Exchange Fields and Optical Zeeman Effect in ErFeO3

The optical spectra of ErFe${\mathrm{O}}_3$ with and without an external magnetic field along each of the three principal crystal axes are reported. The exchange splitting of ${\mathrm{Er}}^{3+}$ levels in zero applied field and the additional splittings due to the external field, at 77°K, are analyzed in terms of a two-sublattice model for the ${\mathrm{Er}}^{3+}$ ions. Values are derived for the $g$-tensor components and site-axis directions for the two lowest levels of ${\mathrm{Er}}^{3+}$ at $E=0\mathrm{}$ and $E=45.7\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$. Interactions with the ${\mathrm{Fe}}^{3+}$ spins are included by means of an effective field $H_{\mathrm{eff}}=12\mathrm{}$ kOe at the ${\mathrm{Er}}^{3+}$ sites. The parameters derived from the optical spectra are used to calculate the sublattice magnetizations for ${\mathrm{Er}}^{3+}$. Assuming a contribution from the ${\mathrm{Fe}}^{3+}$ spins similar to that in YFe${\mathrm{O}}_3$, a compensation point is predicted near the observed temperature $T_0\approx 45°$K. The magnetic dipolar contribution to $H_{\mathrm{eff}}$ is shown to be small, and the exchange contribution lies nearly along the $b$ axis. Above the spin-reorientation temperature $T>\mathrm{}{T}_r$, the ${\mathrm{Fe}}^{3+}$-${\mathrm{Er}}^{3+}$ exchange splitting becomes smaller than the optical linewidth. The optical data give $\frac{H_{\mathrm{eff}}(T<\mathrm{}{T}_r)}{H_{\mathrm{eff}}(T>\mathrm{}{T}_r)}>4\mathrm{}$, and this result is shown to be consistent with the value for $H_{\mathrm{eff}}(T>\mathrm{}{T}_r)$ obtained by other methods. It is suggested that either a model with more than two sublattices for the ${\mathrm{Fe}}^{3+}$ spins must apply for ErFe${\mathrm{O}}_3$, or there must be significant antisymmetric exchange coupling between the ${\mathrm{Er}}^{3+}$ and