Doping Dependence of Vortex Regimes in Y${}_{1-x}$Pr${}_x$Ba${}_2$Cu${}_3$O${}_{7-\delta }$ Single Crystals

Magnetic relaxation measurements on a series of Y${}_{1-x}$Pr${}_x$Ba${}_2$Cu${}_3$O${}_{7-\delta }$ ($x=0.13,0.34,0.47$) single crystals were performed over a large field and temperature range in order to investigate the characteristics of the vortex matter across the second magnetization peak (SMP). The magnitude of the SMP varies non-monotonically with the Pr concentration; i.e., the irreversible magnetization normalized by its value at the onset field $H_{on}$ displays a maximum for the $x=0.34$ single crystal. The two characteristic fields, $H_{on}$ and $H_{sp}$, follow different temperature $T$ dependences: $H_{on}\propto T^{{\nu }_{on}}$ and $H_{sp}\propto [1-(T\mathrm{/}{T}_c{)}^2{]}^{{\nu }_{sp}}$. The extracted values of the apparent activation energy $U^{\ast }$ and the creep exponent $\mu$ display a maximum at a field $H_{on}<H^{\ast }<H_{sp}$. Their field dependences point toward the coexistence of both elastic and plastic creep for $H>H_{on}$. The degree of participation of each creep mechanism is determined by the charge carrier density, which controls both the elastic properties of the vortex matter and the pinning potential.