Diffuse x-ray determination of local atomic order in a spin-glass alloy system

In order to bring additional information pertinent to the so-called scaling laws for the magnetic properties of a spin-glass system, we have investigated the x-ray diffuse scattering of single crystals of $\mathrm{Ag}\mathrm{Mn}$ alloys of 1, 3, 6, 8, 10, 15, 20, and 24 at.% Mn concentration quenched from 900°C. Above 8% short-range order in the alloys manifests itself by the appearance of diffuse spots centered at 1½0 and equivalent points in the fcc reciprocal space. The relative intensity of these diffuse spots increases with increasing concentrations up to 24 at.% A detailed analysis has been undertaken of the possible atomic ordered structures compatible with our findings which are qualitatively similar to those investigated by Sato et al. on the $\mathrm{Cu}\mathrm{Mn}$ system with neutrons. We show, in particular, that the structure $D{O}_{22}$ can neither account for our $\mathrm{Ag}\mathrm{Mn}$ system nor for the $\mathrm{Cu}\mathrm{Mn}$ system for which it was advocated by Sato et al. We propose two possible models based on the structure $\frac{I{4}_1}{\mathrm{amd}}$: one is essentially inhomogeneous in concentration and would imply the presence of microdomains of stoichiometry AgMn whose size and orientation are deduced from the observed shape and width of the diffuse spots; the other, more homogeneous one would imply periodic concentration modulation perpendicular to the (210) planes, as has already been proposed by De Fontaine and others for similar situations. A choice between these two models can be made in principle from the small-angle x-ray scattering data which have been obtained on the same samples. Surprisingly, our results show that for $2\times {10}^{-2\mathrm{}}<2\mathrm{}\frac{sin\theta }{\lambda }<9\mathrm{}\times {10}^{-2\mathrm{}}$ ${\mathrm{\AA }}^{-1\mathrm{}}$ the scattered x-ray intensity is approximately independent of Mn concentration and corresponds to the Laue uniform background expected from a 6% disordered alloy. This finding tends to rule out the concentration wave hypothesis; however, a number of difficulties remain. The magnetic implication of the two models is briefly discussed in view of the known spin-glass parameters.