Exchange coupling in the magnetic molecular cluster Mn₁₂Ac

The magnetic properties of the molecular cluster Mn₁₂Ac are due to the four Mn³⁺ ions that have spins S=3/2 and the eight Mn⁴⁺ ions with spins S=2. These spins are coupled by an exchange mechanism. We determine the four exchange couplings assuming a Heisenberg-type interaction between the ions. We use exact diagonalization of the spin Hamiltonian by a Lánczos algorithm and we adjust the couplings to reproduce the magnetization curve of Mn₁₂Ac. We also impose the constraint of reproducing a gap of 35 K between an S=10 ground state and a first excited state with S=9. We predict that there is an excited level with S=8 at 37 K above the ground state, only slightly above the S=9 excited state that lies at 35 K and the next excited state is an S=9 multiplet at 67 K above the S=10 ground state.