  We investigate the cause of exchange anisotropy in a family of copper-based,
quasi-two-dimensional materials with very similar geometries. This family
differs mainly in the inter-layer separation, but have very different magnetic
interactions even within the basal plane. We use density functional theory and
Wannier functions to parameterize two complimentary tight-binding models and
show that the superexchange between the Cu(II) ions is dominated by a
through-space interaction between hybrid Cu-pyrazine orbitals centered on the
copper atoms. We find no correlations between the strength of this exchange
interaction with homologous geometric features across the compounds, such as Cu
and pyrazine bond lengths and orientations of nearby counter-ions. We find that
the pyrazine tilt angles do not affect the Cu-pyrazine-Cu exchange because the
lowest unoccupied molecular orbital on the pyrazine is at a very high energy
(relative to the frontier orbitals, which are Cu-based). We conclude that the
anisotropy of magnetic interactions within this family of materials is largely
unpredictable before the crystal structure is firmly established -- it is due
to non-homologous geometric features such as the inter-layer organic ligands
previously thought to be benign.
