Magneto-optical properties of the competing-anisotropy model systemFe1−xCoxCl2. I. Linear birefringence and refractive index

The concentration-versus-temperature phase diagram of the random antiferromagnetic mixture with competing spin anisotropies ${\mathrm{Fe}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Co}}_{\mathrm{x}}$ ${\mathrm{Cl}}_2$ is investigated via spin-correlation functions emerging from linear-birefringence and refractive-index measurements. At the upper sharp paramagnetic-to-antiferromagnetic transition at $T_{C1}$ the initial trigonal symmetry is preserved in the Ising regime (x$x_t$≃0.28), whereas it becomes orthorhombic in the XY range (x>$x_t$). In accordance with random-exchange critical behavior, negative exponents α of the specific heat are inferred for both regimes. Fluctuating symmetry-breaking off-diagonal correlations, 〈$S_{?}$ $S_{\perp }$〉, appear below $T_{C1}$, preceding the smeared antiferromagnetic-to-oblique antiferromagnetic (OAF) transition at $T_{C2}$. For 0.35≤x<1 these correlations lower the symmetry to monoclinic, where [120${]}_{\mathrm{h}}$ is the easy in-plane spin direction at all temperatures, T$T_{C1}$. In the range 0.26≤x±60° occurs at T$T_{C2}$, inducing a triclinic OAF phase. This is shown to originate from an 〈$S_{?}$ $S_{\perp }$〉-controlled balance of fourth- and sixth-order magnetocrystalline and magneto-elastic in-plane anisotropy energy terms. In accordance with an expected first-order nature of this transition, marked hysteresis is observed and twinning may be encountered. This might explain the microdomain structure deduced previously from neutron scattering data without invoking random-field effects.