Spin correlations near the percolation threshold in three-dimensional antiferromagnets

Abstract

In this paper we report on a study, using neutron scattering techniques, of the spin fluctuations in the random magnetic-nonmagnetic antiferromagnets, ${\mathrm{Mn}}_c{\mathrm{Zn}}_{1-c}{\mathrm{F}}_2$ and $\mathrm{K}{\mathrm{Mn}}_c{\mathrm{Zn}}_{1-c}{\mathrm{F}}_3$, with $c$ close to the percolation concentration $c_p$. The results for $c<\mathrm{}{c}_p$ are consistent with the multicritical point picture for the percolation point with the temperature scale determined by the inverse correlation length of the appropriate linear chain. This approach gives a very satisfactory account of the spin-space crossover from Heisenberg-like to Ising-like behavior observed in tetragonal ${\mathrm{Mn}}_c{\mathrm{Zn}}_{1-c}{\mathrm{F}}_2$. The exponent ${\nu }_T$ describing the temperature dependence of the inverse correlation length is found to be 0.85 ± 0.10 for this system and, with rather less certainty, we infer ${\nu }_T=0.95\mathrm{}\pm 0.05$ for the cubic $\mathrm{K}{\mathrm{Mn}}_c{\mathrm{Zn}}_{1-c}{\mathrm{F}}_3$. The results for $c>\mathrm{}{c}_p$ show two unexpected features. Firstly the diffuse scattering does not show any critical scattering associated with the onset of long-range order. We suggest this may be because only a small fraction of spins are in the backbone of the infinite cluster. Secondly in $\mathrm{K}{\mathrm{Mn}}_c{\mathrm{Zn}}_{1-c}{\mathrm{F}}_3$ the long-range order decreases on cooling below 6 K. We suggest that this may result from the random magnetic dipole-dipole forces producing a type of spin-glass phase.