Approach of single-molecule magnets to thermal equilibrium

We study the spin-lattice relaxation of single-molecule-magnets (SMM) using time-dependent specific heat C_m measurements. These molecular clusters, intermediate between paramagnetic atoms and ferromagnetic nanoparticles, are ideal systems to investigate if quantum phenomena contribute to relaxation at the mesoscopic scale. Experiments show indeed that relaxation to equilibrium proceeds by quantum tunnelling through the magnetic anisotropy energy barrier. For sufficiently high temperatures tunnelling takes place between excited magnetic states. Tunnelling via lower lying states can be promoted by applying a magnetic field B_⊥ perpendicular to the anisotropy axis. For sufficiently large B_⊥, the lowest energy states become quantum coherent superpositions. The equilibrium C_m is dominated, for T<1 K, by dipolar interactions between the molecular spins. A nearly isotropic Mn₆ cluster compound shows a transition to a ferromagnetic phase at For Ising-like SMM's, such as Mn₄, relaxation takes place by incoherent tunnelling between the lowest lying ±S states, assisted by interactions with phonons and nuclear spins. Tunnelling can then be promoted by lowering the symmetry of the molecule. In this case too, the molecular spins order if tunnelling remains sufficiently fast down to