Thermal relaxation of field-induced irreversible ferromagnetic phase in Pr-doped manganites

We have investigated the magnetic and transport properties of Pr$_{0.65}$Ca$_{0.35}$MnO$_3$ and Pr$_{0.82}$Na$_{0.18}$MnO$_3$ with almost same doping level under various magnetic fields. Upon applying a field of 4 T, both compounds undergo a metamagnetic transition from antiferromagnetic (AFM) to ferromagnetic (FM) in the low temperature region. The field-induced FM state is very stable for at least 10$^5$ s even after removing the field. This irreversible FM behavior is different from the spontaneous FM ordering as well as the FM state in a reversible metamagnetic transition. We discuss this unusual FM phenomenon found in the Pr-doped manganites with the AFM ground state in terms of the reorientation of Mn spins pinned by localized Pr moments.