped ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ films. An ad hoc phenomenological model finds that one should expect this result. Finally, the values of ${\mathit{N}}_{\mathit{S}}$(0) deduced from λ are somewhat larger than values deduced from specific-heat measurements on Zn-doped ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$, which also indicate increasing gaplessness with doping.