  We investigate magnetic properties of strongly interacting four component
spin-3/2 ultracold fermionic atoms in the Mott insulator limit with one
particle per site in an optical lattice with honeycomb symmetry. In this limit,
atomic tunneling is virtual, and only the atomic spins can exchange. We find a
competition between symmetry breaking and liquid like disordered phases.
Particularly interesting are valence bond states with bond centered
magnetizations, situated between the ferromagnetic and conventional valence
bond phases. In the framework of a mean-field theory, we calculate the phase
diagram and identify an experimentally relevant parameter region where a
homogeneous SU(4) symmetric Affleck-Kennedy-Lieb-Tasaki-like valence bond state
is present.
