  The general form of the nearest neighbour exchange interaction for rare earth
pyrochlores is derived based on symmetry. Generally, the rare earth angular
momentum degeneracy is lifted by the crystal electric field (CEF) into singlets
and doublets. When the CEF ground state is a doublet that is well-separated
from the first excited state the CEF ground state doublet can be treated as a
pseudo-spin of some kind. The general form of the nearest neighbour exchange
interaction for pseudo-spins on the pyrochlore lattice is derived for three
different types of pseudo-spins. The methodology presented in this paper can be
applied to other two-state spin systems with a high space group symmetry.
