Field Dependence of Anisotropy in Ytterbium-Doped Yttrium Iron Garnet

Torque curves were measured on two single crystals of Yb‐doped yttrium iron garnet (containing 5% or 10% Yb) at temperatures from 77° to 4.2°K in applied fields ranging from 2500 to 15 000 Oe. At 20°K the maximum peak height of the (110) torque curve for these crystals was reduced by 12% as the applied field increased from 5000 to 15 000 Oe; the change in peak height was proportional to H and is approximately given by the relation ΔL=−0.32 ΔH, where ΔL is measured in ergs/cm³ and H is in oersteds. This field dependence was more pronounced at 14°K but had disappeared at 4.2° and 77°K. We consider the anisotropy energy of the system using the one ion model, and represent the energy of the Yb ground‐state doublet (assumed to be well separated from other states) by a spin Hamiltonian of the form $$\mathcal{H}{\mathrm{=H}}_e{\mathrm{·G·S+H}}_a\mathrm{·g·S,}$$ where H_e·G is the exchange splitting, and H_a is the applied field and g is the usual paramagnetic tensor for this doublet level with S=½, as given by K. A. Wickersheim and R. L. White [Phys. Rev. Letters 8, 483 (1962)]. The temperature variation of the free energy of the system derived from this Hamiltonian was used to compute (110) torque curves as a function of temperature, applied field and concentration of ytterbium. These theoretical curves were then compared with the experimental results, and gave good agreement for the predicted value of ΔL/ΔH at the maximum torque peaks, though as had been previously noted [J. W. Henderson and R. L. White, Phys. Rev. 123, 1627 (1961)] the absolute values of the torque are lower than those found experimentally.