Vortex phase diagram ofHgBa2Ca2Cu3O8+δthin films from magnetoresistance measurements

Abstract

We have investigated the resistive behavior of ${\mathrm{HgBa}}_{2}{\mathrm{Ca}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{8+\ensuremath{\delta}}$ thin films from the Arrhenius form $\ensuremath{\rho}(T,H)={\ensuremath{\rho}}_{0}\mathrm{exp}(\ensuremath{-}{U}_{0}/T).$ The effective activation energy, ${U}_{\mathrm{e}}\ensuremath{\equiv}\ensuremath{-}d(\mathrm{ln}\ensuremath{\rho}{)/d(1/T)=U}_{0}\ensuremath{-}{\mathrm{TdU}}_{0}/dT,$ is compared with the model based on thermally activated flux flow (TAFF), where ${U}_{0}{(T,H)=U}_{0}(0,H)(1\ensuremath{-}{T/T}_{c}{)}^{3/2}.$ In a limited temperature region, ${T}^{*}lTl{T}_{\mathrm{ff}}, \ensuremath{\rho}(T)$ follows the TAFF behavior, and this region is regarded as the pinned liquid state. In the TAFF region, all curves for the effective activation energy for different magnetic fields converge onto one line with a scaling factor ${U}_{0}(0,H)$ proportional to $1/H.$ The crossover temperature, ${T}_{\mathrm{ff}},$ separates TAFF from free flux flow. The intermediate region, ${T}_{\mathrm{irr}}lTl{T}^{*},$ where ${T}_{\mathrm{irr}}$ is the temperature of irreversibility, is called the critical state and is between a pinned liquid and a vortex solid. Finally, based on these analyses, we determine the dynamic vortex phase diagram for different pinning behaviors of the vortex.