Phenomenological analysis of the linear magnetic birefringence in dysprosium iron garnet

Experimental data on linear magnetic birefringence (LMB), previously reported at 1.15 μm wavelength in the 4.2-300 K temperature range and with an applied field up to 20 kOe, in dysprosium iron garnet (DyIG) are analyzed in terms of electric dipole transition within the three magnetic sublattices. Assuming that the garnet symmetry is cubic and that the contribution of the Fe³⁺ ions to LMB is the same as yttrium iron garnet (YIG), the 2nd order magneto-optical (MO) coefficient (Γ₂) of the Dy³⁺ ions is deduced. In the spontaneous state, Γ₂ is linear temperature dependent as previously found for the 1st order (MO) coefficient. It is shown that Γ₂ must be field dependent to explain the evolution of the LMB.