Calculated x-ray dichroic signals and resonant Bragg diffraction structure factors forDyB2C2

Abstract

Low-temperature properties of dysprosium borocarbide display evidence of two phase transitions; it has been proposed that the first involves ordering of Dy quadrupole moments and the second, at a lower temperature, involves ordering of Dy magnetic moments. The latter has been established by magnetic neutron diffraction. Insight into the first phase transition, at ${T}_{Q},$ has been sought by resonant x-ray Bragg diffraction, which reveals charge-forbidden (Templeton-Templeton) intensities $(00l+\frac{1}{2})$ that increase with decreasing temperature. We show that this scattering is absent if the space group is $P4/mbm,$ which has been proposed for the high-temperature crystal structure. Tanaka et al. report evidence that at ${T}_{Q}$ the lattice distorts and the new space group is ${P4}_{2}/mnm.$ The lower point-group symmetry of Dy ions in this space group is shown by us to allow diffraction at $(00l+\frac{1}{2}).$ In the magnetically ordered phase two neighboring Dy moments along the c axis are mutually perpendicular and two neighboring moments in the plane normal to the c axis are almost oppositely aligned. This magnetic configuration and point-group symmetry $2/m$ for Dy sites lead us to predict magnetic and charge scattering at reflections $(00l+\frac{1}{2})$ in the magnetically ordered phase. At reflections $(h0l)$ and h odd calculated structure factors are purely magnetic. Our finding is consistent with data collected by Hirota et al. at the reflection (102). We report expressions for circular and linear dichroic signals and structure factors for Bragg scattering for the interpretation of future experiments. The structure factors are appropriate for azimuthal-angle scans in which the crystal is rotated about the $(00l+\frac{1}{2})$ or the $(h0l)$ Bragg scattering vectors.