Magnetic Properties of Diamagnetic-Substituted Ytterbium Iron Garnet Explained by the Statistical Model of the Molecular Field. I. The Spontaneous Magnetization of Si-Ca-Substituted Ytterbium Iron Garnet

The magnetic moments of the single-crystal garnets ${\mathrm{Yb}}_{2.9-x}{\mathrm{Bi}}_{0.1}{\mathrm{Ca}}_x{\mathrm{Fe}}_{5-x}{\mathrm{Si}}_x{\mathrm{O}}_{12}$, with $0<x\le 1.4$, have been determined between 4.2 and 295°K, in magnetic fields up to 15 kOe. Using the molecular-field model and assuming a random distribution of the substituted ions with a random distribution of canting angles, the temperature dependence of the spontaneous magnetization of the Si-Ca-substituted ytterbium iron garnet (YbIG) was explained. A theoretical fit to the experimental results was obtained using the exchange parameters of pure YbIG, assuming they are the same for the substituted crystals.