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A quantitative estimation of the effect of simultaneously applied externalpressure (P) and magnetic field (H) on the phase coexistence has been presentedfor Pr0.5Ca0.5Mn0.975Al0.025O3 and La0.5Ca0.5MnO3, where the ferromagnetic(FM)-metal and antiferromagnetic (AFM)-insulator phases compete in real space.We found that the nonequilibrium dynamics across the FM-AFM transition isprimarily dictated by the effect of P and H on the supercooling, superheatingtemperatures, and the nucleation and growth rate of the equilibrium phase.These effects across the transition is also responsible for the relative volumefraction of the competing phases at low temperature. Importantly in the entiremagnetic field-pressure-temperature range of phase coexistence, the interfacebetween the two competing phases having different spin and structural orderplays a very important role in controlling the non-equilibrium dynamics.

Phase coexistence and associated non-equilibrium dynamics under simultaneously applied magnetic field and pressure