Pair Spectra and the Magnetic Properties ofCo2+in Double Nitrate Crystals

Measurements of the pair spectra of ${\mathrm{Co}}^{2+}$ ions in ${\mathrm{La}}_2$ ${\mathrm{Zn}}_3$ ${\left(\mathrm{N}{\mathrm{O}}_3\right)}_{12}$·24${\mathrm{H}}_2$O and ${\mathrm{La}}_2$ ${\mathrm{Mg}}_3$ ${\left(\mathrm{N}{\mathrm{O}}_3\right)}_{12}$·24${\mathrm{H}}_2$O are reported and interpreted. The two types of sites for divalent ions (two $X$ sites and one $Y$ site in the unit cell) lead to spectra corresponding to pairs of similar and dissimilar anisotropic ions. The theory for the interpretation of these spectra in terms of a phenomenological spin-spin interaction is given and used to show that there are only two large interactions: the nearest-neighbor $X-X$ and nearest-neighbor $X-Y$. All other interactions are small and dipolar. The nondipolar part of the interactions are shown to be of the form $K_{\mathrm{II}}{S_{\perp }}^z{S_2}^z+K_{\perp }({S_1}^x{S_2}^x+{S_1}^y{S_2}^y)$. This form is given by the projection of isotropic exchange between ionic spins onto the effective spin states. This model gives a value for $\frac{K_{\mathrm{II}}}{K_{\perp }}$ which agrees well with the experimental value for the $X-Y$ but not for the $X-X$. It is shown that the validity of isotropic exchange between ionic spins hinges upon the involvement of only $e_g$ orbitals in the exchange process, and that this is probable for the $X-Y$ pairs because of the hydrogen bonding between the complexes. Similar bonding does not exist between the $X$ complexes. In a general way this accounts for the fact that the nondipolar part of the $X-X$ interaction is smaller than that for the $X-Y$ despite the interionic separations of 4.99 and 7.14 Å, respectively; and it also renders plausible the failure of the isotropic ionic exchange for the $X-X$ interaction. The measured spin-spin interactions are used to calculate the magnetic properties of