NMR evidence for an inhomogeneous transition between the ferromagnetic and antiferromagnetic ground states in Pr$_{1-x}$Ca$_{x}$MnO$_{3}$ manganites

The low temperature behavior of Pr$_{1-x}$Ca$_{x}$MnO$_{3}$ manganites are known to undergo a transition at $x\sim$0.3, from an insulating ferromagnetic state, at low Ca concentration, to an insulating antiferromagnetic state. Above the onset concentration for the charge-ordering effect ($x\sim 0.3$), a metal-insulator transition induced by an external magnetic field is also observed and related to the collapse of the charge-ordered state. In this paper we show that the ferro-antiferromagnetic transition takes place in an inhomogeneous way: around the critical concentration the sample is a mixture of ferromagnetic and antiferromagnetic regions. The zero-field NMR measurements show that a fraction of the ferromagnetic regions is in a fast hopping regime, which suggests that a small fraction of the sample could be metallic, even in zero field. This fraction of fast hopping regions is maximal at $x=$0.3, which is also the concentration for which the insulator-metal transition has been observed in the smallest field.