Quantum tunnelling of the magnetisation in molecular nanomagnets

Abstract

The first term is the axial anisotropy responsible for the energy barrier which separates up and down configurations as shown in Figure 2, where the states are labelled with the eigenvalue of S., M. The double well potential drawn in the figure is reminiscent of that observed in classical single domain particles. Here only 21 well defined levels are presentbut at low temperature the thermally activated reversal of the magnetisation follows an Arrhenius law and the characteristic time becomes macroscopically long. If it grows over the time needed to measure an hysteresis cycle, a remanent magnetisation appears, with a coercive field which increases on lowering the temperature. The Molecular nanomagnets In the beginning of the nineties chemists, and in particular molecular chemists, entered into the game by starting to synthesise and investigate objects that can be seen as the missing link between the quantum word of paramagnetic metal centres and the classical one of magnetic particles. These new materials, known as molecular nanomagnets or as Single Molecule Magnets, are indeed clusters comprising a relatively small number of paramagnetic centres. These are usually paramagnetic transition metal ions, which interacts through bridging atoms, e.g. oxygen, or groups of atoms, e.g. the cyanide bridge. One example of this kind of molecules is the octanuclear iron cluster of formula [Fes02(OH) n(tacn)6]Brs, abbreviated from here on as FeB, whose structure is shown in Figure 1. The coordination sites of the iron atoms are saturated by the organic ligand tacn=triazacyclonane, which provides a hydrophobic shell preventing the growth of the metal hydroxide-oxide core to an extended lattice. The major advantage of the molecular approach, compared to the coating of nanosized particles, is that the clusters are arranged in a crystal structure and, in the most favourable cases neglecting also crystal defects, all the clusters are identical, equally oriented and weakly interacting among themselves. Despite the fact that oxygen atoms very often mediate moderate antiferromagnetic interactions, the complex connectivity and the related spin topology leads in some caseS to a large spin multiplicity of the ground state. The example of Figure I, Fe8, possess a ground S=10 spin state. In this case the individual spins are those of rather isotropic, dS, iron(Ill) ions, with no orbital contribution. Also in the case ofmore anisotropic metal ions, as manganese(III), the orbital contribution is quenched by the low symmetry. Its presence is however important in the magneto-crystalline anisotropy, which is commonly described using an effective spin Hamiltonian of the form: in fact due to the strong dependence of tunnelling on the axial and transverse magnetic anisotropy that, on their turn, are related to the dimensions of the nanoparticle. Ensembles of nanoparticles are unfortunately characterised by a distribution in size and shape.