Magnetic-field and temperature dependence of the thermally activated dissipation in thin films of ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_{8+\mathrm{\delta }}$

The resistive transitions of a wide variety of ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_{8+\mathrm{\delta }}$ thin films have been measured in ${\mathrm{\mu }}_0$ H∥c^ from 0.01 to 15 T. For all samples, the transitions can be well approximated by the thermally activated form: R(T,H)≊${\mathit{R}}_{\mathit{n}}$exp{-A(1-T/${\mathit{T}}_{\mathit{c}}$)/${\mathit{k}}_{\mathit{B}}$T √H } in the range ${10}^{\mathrm{-}6}$ ${\mathit{R}}_{\mathit{n}}$<R<${10}^{\mathrm{-}2}$ ${\mathit{R}}_{\mathit{n}}$. The energy scale A is 1740 K for smooth, in situ films made by molecular-beam epitaxy, and is 890 K for rough, polycrystalline films made by ambient temperature sputtering with an ex situ anneal. The field and temperature dependence of the activation energy, as well as its overall magnitude, is consistent with a model in which U(T,H) arises from plastic deformations of a viscous flux liquid above the vortex-glass transition temperature. The flux lattice shear mechanism proposed by this model is shown to be energetically preferable to direct lattice shear in highly anisotropic materials, thus explaining why the activation energy in ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$O ${}_{8+\mathrm{\delta }}{}^{}{}_{}{}^{}$ has a different field dependence than that for ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$.