  Metallic magnetism is both ancient and modern, occurring in such familiar
settings as the lodestone in compass needles and the hard drive in computers.
Surprisingly, a rigorous theoretical basis for metallic ferromagnetism is still
largely missing. The Stoner approach perturbatively treates Coulomb
interactions when the latter need to be large, while the Nagaoka approach
incorporates thermodynamically negligible electrons into a half-filled band.
Here, we show that the ferromagnetic order of the Kondo lattice is amenable to
an asymptotically exact analysis over a range of interaction parameters. In
this ferromagnetic phase, the conduction electrons and local moments are
strongly coupled but the Fermi surface does not enclose the latter (i.e. it is
small). Moreover, non-Fermi liquid behavior appears over a range of frequencies
and temperatures. Our results provide the basis to understand some
long-standing puzzles in the ferromagnetic heavy fermion metals, and raises the
prospect for a new class of ferromagnetic quantum phase transitions.
