  In the band theory of ferromagnetism there is a relative shift in the
position of majority and minority spin bands due to the self-consistent field
due to opposite spin electrons. In the simplest realization, the Stoner model,
the majority and minority spin bands are rigidly shifted with respect to each
other. Here we consider models at the opposite extreme, where there is no
overall shift of the energy bands. Instead, upon spin polarization one of the
bands broadens relative to the other. Ferromagnetism is driven by the resulting
gain in kinetic energy. A signature of this class of mechanisms is that a
transfer of spectral weight in optical absorption from high to low frequencies
occurs upon spin polarization. We show that such models arise from generalized
tight binding models that include off-diagonal matrix elements of the Coulomb
interaction. For certain parameter ranges it is also found that reentrant
ferromagnetism occurs. We examine properties of these models at zero and finite
temperatures, and discuss their possible relevance to real materials.
