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

Quasielastic neutron scattering studies of the static critical behavior in the two-dimensional antiferromagnets ${\mathrm{K}}_2$Ni${\mathrm{F}}_4$, ${\mathrm{K}}_2$Mn${\mathrm{F}}_4$, and ${\mathrm{Rb}}_2$ ${\mathrm{Mn}}_{0.5}$ ${\mathrm{Ni}}_{0.5}$ ${\mathrm{F}}_4$ are reported. For $T<\mathrm{}0.95\mathrm{}{T}_N$ the diffuse scattering arises principally from the noncritical transverse susceptibility ${\chi }^{\perp }\left(\overrightarrow{\mathrm{Q}}\right)$. In all three materials ${\chi }^{\perp }\left(\overrightarrow{\mathrm{Q}}\right)$ is found to be only weakly temperature dependent for $T<\mathrm{}{T}_N$ with a half width, ${\kappa }^{\perp }$, consistent with spin-wave theory. For $|1-\frac{T}{T_N}|<\mathrm{}0.05\mathrm{}$. the overall scattering is dominated by the critical Ising component ${\chi }^{\parallel }\left(\overrightarrow{\mathrm{Q}}\right)$. The total scattering is proportional to ${\chi }^{\parallel }\left(\overrightarrow{\mathrm{Q}}\right)+{\chi }^{\perp }\left(\overrightarrow{\mathrm{Q}}\right)$ so that, with an appropriate correction for ${\chi }^{\perp }\left(\overrightarrow{\mathrm{Q}}\right)$, the detailed critical behavior for ${\chi }^{\parallel }\left(\overrightarrow{\mathrm{Q}}\right)$ may be determined. For the reduced temperature range $0.008<\mathrm{}\frac{T}{T_N}-1<0.15\mathrm{}$ one finds in all three materials $v=0.9\mathrm{}\pm 0.1$, $\gamma =1.6\mathrm{}\pm 0.15$, and from the scaling relation $\gamma =\nu (2-\eta )$, $\eta =0.2\mathrm{}\pm 0.05$. For $T<\mathrm{}{T}_N$ one finds $\beta =0.15\mathrm{}\pm 0.015$ in the three systems: Finally, in ${\mathrm{K}}_2$Ni${\mathrm{F}}_4$ for $T<\mathrm{}{T}_N$, ${\chi }^{\parallel }\mathrm{}\left(0\right)\mathrm{}$ and ${\kappa }^{\parallel }$ are consistent with two-dimensional Ising behavior with exponents ${\gamma }^{\prime }=1.75\mathrm{}$, ${\nu }^{\prime }=1\mathrm{}$; further ${\chi }^{\parallel }\mathrm{}(+|\mathrm{}\epsilon \left|\simeq \right(50\mathrm{}\pm 10\left){\chi }^{\parallel }\mathrm{}\right(-\left|\mathrm{}\epsilon \mathrm{}\right|)\mathrm{}$ 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.