This dissertation is a study of praseodymium (Pr) doped YBCO single crystals in the underdoped regime starting from very close to the critical doping. The normalized critical current density varies non monotonically with the decrease in carrier concentration, which is found to be maximum for the 34% of Pr doping. 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 Pr concentration; i.e., the irreversible magnetization normalized by its value at the onset field Hon displays a maximum for the
x = 0.34 single crystal. The two characteristic fields, Hon and Hsp, follow different temperature T dependences: Hon proportional to T^(nu on) and Hsp proportional to [1-(T/Tc)^2]^(nu sp) . The extracted values of the apparent activation energy U^(star) and the creep exponent mu display a maximum at a field Hon < H^(star) < Hsp. Their
field dependencies point toward the coexistence of both elastic and plastic creep for H > Hon. 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.
The magnetic response of the strongly underdoped Y(0.47)Pr(0.53)Ba(2)Cu(3)O(7-delta) was investigated. We found the presence of superconducting order and magnetic order deep into the paramagnetic
state, up to 200 K, which manifest as diamagnetic like response and hysteresis, respectively. We propose that the main source of irreversibility in this T range is the softening and melting of the glassy state into a viscous liquid of entities that behave like superparamagnetic particles with antiferromagnetic cores.