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

The princess and the pea: on the outsized role of inter-layer ligands in copper-pyrazine antiferromagnets