Spin-Spin Interaction Constants from the Hyperfine Structure of Pairs of Coupled Ions

The hyperfine structure of pairs of paramagnetic ions with identical nuclear spins and a spin-spin interaction effectively of the form ${K}_{0}{\mathrm{S}}_{1}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{S}}_{2}+{K}_{z}{{S}_{1}}^{z}{{S}_{2}}^{z}$ is discussed. The structure of the spectra depends on the ratio $p=\frac{{K}_{0}}{A}$, and a general discussion of the key features of the spectra is given for $p$ in the range zero to infinity. The technique by which the spin-spin interactions may be extracted from the spectra is demonstrated by four examples which correspond to $p$ values of 2, 5.7, 11, and 48. In all cases ${K}_{z}$ is sufficiently large that a major part of the hyperfine structure of the pairs is clear of the spectrum of the isolated ions. For the nearest-neighbor axial pairs of ${\mathrm{Pr}}^{3+}$ in ${\mathrm{La}}_{2}$ ${({\mathrm{C}}_{2}{\mathrm{H}}_{5}\mathrm{S}{\mathrm{O}}_{4})}_{6}$\ifmmode\cdot\else\textperiodcentered\fi{}9${\mathrm{H}}_{2}$O, ${K}_{0}=+0.467$ ${\mathrm{cm}}^{\ensuremath{-}1}$ and ${K}_{z}=\ensuremath{-}0.474$ ${\mathrm{cm}}^{\ensuremath{-}1}$; for ${\mathrm{Pr}}^{3+}$ in La${\mathrm{Cl}}_{3}$, the nearest-neighbor axial pairs have $|{K}_{0}|=2.44$ ${\mathrm{cm}}^{\ensuremath{-}1}$ and $|{K}_{z}|=1.79$ ${\mathrm{cm}}^{\ensuremath{-}1}$, where the $z$ axis here and below is the interionic axis and the trigonal axis of the crystal. The other two examples are provided by ${\mathrm{Co}}^{2+}$ in the nearest-neighbor $X$ sites of ${\mathrm{La}}_{2}$${\mathrm{Mg}}_{3}$${(\mathrm{N}{\mathrm{O}}_{3})}_{12}$\ifmmode\cdot\else\textperiodcentered\fi{}24${\mathrm{H}}_{2}$O; one for the magnetic field along the interionic axis, and the other for the magnetic field perpendicular to this axis. One finds ${K}_{0}=+0.105$ ${\mathrm{cm}}^{\ensuremath{-}1}$, and ${K}_{z}=\ensuremath{-}0.170$ ${\mathrm{cm}}^{\ensuremath{-}1}$.

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