  A nano-scale metallic grain in which the single-particle dynamics are chaotic
is described by the so-called universal Hamiltonian. This Hamiltonian includes
a superconducting pairing term and a ferromagnetic exchange term that compete
with each other: pairing correlations favor minimal ground-state spin, while
the exchange interaction favors maximal spin polarization. Of particular
interest is the fluctuation-dominated regime where the bulk pairing gap is
comparable to or smaller than the single-particle mean level spacing and the
Bardeen-Cooper-Schrieffer theory of superconductivity breaks down.
Superconductivity and ferromagnetism can coexist in this regime. We identify
signatures of the competition between superconductivity and ferromagnetism in a
number of quantities: ground-state spin, conductance fluctuations when the
grain is weakly coupled to external leads and the thermodynamic properties of
the grain, such as heat capacity and spin susceptibility.
