The theoretical behavior of the ${\mathrm{Yb}}^{3+}$ ion on octahedral $a$ sites in ytterbium-doped YIG is examined with regard to some of the so-called anomalous properties of this substance. First, a simple spin Hamiltonian is proposed and discussed in the light of the crystal-field properties of the anomalous site. Next, the implications of the model for static torque are derived and compared with experiment. Excellent agreement may be achieved provided that the maximum separation of the doublet levels is taken to be 55 ${\mathrm{cm}}^{-1\mathrm{}}$. The minimum level spacing is not precisely determined, but is surely less than 2 ${\mathrm{cm}}^{-1\mathrm{}}$, and is thus the smallest to be observed in rare-earth-doped YIG. Last, the prediction of the model for the resonance anomaly is derived in a molecular-field model. A version of the theory involving only two adjustable parameters may be used to explain many details of the resonance measurements, including the variation of properties with angle and, to a lesser extent, with frequency. Since measurements are available at frequencies above the assumed level splitting, the degree of agreement is very sensitive to the form chosen for the susceptibility of the anomalous ytterbium ions to the exchange field. None of the forms examined produced quantitative agreement for the entire range of frequencies, although a form of inhomogeneous broadening is indicated. A more complete understanding of the problem could probably be achieved if resonance measurements at higher frequencies, and torque measurements at lower temperatures, became available.

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