SMMs basics

Hamiltonian

The spin-Hamiltonian describing a SMM (equivalent for all SMMs) is given by

The first term is the uniaxial anisotropy, which results from spin-orbit interaction and generates an easy-magnetic-axis along which the magnetic moment of the molecule prefers to be aligned (see fig. B). This term generates an energy barrier (DS² ~ 30-60 K) separating opposite spin projections that are distributed at both sides of the barrier (see fig. C). The second term is the Zeeman energy resulting from the interaction of the spin of the molecule with an externally applied magnetic field. The other terms correspond to transverse anisotropies (H_A) and inter- or intra-molecular interactions such as dipolar, exchange or hyperfine interactions (H’).

A magnetic field applied along the easy axis of the molecule tilts the potential energy wells favoring the spin projections in the direction of the field (see background of figure on the right). There are certain values of the field, known as resonances (H_k = kD/g_B, with k = 0,1,2… being the resonance number), for which opposite levels at both sides of the barrier coincide in energy (on the background of fig. 3 is shown the structure of spin levels for resonance k = 6). At low temperatures, the hysteresis magnetization curve shows accelerations (jumps) of the magnetic relaxation coinciding with these resonant fields (blue line in figure on the right). This phenomenon was first observed in 1996 by Friedman et al. in Mn₁₂-acetate SMM and interpreted in terms of resonant magnetic quantum tunneling (R-MQT) between degenerated spin levels at opposite sides of the anisotropy barrier.

MQT has been observed in many SMMs to date. The characteristics of MQT in SMMs depend on several factors such us spin, anisotropy, symmetry and composition of the molecules, temperature and applied magnetic fields or internal magnetic interactions.