Pair Spectra and the Magnetic Properties of Co 2 + in Double Nitrate Crystals

Measurements of the pair spectra of ${\mathrm{Co}}^{2+}$ ions in ${\mathrm{La}}_{2}$${\mathrm{Zn}}_{3}$${(\mathrm{N}{\mathrm{O}}_{3})}_{12}$\ifmmode\cdot\else\textperiodcentered\fi{}24${\mathrm{H}}_{2}$O and ${\mathrm{La}}_{2}$${\mathrm{Mg}}_{3}$${(\mathrm{N}{\mathrm{O}}_{3})}_{12}$\ifmmode\cdot\else\textperiodcentered\fi{}24${\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 $X\ensuremath{-}X$ and nearest-neighbor $X\ensuremath{-}Y$. All other interactions are small and dipolar. The nondipolar part of the interactions are shown to be of the form ${K}_{\mathrm{II}}{{S}_{\ensuremath{\perp}}}^{z}{{S}_{2}}^{z}+{K}_{\ensuremath{\perp}}({{S}_{1}}^{x}{{S}_{2}}^{x}+{{S}_{1}}^{y}{{S}_{2}}^{y})$. This form is given by the projection of isotropic exchange between ionic spins onto the effective spin states. This model gives a value for $\frac{{K}_{\mathrm{II}}}{{K}_{\ensuremath{\perp}}}$ which agrees well with the experimental value for the $X\ensuremath{-}Y$ but not for the $X\ensuremath{-}X$. 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 $X\ensuremath{-}Y$ 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 $X\ensuremath{-}X$ interaction is smaller than that for the $X\ensuremath{-}Y$ despite the interionic separations of 4.99 and 7.14 \AA{}, respectively; and it also renders plausible the failure of the isotropic ionic exchange for the $X\ensuremath{-}X$ interaction. The measured spin-spin interactions are used to calculate the magnetic properties of ${\mathrm{La}}_{2}$${\mathrm{Co}}_{3}$${(\mathrm{N}{\mathrm{O}}_{3})}_{12}$\ifmmode\cdot\else\textperiodcentered\fi{}24${\mathrm{H}}_{2}$O, which are compared with experiment. The susceptibility perpendicular and parallel to the symmetry axis agrees well with the results of Leask and Wolf over the entire temperature range. The calculated magnetic specific-heat tail agrees very well with experimental values reported in the literature. The spin-spin interactions suggest that the ordered state consists of layers of $Y$ ions with their spins along the trigonal axis, and with the layer of $X$ ions on either side ordered in the opposite sense. It is shown that the energy of the antiferromagnetic structure given by alternating the sense of polarization for the $X\ensuremath{-}Y\ensuremath{-}X$ sandwiches is only marginally lower than that for the ferrimagnetic array in which all sandwiches are polarized in the same sense. The calculated ordering energy is 6% less than that obtained by Mess et al. from calorimetric measurements. The implications of these results for other iron-group ions in the double nitrates and for hydrated complexes in general is briefly examined.