Spin fluctuations in random magnetic-nonmagnetic two-dimensional antiferromagnets. III. An Ising system

This paper reports a study using neutron scattering techniques of the spin fluctuations in the two-dimensional diluted Ising system, ${\mathrm{Rb}}_2{\mathrm{Co}}_c{\mathrm{Mg}}_{1-c}{\mathrm{F}}_4$. The explicit concentrations studied, $c=0.55,0.575,0.585,\mathrm{and} 0.595$ are all close to the percolation concentration for nearest-neighbor interactions $c_p=0.594\mathrm{}$, so that these experiments span the percolation threshold. The experiments were performed at the Brookhaven high-flux beam reactor. A detailed study was made of the dynamics for $c=0.575\mathrm{}$. The results showed four dispersionless bands corresponding to spin deviations on Co ions surrounded by one, two, three, or four Co ions. Calculations of the spectra using the equation-of-motion method for computer simulations gave a good account of the results. The few minor discrepancies probably arise from the effects of those crystal-field levels of the Co ion which have energies above the ground-state doublet. The $c=0.595\mathrm{}$ crystal has a transition at 30 K to a state of two-dimensional order with negligible order in the third direction. The inverse correlation length in this system is zero to within the errors at 30 K. In the more dilute systems the inverse correlation length is found to be well described as an additive sum of a geometrical and a thermal part as observed previously in ${\mathrm{Rb}}_2{\mathrm{Mn}}_c{\mathrm{Mg}}_{1-c}{\mathrm{F}}_4$. The thermal part is given by ${\left[{\kappa }_1\mathrm{}\right(T\left)\right]}^{1.32\pm 0.05}$ where ${\kappa }_1\mathrm{}\left(T\right)\mathrm{}$ is the inverse correlation length of a one-dimensional chain of Co ions. This exponent is consistent with the percolation exponent ${\nu }_p=1.35\mathrm{}$ and the theoretically calculated crossover exponent, $\phi =1\mathrm{}$. The intensity of the scattering is more difficult to analyze in the absence of a knowledge of the form of the scaling function, but the behavior is consistent with the multicritical picture with $\phi =1\mathrm{}$.