Long-range magnetic order in very dilute YEr alloys

Neutron-diffraction and magnetization measurements (including nonlinear susceptibility) were performed on single crystals of very dilute YEr alloys (0.5--3 at. %). The modulated long-range order, characterized by satellites of the nuclear peaks, persists down to 0.5 at. % Er (TN=0.2 K). The wave vector of the long-range-order modulation is independent of both the concentration and the temperature. It is clearly incommensurate (0.27±0.01 in units of 2π/c). The critical exponent for the staggered magnetization is β=1/2 (mean-field value). The third harmonic was not detected. At low enough T/TN (saturation) the integrated intensities are consistent with a model in which the average magnetization of each hexagonal layer is sinusoidally modulated in the c direction, with an amplitude equal to the Er moment. The correlation length of the modulated order is resolution limited in all directions for the 3-at. % sample, but in the c direction only for 0.5 at. %: For that sample, the correlation length in the basal direction is reduced to 60 A