We report the observation of strong coupling of a macroscopic ensemble of ~10^{16} Fe_8 molecular nanomagnets to the resonant mode of a microwave cavity. We use millimeter-wave spectroscopy to measure the splitting of the systems resonant frequency i
nduced by the coupling between the spins and the cavity mode. The magnitude of this splitting is found to scale with Sqrt[N], where N is the number of collectively coupled spins. We control N by changing the systems temperature and, thereby, the populations of the relevant spin energy levels. Strong coupling is observed for two distinct transitions between spin energy states. Our results indicate that at low temperatures nearly all of the spins in the sample couple with the cavitys resonant mode even though there is substantial inhomogeneous broadening of the Fe8 spin resonances.
We study the magnetic relaxation rate Gamma of the single-molecule magnet Mn_{12}-tBuAc as a function of magnetic field component H_T transverse to the molecules easy axis. When the spin is near a magnetic quantum tunneling resonance, we find that Ga
mma increases abruptly at certain values of H_T. These increases are observed just beyond values of H_T at which a geometric-phase interference effect suppresses tunneling between two excited energy levels. The effect is washed out by rotating H_T away from the spins hard axis, thereby suppressing the interference effect. Detailed numerical calculations of Gamma using the known spin Hamiltonian accurately reproduce the observed behavior. These results are the first experimental evidence for geometric-phase interference in a single-molecule magnet with true four-fold symmetry.
We analyze the interference between tunneling paths that occurs for a spin system with both fourth-order and second-order transverse anisotropy. Using an instanton approach, we find that as the strength of the second-order transverse anisotropy is in
creased, the tunnel splitting is modulated, with zeros occurring periodically. This effect results from the interference of four tunneling paths connecting easy-axis spin orientations and occurs in the absence of any magnetic field.
We measure magnetization changes in a single crystal of the single-molecule magnet Fe8 when exposed to intense, short (<20 $mu$s) pulses of microwave radiation resonant with the m = 10 to 9 transition. We find that radiation induces a phonon bottlene
ck in the system with a time scale of ~5 $mu$s. The phonon bottleneck, in turn, drives the spin dynamics, allowing observation of thermally assisted resonant tunneling between spin states at the 100-ns time scale. Detailed numerical simulations quantitatively reproduce the data and yield a spin-phonon relaxation time of T1 ~ 40 ns.
