AC relaxation in the iron(8) molecular magnet

We investigate the low energy magnetic relaxation characteristics of the “iron eight” (Fe₈) molecular magnet. Each molecule in this material contains a cluster of eight Fe 3+ ions surrounded by organic ligands. The molecules arrange themselves into a regular lattice with triclinic symmetry. At sufficiently low energies, the electronic spins of the Fe3+ ions lock together into a “quantum rotator” with spin S = 10.; We derive a low energy effective Hamiltonian for this system, valid for temperatures less than T_c ∼ 360 mK , where T_c is the temperature at which the Fe₈ system crosses over into a “quantum regime” where relaxation characteristics become temperature independent. We show that in this regime the dominant environmental coupling is to the environmental spin bath in the molecule. We show how to explicitly calculate these couplings, given crystallographic information about the molecule, and do this for Fe₈. We use this information to calculate the linewidth, topological decoherence and orthogonality blocking parameters. All of these quantities are shown to exhibit an isotope effect. We demonstrate that orthogonality blocking in Fe₈ is significant and suppresses coherent tunneling.; We then use our low energy effective Hamiltonian to calculate the single-molecule relaxation rate in the presence of an external magnetic field with both AC and DC components by solving the Landau-Zener problem in the presence of a nuclear spin bath. Both sawtooth and sinusoidal AC fields are analyzed. This single-molecule relaxation rate is then used as input into a master equation in order to take into account the many-molecule nature of the full system. Our results are then compared to quantum regime relaxation experiments performed on the Fe₈ system.