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We discuss the effects caused by a resonant cavity around a sample of amagnetic molecular crystal (such as Mn${}_{12}$-Ac), when a time dependentexternal magnetic field is applied parallel to the easy axis of the crystal. Weshow that the back action of the cavity field on the sample significantlyincreases the possibility of microwave emission. This radiation process can besupperradiance or a maser-like effect, depending on the strength of thedephasing. Our model provides further insight to the theoretical understandingof the bursts of electromagnetic radiation observed in recent experimentsaccompanying the resonant quantum tunneling of magnetization. The experimentalfindings up to now can all be explained as being a maser effect rather thansuperradiance. The results of our theory scale similarly to the experimentalfindings, i.e., with increasing sweep rate of the external magnetic field, theemission peaks are shifted towards higher field values.Comment: 12 pages, 6 figures. To appear in Phys. Rev.

Microwave emission from a crystal of molecular magnets: The role of a resonant cavity