  We consider the electronic structure of, and magnetic exchange (spin)
interactions between, nominally nonmagnetic Eu^3+ ions (4f^6, S=3, L=3, J=0)
within the context of the rocksalt structure compounds EuN and EuP. Both
compounds are ionic [Eu^3+; N^3- and P^3-] semimetals similar to isovalent GdN.
Treating the spin polarization within the 4f shell, and then averaging
consistent with the J=0 configuration, we estimate semimetallic band overlaps
(Eu 5d with pnictide 2p or 3p) of ~0.1 eV (EuN) and ~1.0 eV (EuP) that increase
(become more metallic) with pressure. The calculated bulk modulus is 130 (86)
GPa for EuN (EuP). Exchange (spin-spin) coupling calculated from correlated
band theory is small and ferromagnetic in sign for EuN, increasing in magnitude
with pressure. Conversely, the exchange coupling is antiferromagnetic in sign
for EuP and is larger in magnitude, but decreases with compression. Study of a
two-site model with S_1*S_2 coupling within the J=0,1 spaces of each ion
illustrates the dependence of the magnetic correlation functions on the model
parameters, and indicates that the spin coupling is sufficient to alter the Van
Vleck susceptibility. We outline a scenario of a spin-correlation transition in
a lattice of S=3, L=3, J=0 nonmagnetic ions.
