Quantum nanomagnets: From relaxation to coherence

At the nanometer scale, a magnet is quantum. A single crystal made of a network of nanomagnets is a macroscopic quantum object (incoherent). The first object of this class which was discovered is the so-called molecular complex Mn12-ac with a spin S = 10 per molecule. With vanishingly small tunneling gaps this system opened the field of slow quantum dynamics, allowing in particular the study of interplays between classical and quantum magnetism. The first part of this paper gives an overview of this new type of mesoscopic physics. An extension to the case non-interacting rare-earth ions is presented in the second part, showing that mesoscopic magnetism can reach the atomic scale. Modifications occur in the spin-bath allowing the observation of two- and four-spins entanglements of electro-nuclear states. If rare-earth ions are more diluted this system undergoes a progressive transition from the relaxation regime to the coherence regime where Rabi oscillations are observed. This leads to the rare-earth spin qubits with new possibilities in quantum computation.