Field-tuned quantum tunneling in the supramolecule dimer $[{\mathrm{Mn}}_4{]}_2$

Field-tuned quantum tunneling of the supramolecular magnet $\left[{\mathrm{Mn}}_4\right]$${}_2$ is studied. It is a dimer constructed by two single-molecular clusters, ${\mathrm{Mn}}_4\mathrm{}(S=9/2\mathrm{}),$ coupled antiferromagnetically. By means of the time-dependent Schrödinger equation, The exact solution of the time dependent quantum state is numerically calculated. We obtain the curve of magnetization versus magnetic field applied along the easy axis of magnetization of $[{\mathrm{Mn}}_4{]}_2;$ it clearly displays steplike features separated by plateaus that are relevant to spin tunneling. Our result shows that transition of magnetization is sensitive to the sweep rate. Some resonance transitions may not occur, but they can occur at a more lower sweeping rate of the applied field. Our theoretical result agrees well with the recent experiment [W. Wernsdorfer et al., Nature (London) 416, 406 (2002)].