dc magnetization measurements, for zero-field cooled (M-ZFC) and field-cooled (M-FC) cases, have been carried out for flash-evaporated Pd-doped NiMn thin films. These included reentrant phases (Ni76-xPdx)Mn-24, for 0 less than or equal tox less than or equal to5, and Ni75Mn23Pd2, a pure spinglass phase. The studies were performed over the temperature range 3-300 K. Low-field magnetization measurements show the irreversibility effect (M-ZFC and M-FC diverge) at temperatures below the Curie temperature T-c. In Ni75Mn23Pd2, M-ZFC falls below M-FC, as usually observed. However, in reentrant compositions, M-ZFC crosses M-FC upon warming into the ferromagnetic regime, where it stays above M-FC at temperatures below T-c. This unusual behavior is attributed to a model of Imry and Ma in which, in a ferromagnet with antiferromagnetic impurities, the impurities can couple to the host ferromagnetic alignment and force the system to break into domains antiferromagnetically coupled to each other. Field-cooled hysteresis measurements indicate the uniaxial anisotropy in these samples to be small, in contrast with the rigid uniaxial anisotropy reported for the corresponding polycrystalline bulk samples. Since the lattice-orbit coupling is weak in the amorphous phase, this clearly demonstrates that the physical origin of the unidirectional anisotropy is associated with the spin-orbit coupling. (C) 2001 American Institute of Physics.