Critical behavior of pure and site-random two-dimensional antiferromagnets

Quasielastic neutron scattering studies of the static critical behavior in the two-dimensional antiferromagnets K₂NiF₄, K₂MnF₄, and Rb₂{Mn}0.5Ni0.5{F}₄$ are reported. For $T<0.95{T}N$ the diffuse scattering arises principally from the noncritical transverse susceptibility ${{χ}}^{{⊥}}({{→}}{Q})$. In all three materials ${{χ}}^{{⊥}}({{→}}{Q})$ is found to be only weakly temperature dependent for $T<{T}N$ with a half width, ${{κ}}^{{⊥}}$, consistent with spin-wave theory. For $|1{-}{T}{{T}N}|<0.05$. the overall scattering is dominated by the critical Ising component ${{χ}}^{{∥}}({{→}}{Q})$. The total scattering is proportional to ${{χ}}^{{∥}}({{→}}{Q})+{{χ}}^{{⊥}}({{→}}{Q})$ so that, with an appropriate correction for ${{χ}}^{{⊥}}({{→}}{Q})$, the detailed critical behavior for ${{χ}}^{{∥}}({{→}}{Q})$ may be determined. For the reduced temperature range $0.008<{T}{{T}N}{-}1<0.15$ one finds in all three materials $v=0.9±{}0.1$, ${γ}=1.6±{}0.15$, and from the scaling relation ${γ}={ν}(2{-}{η})$, ${η}=0.2±{}0.05$. For $T<{T}N$ one finds ${β}=0.15±{}0.015$ in the three systems: Finally, in ${K}₂$Ni${F}₄$ for $T<{T}N$, ${{χ}}^{{∥}}(0)$ and ${{κ}}^{{∥}}$ are consistent with two-dimensional Ising behavior with exponents ${{γ}}^{{'}}=1.75$, ${{ν}}^{{'}}=1$; further ${{χ}}^{{∥}}(+|{ε}|{}(50±{}10){{χ}}^{{∥}}({-}|{ε}|)$ compared with the Ising asymmetry factor of 37. These results thence demonstrate that the site-random and pure systems have identical critical behavior in agreement with current theory. Further, the critical behavior is close to that of the two-dimensional Ising model, although there are small differences assumedly due to the fact that the experiments do not probe the true asymptotic region. Finally a number of inconsistencies in earlier experiments are resolved.