Quantum Tunneling of Magnetization in Trigonal Single-Molecule Magnets

We perform a numerical analysis of the quantum tunneling of magnetization (QTM) that occurs in a spin $S$ = 6 single-molecule magnet (SMM) with idealized $C_{3}$ symmetry. The deconstructive points in the QTM are located by following the Berry-phase interference (BPI) oscillations. We find that the $\hat {O}_4^3 $ ($=\frac{1}{2}[\hat {S}_z ,\hat {S}_+^3 +\hat {S}_-^3 ])$ operator unfreezes odd-$k$ QTM resonances and generates three-fold patterns of BPI minima in all resonances, including $k$~=~0! This behavior cannot be reproduced with operators that possess even rotational symmetry about the quantization axis. We find also that the $k$ = 0 BPI minima shift away from zero longitudinal field. The wider implications of these results will be discussed in terms of the QTM behavior observed in other SMMs.