388 Acta Cryst. (1997). A53, 388-395 Combined Effects of Magnetic Structure and Local Crystal Fields in Anisotropic X-ray Anomalous Scattering E. N. OVCHINNIKOVA a* AND V. E. DMITRIENKO b "Moscow State University, Physical Department, 119899, Moscow, Russia, and bA. V. Shubnikov Institute of Crystallography, 117333, Moscow, Russia. E-mail: eno @runar.phys, msu. su (Received 7 October 1996; accepted 6 FebruaD' 1997) Abstract The X-ray extinction conditions are studied for the cases when both magnetic interaction and crystalline fields cause the anisotropy of X-ray scattering ampli- tudes near the absorption edge. It is demonstrated that the simultaneous existence of those two anisotropies, referred to as the combined anisotropy, can result in excitation of additional Bragg reflections otherwise for- bidden by extinction rules. To show this, the structure amplitudes of reflections are computed and two Laue (L) groups are compared: one, L m, which corresponds to the anomalous X-ray scattering in the presence of magnetic structure and another one, Lq, which takes into account the anisotropic atomic environment. Both groups can contain additional reflections and differ from the Laue group, L , associated with the usual potential X-ray scattering. TPhe cross of these groups is considered and it is shown that several extinctions, typical for the Lp group, still remain in L and L Nevertheless, the q m" new reflections may appear instead of those extinctions when the combined anisotropy is taken into account. In this case, the diffraction pattern is characterized by the L group. Then, the transformation of L into L. under the phase transition is studied. It is shqown thai the additional reflections, not typical for Lm, can appear in the diffraction pattern below the magnetic ordering temperature 7"... Two cases are discussed" (i) L above • q T M contains the same reflections as LC and (ii) L contains the extinctions corresponding to the additional reflections in L.. Several examples are considered for real magnetic crystals. 1. Introduction Recently, a rich variety of phenomena related to different types of crystal anisotropy was revealed and surveyed in resonant X-ray absorption (Brouder, 1990) and scatter- ing (Belyakov & Dmitrienko, 1989; Blume, 1994; Carra & Thole, 1994) near absorption edges of atoms. These phenomena occur when the energy of the incident radi- ation approaches those values that are required to excite an inner-shell electron to an empty state of a valence shell. The valence shells are strongly affected by the atomic environment and therefore the atomic scattering amplitude can depend on the local crystal fields and (or) the atomic magnetic moments. One of the phenomena is the excitation of forbidden reflections, which are absent in the potential (Thomson) X-ray scattering. The forbidden magnetic reflections and those that exist even in non-magnetic crystals owing to an anisotropic atomic environment have been studied both theoretically and experimentally (Gibbs, Moncton & D'Amico, 1985; Hannon, Trammel, Blume & Gibbs, 1988; Templeton & Templeton, 1980; Dmitrienko, 1983). The natural language for the description of pos- sible reflections is group theory. The homomorphic correspondence between 230 space groups and 122 diffraction (Laue) groups is a fundamental fact for X-ray potential scattering. Each Laue group contains a set of extinctions, listed in International Tables for X-ray Crystallography (1965). The anisotropic character of the anomalous diffraction violates the extinction rules computed for isotropic scattering. Hence, in the case of anomalous scattering, the diffraction group Lanom may differ from a group L describing only the potential scattering. The differencPe between the Laue groups may be classified as a difference in the symmetry of structures studied by the anomalous diffraction method compared with the space-group symmetry. This statement is clear for magnetic structures, for which symmetry is described by magnetic groups and the diffraction pattern can be characterized by the Laue group Lm. But the crystal fields and electrical multipole moments should be invariant under space-group transformations. Nevertheless, the extinction rules of the Lp group can be violated when a resonant interaction with an electromagnetic field occurs because the crystallographically equivalent atoms may become non-equivalent scatterers owing to the local crystal anisotropy. In this case, the resonant X-ray diffraction pattern is characterized by the Laue group L, . . . . q which differs from L and contains additional reflections p excited owing to the local crystalline environment of the scattering atom (Templeton & Templeton, 1980; Dmitrienko, 1983). The local crystal-field anisotropy violates the screw-axis and glide-plane extinction rules, whereas the magnetic moments can violate the transla- tion symmetry too. The extinction rules for these groups, Lm and Lq, can differ from each other, but some extinctions may coincide. The simultaneous existence of two types of © 1997 International Union of Crystallography Printed in Great Britain - all rights reserved Acta Cr3"stallographica Section A ISSN 0108-7673 © 1997