1A Microscopic and Spectroscopic View of Quantum Tunneling of Magnetization

Abstract. This chapter takes a microscopic view of quantum tunneling of mag-netization (QTM) in single-molecule magnets (SMMs), focusing on the interplay between exchange and anisotropy. Careful consideration is given to the relation-ship between molecular symmetry and the symmetry of the spin Hamiltonian that dictates QTM selection rules. Higher order interactions that can modify the usual selection rules are shown to be very sensitive to the exchange strength. In the strong coupling limit, the spin Hamiltonian possess rigorous D2h symmetry (or C ∞ in high-symmetry cases). In the case of weaker exchange, additional symmetries may emerge through mixing of excited spin states into the ground state. Group theoretic argu-ments are introduced to support these ideas, as are extensive results of magnetization hysteresis and electron paramagnetic resonance measurements. 1.1 Spin Hamiltonian The concept of an effective spin-Hamiltonian involving only spin variables has been employed in the study of paramagnetic species for well over half a century. This formalism is particularly suited to the study of transition metal complexes in which the ground state is very often an orbital singlet that is well isolated from excited orbital states due to the strong influence of the ligand field [1]. The ground state multiplicity is determined entirely by the spin state of the ion in this situation, even though the ground wave functions are not exact eigenstates of Ŝ2 because of residual spin-orbit (SO) coupling. It is this coupling that gives rise to the familiar anisotropic zero-field splitting (zfs) and Zeeman terms in the resultant spin Hamiltonian, parameterized by the zf