RESUMEN

Resonant diffraction of x-rays by crystals with anisotropic optical properties is investigated theoretically, to assess how the intensity of a Bragg spot is influenced by effects related to dispersion (birefringence) and absorption (dichroism). Starting from an exact but opaque expression, simple analytic results are found to expose how intensity depends on dispersion and absorption in the primary and secondary beams and, also, the azimuthal angle (rotation of the crystal about the Bragg wavevector). If not the full story for a given application, our results are more than adequate to explore consequences of dispersion and absorption in the intensity of a Bragg spot. Results are evaluated for antiferromagnetic copper oxide, and low quartz. For CuO, one of our results reproduces all salient features of a previously published simulation of the azimuthal-angle dependence of a magnetic Bragg peak. It is transparent in our analytic result that dispersion and absorption effects alone cannot reproduce published experimental data. Available data for the azimuthal-angle dependence of space-group forbidden reflections (0,0, l), with l ≠ 3n, of low quartz depart from symmetry imposed by the triad axis of rotation symmetry. The observed asymmetry can be induced by dispersion and absorption even though absorption coefficients are constant, independent of the azimuthal angle, in this class of reflections.

Asunto(s)

RESUMEN

We investigate how the order parameter of a continuous phase transition can be protected from view by symmetry in a magnetic crystal. The symmetry in question forbids atomic displacements and formation of magnetic dipoles, rendering the order parameter invisible in standard x-ray and magnetic neutron Bragg diffraction. Analysis of the allowed magnetic space-groups reveals exact properties of the hidden order parameter. We demonstrate that Bragg spots forbidden by the chemical structure can unveil magnetic hidden order. The method is applied to URu2Si2, which has been thoroughly investigated in the past few decades using all manner of experimental techniques. Starting from the established chemical structure of URu2Si2, we have performed a critical analysis of available data for magnetic neutron Bragg diffraction.

RESUMEN

Analysis of published data gathered on a sample of Na(2)IrO(3), held deep inside the antiferromagnetic phase at 1.58 K, shows that iridium magnetic dipole moments, measured in resonant x-ray Bragg diffraction, lie in the a-c plane of the monoclinic crystal and enclose an angle ≈118° with the c-axis. These findings, together with bulk measurements, are united in a plausible magnetic ground state for an iridium ion constructed from a Kramers doublet. A magnetic space group, derived from the chemical space group C2/m (unique axis b), possesses an anti-translation, to accommodate antiferromagnetic order, and an odd, two-fold axis of rotation symmetry on the b-axis, C'(2b), placing Ir magnetic dipoles perpendicular to the b-axis. Anapoles (toroidal dipoles) are predicted to be likewise confined to the a-c plane, and magnetic charges forbidden.