X-ray-scattering study of higher harmonic satellites near the antiferromagnetic phase transitions in rare-earth metals

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Abstract
We present resonant x-ray magnetic scattering studies of the temperature dependence of the magnetic order parameters of Dy, Ho, Er, and Tm single crystals near their antiferromagnetic phase transitions. The experimentally determined values of the critical exponent β of Er and Tm, which have c-axis modulated structures, are nearly equal and consistent with the mean-field value (β=0.47±0.05 and β=0.49±0.06, respectively). The measured values of Dy and Ho, which have spiral magnetic structures, are lower (β=0.36±0.04 and β=0.41±0.04, respectively). In addition to the primary magnetic order parameters, we have measured the temperature dependence of the intensities of up to four higher harmonics. The exponents of the higher harmonic satellites of Er and Tm exhibit mean-field-like scaling, while those of Ho do not. We discuss these results within the context of simple corrections to mean-field scaling, based on the three-dimensional XY model. We also report measurements of the temperature dependence of the c-axis lattice constants and magnetic wave vectors of all four metals. It is found that the magnetic correlation lengths are reduced near transitions to ferrimagnetic and ferromagnetic phases.