Asymmetric Berry-Phase Interference Patterns in a Mn$_{4}$ Single-Molecule Magnet

We present a low temperature magnetometry study of the quantum interference effect in a Mn$_{4}$ single-molecule magnet. Asymmetric modulations of the Berry phase interference patterns upon application of a transverse field are observed for $k$~$>$~0 resonances (i.e. non-zero longitudinal field), contrary to the symmetric patterns obtained at $k$~=~0. These asymmetries can be reversed by a full inversion of the total applied field. The observation of a fascinating motion of the Berry-phase minima as a function of both the magnitude and direction of the transverse field can be understood as an outcome of a competition between different intramolecular magnetic interactions. A multi-spin description using non-collinear zero-field splitting tensors and intra molecular dipolar interactions between the manganese ions is employed to explain the results.