Environmental Effects on Quantum Reversal of Mesoscopic Spins

We describe what we learnt these last years on quantum reversal of large magnetic moments, using mainly conventional SQUID or micro-SQUID magnetometry. Beside the case of ferromagnetic nanoparticles with 10³ - 10⁵ atoms (e.g. Co, Ni, Fe, Ferrites), most fruitful systems appeared to be ensembles of magnetic molecules. These molecules, generally arranged in single crystals, carry relatively small magnetic moments (S = 10 in Mn₁₂-ac and Fe₈). They are sufficiently apart from each other not to be coupled by exchange interactions. The ground multiplet is split over an energy barrier of tens of kelvin (≈ 67 K for Mn₁₂) by a strong local crystal field, leading to an Ising-type ground-state. Only weak inter-molecular dipolar interactions are present, as well as intra-molecular interactions, such as hyperfine interactions. Quantum properties of molecule spins are crucially dependent on their magnetic environment of electronic and nuclear spins (the spin bath). Energy fluctuations of the spin bath of about 0.1 K are important, especially at very low temperatures. In particular, they are much larger than the ground-state tunnel splitting of large-spin molecules in low applied fields, of about 10^-8 K or even less (such a low value is due to the presence of large energy barriers). Theoretical predictions are experimentally checked for tunneling effects in the presence of non-equilibrated or equilibrated spin-energy distribution. It is also shown that the phonon-bath plays no role in low field, except when the temperature approaches the cross-over temperature to the thermal activation regime. In fact, spin-phonon transitions can play a role only if the tunnel splitting is not too small in comparison with k_BT. This is the case both for large-spin molecules in a large magnetic field (e.g. Mn₁₂-ac in a few tesla) and for low-spin molecules, as shown with the study of the molecule V₁₅ (Hilbert space dimension as large as 2¹⁵ and spin 1/2). We also give our latest results on the extension of these studies beyond molecular magnetism. Single-ion slow quantum relaxation is observed in rare-earth Ho³⁺ ions highly diluted in an insulating matrix LiYF₄. This relaxation is due to the coherent tunneling of individual Ho³⁺ spins strongly coupled to their nuclear spins, leading to electro-nuclear entangled states at avoided level crossings. In fact tunneling of the spin system is induced by the hyperfine coupling. Together with the important role of the "spin bath", the roles of cross-spin and spin-phonon relaxations are also considered. All these results confirm the emergence of a new field of research: "mesoscopic magnetism".