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A microscopic model of the molecular magnet V15 is used to study mechanisms for the adiabatic change of the magnetization in time-dependent magnetic fields. Effects of the Dzyaloshinskii-Moriya interaction, the most plausible source for the energy-level repulsions that lead to adiabatic changes of the magnetization, are studied in detail. We find that the energy-level repulsions that result from this interaction exhibit a strong dependence on the direction of the applied field. We also discuss the role of magnetic anisotropy in the molecule Mn12 -acetate.

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