The pyrochlore lattice, which is composed by corner sharing tetrahedra is a typical example of a highly frustrated three dimensional structure.
It is believed that Heisenberg AFM on a pyrochlore
structure does not support a magnetically ordered ground state.
Often in real systems, for example, in spinels, with the general formula AB$_2$O$_4$, a magnetic ion can also possesses an
orbital degeneracy in addition to the spin one. The physical behavior of
such systems may be drastically different from that of pure spin models, as the occurrence of an orbital ordering can modulate the spin exchange
and thus lift the geometrical degeneracy of the underlying lattice.
As an example, I will discuss two compounds with such properties: the B-spinels MgTi2O4 and ZnV2O4, where novel magnetic phases can occur as a ground state.
