Experimental study of the critical scattering from a two-dimensional random Ising antiferromagnet

The magnetic critical fluctuations in the d=2 random-exchange antiferromagnet Rb₂{Co}0.7Mg0.3{F}₄$ have been studied by neutron diffraction at temperatures both above and below the N\'eel temperature ${T}N$=40.8 K. At temperatures above ${T}N, the line shape of the critical scattering is well described by the Lorentzian form, and the critical exponents ν and γ for the inverse correlation length{{κ}}⁺$=${{κ}}₀⁺t{{}}^{{ν}}$ and the staggered susceptibility ${{χ}}⁺$=${C}₀⁺t{{}}^{{{-}}{γ}}are in good agreement with the values for the pure d=2 Ising model.The critical exponent β, which, along with the critical amplitude{M}₀$, describes the temperature dependence of the d=2 long-range antiferromagnetic order just below ${T}N$ through M=${M}₀t{{}}^{{β}}is also in good agreement with the value of β for the pure d=2 Ising model. Furthermore, the combination of critical amplitudes{R}ₛ$=${C}₀⁺$(${{κ}}₀⁺)²/M0², which, from the hypothesis of two-scale-factor universality, is a universal quantity also agrees well with the values of Rₛ for the pure d=2 Ising model and the value of Rₛ found experimentally for the pure d=2 Ising antiferromagnet K₂{CoF}₄$. The line shape of the critical scattering below ${T}N$ has been analyzed both by using a Lorentzian form and by using the form proposed by Tarko and Fisher for the pure d=2 Ising model below ${T}N$.The analysis using the Lorentzian form leads to a physically unreasonable description of the critical scattering below ${T}N$ and hence to the conclusion that the Lorentzian form is an inappropriate description of the critical scattering below ${T}N$ in a d=2 random Ising system. The results of the analysis using the Tarko-Fisher form provide a better description of the critical scattering below ${T}N$ and the critical exponents for the inverse correlation length ${{κ}}^{{{-}}}$=${{κ}}₀^{{{-}}}t{{}}^{{ν}}$ and the staggered susceptibility ${{χ}}^{{{-}}}$=${C}₀^{{{-}}}t{{}}^{{{-}}{γ}}$ agree well with the values for the pure d=2 Ising model. However, the values of the universal critical amplitude ratios ${{κ}}₀^{{{-}}}$/${{κ}}₀⁺$ and ${C}₀⁺$/${C}₀^{{{-}}}$, which result from this latter analysis, differ significantly from the values for the universality class of the pure d=2 Ising model. This difference in the amplitude ratios may arise because the d=2 random Ising model is in a different universality class than the pure d=2 Ising model or because the Tarko-Fisher form for the line shape may not be appropriate for the d=2 random Ising model below TN.An investigation of this latter possibility using a modified version of the Tarko-Fisher form which preserved the amplitude ratio of the inverse correlation lengths at the pure d=2 Ising model value suggests that this is a strong possibility.