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

Abstract

The hyperfine structure of pairs of paramagnetic ions with identical nuclear spins and a spin-spin interaction effectively of the form $K_0{\mathrm{S}}_1·{\mathrm{S}}_2+K_z{S_1}^z{S_2}^z$ 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 ${\mathrm{La}}_2$ ${\left({\mathrm{C}}_2{\mathrm{H}}_5\mathrm{S}{\mathrm{O}}_4\right)}_6$·9${\mathrm{H}}_2$O, $K_0=+0.467\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$ and $K_z=-0.474\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$; for ${\mathrm{Pr}}^{3+}$ in La${\mathrm{Cl}}_3$, the nearest-neighbor axial pairs have $\left|K_0\right|=2.44\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$ and $\left|K_z\right|=1.79\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, 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 ${\mathrm{La}}_2$ ${\mathrm{Mg}}_3$ ${\left(\mathrm{N}{\mathrm{O}}_3\right)}_{12}$·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 $K_0=+0.105\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, and $K_z=-0.170\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$.