Long-range magnetic order in very diluteYEr 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 2{π}/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 {}.These findings contradict typical spin-glass features of this system: The magnetic measurements show irreversibilities, increasing strongly with dilution, and the nonlinear susceptibility is singular at the N\'eel temperature, with critical exponents γSG=1±{}0.1 and δSG=2±{}0.1. The contradiction between long-range order and spin-glass features can be resolved by considering that the dilution enables a coupling between the modulated order parameter and a uniform magnetic field. In this case, ``spin-glass'' and long-range-order critical exponents can be related: The latter are βAF=0.5±{}0.1 and γAF=1.9±{}0.2. These values are compatible with {α}=-1, i.e., no divergence of the specific heat, but rather a cusp. The {β} value is consistent with the temperature dependence of the staggered magnetization. Combined together, our results suggest that the dilute YEr system presents long-range antiferromagnetism along the c axis but remains spatially disordered within most of the planes perpendicular to the c axis.