The level splittings in a dimer with the antiferromagnetic coupling between two single-molecule magnets are calculated perturbatively for arbitrary spin. It is found that the exchange interaction between two single-molecule magnets plays an important role in the level splitting. The results are discussed in comparison with the recent experiment. 75.45.+j, 75.50.Xx, 75.50.Tt Typeset using REVTEXThe quantum properties of single-molecule magnets have generated considerable interest over the past decade in connection with macroscopic quantum phenomena . High-spin molecules with spin-10, Mn12 and Fe8 have been such good candidates because all the clusters are identical with no dispersion on the size of the clusters and the number of interaction spins, and the spin ground state and the magnetic anisotropy are known with great accuracy. These molecules display particularly interesting phenomena such as quantum resonant tunneling [2,3] and quantum phase interference . Such phenomena have received much attention, both theoretically and experimentally in view of macroscopic realization of quantu
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