  When the Fermi Hubbard model was first introduced sixty years ago, one of the
original motivations was to understand correlation effects in itinerant
ferromagnetism. In the past two decades, ultracold Fermi gas in an optical
lattice has been used to study the Fermi Hubbard model. However, the metallic
ferromagnetic correlation was observed only in a recent experiment using
frustrated lattices, and its underlying mechanism is not clear yet. In this
letter, we point out that, under the particle--hole transformation, the
single-particle ground state can exhibit double degeneracy in such a frustrated
lattice. Therefore, the low-energy state exhibits valley degeneracy,
reminiscent of multi-orbit physics in ferromagnetic transition metals. The
local repulsive interaction leads to the valley Hund's rule, responsible for
the observed ferromagnetism. We generalize this mechanism to distorted
honeycomb lattices and square lattices with flux. This mechanism was first
discussed by M\"uller-Hartmann in a simpler one-dimension model. However, this
mechanism has not been widely discussed and has not been related to
experimental observations before. Hence, our study not only explains the
experimental findings but also enriches our understanding of itinerant
ferromagnetism.
