Phonon-Assisted Tunneling in the Quantum Regime of Mn₁₂ Acetate

Longitudinal or transverse magnetic fields applied on a crystal of Mn₁₂ acetate allows one to observe independent tunnel transitions between m = -S+p and m = S-n-p ( n = 6–10, p = 0–2 in longitudinal field and n = p = 0 in transverse field). We observe a smooth transition (in longitudinal) from coherent ground-state to thermally activated tunneling. Furthermore, two ground-state relaxation regimes show a crossover between quantum spin relaxation far from equilibrium and near equilibrium, when the environment destroys multimolecule correlations. Finally, we stress that the complete Hamiltonian of Mn₁₂ should contain odd spin operators of low order.