EPR study of spin dynamics near the percolation threshold of ${\mathrm{Rb}}_2{\mathrm{Mn}}_c{\mathrm{Mg}}_{1-c}{\mathrm{F}}_4$

Electron-paramagnetic-resonance studies of the dilute two-dimensional antiferromagnet ${\mathrm{Rb}}_2{\mathrm{Mn}}_c{\mathrm{Mg}}_{1-c}{\mathrm{F}}_4$ are reported versus both concentration and temperature. Particular attention has been paid to the temperature-dependent resonance linewidth near the percolation threshold, $c\simeq c_p=0.59\mathrm{}$, where a variety of interesting effects are observed: At high temperatures the linewidth is dominated by the long-time, $q\to 0$ diffusive part of the dipolar interaction having ${(3\mathrm{}{cos}^2\theta -1)}^2$ anisotropy characteristic of two-dimensional systems. This contribution increases rapidly below the percolation concentration due to slowing of spin diffusion as the spin network breaks up into finite clusters. For $T<\mathrm{}30\mathrm{}$ K and $c\sim c_p$ the linewidth is dominated by antiferromagnetic correlation effects leading to rapid line broadening as $T$ decreases and a change of anisotropy. Both effects are only crudely described by the RPA theory. For $c<\mathrm{}{c}_p$ most of the resonance intensity remains centered at $g=2\mathrm{}$ down to the lowest temperatures reflecting the absence of long-range order. Near and above $c_p$ and for $T<\mathrm{}4.2\mathrm{}$ K some intensity is shifted to lower fields, however, as the percolation cluster orders. Most remarkable is the appearance of a nine-line superstructure on the $g=2\mathrm{}$ resonance at 1.6 K in samples near the percolation concentration. This illustrates the critical slowing of spin dynamics on a time scale of ${10}^{-9\mathrm{}}$ sec and is believed to be the resonance of spins surrounded by nonmagnetic nearest neighbors but coupled to next-nearest-neighbor spins, most of which are locked to clusters. Evidence of anisotropic spin fluctuations and the possibility of reduced next-nearest-neighbor exchange or very large zero-point spin deviation is found in this regime.