Evolution of Depinning Force Density of $Y_{1-x}Pr_{x}Ba_{2}Cu_{3}O_{7-\delta}$ Single Crystals with Temperature and Magnetic Fields*

We measured the zero field cooled magnetic hysteresis of the $Y_{1-x}Pr_{x}Ba_{2}Cu_{3}O_{7-\delta}$ single crystals with x = 0.14, 0.34, 0.47, 0.53 at various temperatures and magnetic fields. The critical current density $J_{c}$ was determined using the Bean's critical state model. The magnetic field and temperature dependences of the depinning force density $F_{dp}$ were then calculated. The $F_{dp}$ changes nonmonotonically with magnetic field. Specifically, it increases linearly with H to a peak value and then decreases with further increasing magnetic field. The position of the peak shifts to lower H values with increasing temperature. Also, for all measured H, the value of $F_{dp}$ decreases with increasing temperature. While previous studies have shown that small Pr amounts lead to an increase in the pinning energy of $YBa_{2}Cu_{3}O_{7-\delta}$, our results show that a higher concentration of Pr in $YBa_{2}Cu_{3}O_{7-\delta}$ decreases the pinning energy.