Induced Anisotropy of Silicon-Doped YIG

The induced anisotropy of single‐crystal silicon‐doped YIG (Y₃Fe_5−δSi_δO₁₂; 0≤δ≤0.18) was studied by means of a torque magnetometer. It was found that the annealed component of the torque could be adequately described by a free energy of the form $$A^{\mathrm{an}}\mathrm{=-G\Sigma }{\displaystyle {lim}_{\mathrm{i>i}}}{\alpha }_i{\alpha }_j{\beta }_i{\beta }_j\mathrm{,\hspace{0.17em}\hspace{0.17em}i,j=x,y,z}$$ where α_i and β_i, respectively, specify the direction cosines of M during measurement and anneal. A model consistent with these observations was formulated. Specifically, it was assumed that the annealed anisotropy was caused by an ordering of the Fe²⁺ ions over the four types of magnetically inequivalent octahedral sites. Taking into account the interaction of crystal field, spin‐orbit, and exchange interaction, a calculation of the energy levels of the octahedrally coordinated Fe²⁺ ion provides an eigenvalue spectra compatible with the symmetry and magnitude of A^an.