Antiferromagnetic-insulating (AF-I) and ferromagnetic-metallic (FM-M) phases coexist in various half-doped manganites over a range of temperature and magnetic field, and this is often believed to be an essential ingredient of their colossal magnetoresistance. We present magnetization and resistivity measurements on Pr0.5Ca0.5Mn0.975Al0.025O3 and Pr0.5Sr0.5MnO3 showing that the fraction of the two coexisting phases at low temperature in any specified measuring field, H, can be continuously controlled by following designed protocols traversing field-temperature space; for both materials the FM-M fraction rises under similar cooling paths. Constant-field temperature variations, however, show that the former sample undergoes a first-order transition from AF-I to FM-M with decreasing T, while the latter undergoes the reverse transition. We suggest that the observed path-dependent phase-separated states result from the low-T equilibrium phase coexisting with supercooled glass-like high-temperature phase, where the low-T equilibrium phases are actually homogeneous FM-M and AF-I phases respectively for the two materials.
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