  Spin-changing collisions in trapped Fermi gases may acquire a resonant
character due to the compensation of quadratic Zeeman effect and trap energy.
These resonances are absent in spinor condensates and pseudo-spin-1/2 Fermi
gases, being a characteristic feature of high-spin Fermi gases that allows
spinor physics at large magnetic fields. We analyze these resonances in detail
for the case of lattice spinor fermions, showing that they permit to
selectively target a spin-changing channel while suppressing all others. These
resonances allow for the controlled creation of non-trivial quantum
superpositions of many-particle states with entangled spin and trap degrees of
freedom, which remarkably are magnetic-field insensitive. Finally, we show that
the intersite tunneling may lead to a quantum phase transition described by an
effective quantum Ising model.
