Geometric-Phase Effect in the Thermally Assisted Resonant Tunneling of Mn$_{12}$-tBuAc

Mn$_{12}$-tBuAc, like the better-known single-molecule magnet Mn$_{12}$-Ac, relaxes between up and down spin states by thermally assisted resonant tunneling when a longitudinal magnetic field (H$_{L})$ brings energy levels into resonance. In Mn$_{12}$-Ac, tunneling is induced by a second-order transverse anisotropy produced by local solvent disorder. Such disorder makes the observation of any possible geometric-phase interference effect impractical. Mn$_{12}$-tBuAc, in contrast, has negligible solvent disorder and an intrinsic fourth-order transverse anisotropy. We present experimental data on the transverse-field (H$_{T})$ dependence of the magnetic relaxation rate for Mn$_{12}$-tBuAc. When on resonance (H$_{L}$=0), the rate increases as a function of H$_{T }$ in a series of steps and plateaus due to abrupt changes in the dominant tunneling pair of levels. Surprisingly, a similar effect occurs when off resonance (i.e. large H$_{L})$. Detailed numerical simulations show that the experimental results, both on and off of resonance, can be well described if the fourth-order anisotropy is included in the spin Hamiltonian. The results can be understood as arising from a geometric-phase effect that occurs when H$_{T}$ is applied along the hard axis. Support: NSF grant {\#}DMR-0449516.