Observation of Antisymmetric Exchange Interaction in Yttrium Orthoferrite

Sensitive static torque measurements were carried out on single crystals of YFeO₃ in order to determine if weak ferromagnetism in this material is caused by single ion magnetocrystalline anisotropy or by anisotropic exchange interaction. The following symmetry considerations show a priori which cubic and higher terms in the torque can be nonzero. The magnetic energy F is expanded in a series in the applied field H $${\mathrm{F=\Sigma \hspace{0.17em}\sigma }}_i{\text{(0)H}}_i+\frac{1}{2}{\mathrm{\hspace{0.17em}\Sigma \hspace{0.17em}\chi }}_{\mathrm{ij}}{H}_i{H}_j{\mathrm{+\Sigma \hspace{0.17em}C}}_{\mathrm{ijk}}{H}_i{H}_j{H}_k\mathrm{+\dots }$$ . Using the fact that F must be invariant under all the symmetry operations of the magnetic point group appropriate to these crystals, one finds that the only cubic coefficients that may be nonzero are C_xxz, C_yyz, C_zzz. The expression for the torque T is found using the relation σ_i = ∂F/∂H_i, where σ_i are the components of the total magnetization, and T=H×σ. The ferromagnetic component σ(0), the susceptibility χ, and cubic coefficients C_ijk were calculated assuming a two sublattice system for the anisotropic exchange model and also for the single ion magnetocrystalline anisotropy model. The comparison of the measured coefficients to those calculated for the two models indicates that the anisotropic exchange mechanism is predominant in causing weak ferromagnetism in YFeO₃.