  Combining strong magnetic anisotropy with strong exchange interaction is a
long standing goal in the design of quantum magnets. The lanthanide complexes,
while exhibiting a very strong ionic anisotropy, usually display a weak
exchange coupling, amounting to only a few wavenumbers. Recently, an
isostructural series of mixed Ln$^{3+}$-N$_2^{3-}$-Ln$^{3+}$ (Ln $=$ Gd, Tb,
Dy, Ho, Er) have been reported, in which the exchange splitting is estimated to
reach hundreds wavenumbers. The microscopic mechanism governing the unusual
exchange interaction in these compounds is revealed here by combining detailed
modeling with density-functional theory and {\it ab initio} calculations. We
find it to be basically kinetic and highly complex, involving non-negligible
contributions up to seventh power of total angular momentum of each lanthanide
site. The performed analysis also elucidates the origin of magnetization
blocking in these compounds. Contrary to general expectations the latter is not
always favored by strong exchange interaction.
