  This paper is concerned with the weak-moment magnetism in heavy-fermion
materials and its relation to the non-Fermi liquid physics observed near the
transition to the Fermi liquid. We explore the hypothesis that the primary
fluctuations responsible for the non-Fermi liquid physics are those associated
with the destruction of the large Fermi surface of the Fermi liquid. Magnetism
is suggested to be a low-energy instability of the resulting small Fermi
surface state. A concrete realization of this picture is provided by a
fractionalized Fermi liquid state which has a small Fermi surface of conduction
electrons, but also has other exotic excitations with interactions described by
a gauge theory in its deconfined phase. Of particular interest is a
three-dimensional fractionalized Fermi liquid with a spinon Fermi surface and a
U(1) gauge structure. A direct second-order transition from this state to the
conventional Fermi liquid is possible and involves a jump in the electron Fermi
surface volume. The critical point displays non-Fermi liquid behavior. A
magnetic phase may develop from a spin density wave instability of the spinon
Fermi surface. This exotic magnetic metal may have a weak ordered moment
although the local moments do not participate in the Fermi surface.
Experimental signatures of this phase and implications for heavy-fermion
systems are discussed.
