Interplay of superconductivity and ferromagnetism in ultra-small metallic grains

We investigate the competition between superconductivity and ferromagnetism in ultra-small metallic grains in a regime where both phases can coexist. We use an effective Hamiltonian in the mesoscopic regime that combines a BCS-like pairing term and a ferromagnetic Stoner-like spin exchange term. The presence of spin jumps in the ground-state phase diagram of the grain is a unique feature of the coexistence of pairing and ferromagnetic correlations. We show that the coexistence regime can be made accessible to experiments by tuning an external Zeeman field [1]. We also study the transport properties of the grain in the Coulomb blockade regime and identify signatures of the competition between superconductivity and ferromagnetism in the mesoscopic fluctuations of the conductance [2]. \newline [1] S. Schmidt, Y. Alhassid and K. Van Houcke, Europhys. Lett. 80, 47004 (2007). \newline [2] S. Schmidt, Y. Alhassid, to be published (2007).