Phase locking dynamics of dipolarly coupled vortices excited by spin-polarized current in two identical nanopillars is studied as a function of the interpillar distance L. Numerical study and analytical model have proved the remarkable efficiency of magneto-static interaction to achieve phase locking. Investigating the dynamics in the transient regime towards phase locking, we extract the evolution of the locking time τ , the coupling strength µ and the interaction energy W . Finally, we compare this coupling energy with the one obtained by simple model.

Theoretical investigation of the magnetisation process in high-spin cluster is performed. The source of hysteresis is studied; magnetisation jumps on hysteresis loops of a cluster corresponding to intersections of energy levels are described theoretically. An analytical formula for the dependence of the height of a jump on the sweeping rate of external field is obtained. It is shown that the width of a jump is crucially influenced by fluctuating fields produced by the cluster environment.

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If a single spin possessing an easy-axis anisotropy is subjected to an external field perpendicular to the easy axis, the susceptibility exhibits a peculiar peak. We establish that the specific spectral properties of quantum fluctuations give rise to this peak. We predict that this effect takes place in real many-spin systems, such as Mn 12 clusters, and can be studied at finite temperatures in real experiments with attainable resolution. This offers an approach for studying quantum fluctuations in magnetic molecules, in addition to relaxation rate measurements.