ISSN 1027-4510, Journal of Surface Investigation. X-ray, Synchrotron and Neutron Techniques, 2008, Vol. 2, No. 4, pp. 560–563. © Pleiades Publishing, Ltd., 2008.
Original Russian Text © A.A. Antonenko, E.N. Ovchinnikova, V.E. Dmitrienko, S.P. Collins, 2008, published in Poverkhnost’. Rentgenovskie, Sinkhrotronnye i Neitronnye Issledovaniya,
No. 7, pp. 56–59.
560
INTRODUCTION
Recently, resonant scattering of x-ray radiation has
become a very popular method for studying physical
properties of condensed media [1–3]. The method is
selective, i.e., allows the study of scattering at only
“resonant” atoms with absorption edges close to the
energy of incident electromagnetic radiation. In some
cases, purely resonant (“forbidden”) reflections can be
observed near absorption edges, which are absent far
from absorption edges due to symmetry properties of
an object under study. Magnetic reflections were the
first type of “forbidden” reflections studied experimen-
tally [4, 5]. However, the appearance of purely resonant
reflections is also possible in non-magnetic crystals due
to the local non-cubic symmetry of the resonant atom
position, which causes atomic factor anisotropy [6, 7].
Currently, purely resonant reflections were experimen-
tally detected in a quite large number of magnetic and
non-magnetic structures. In almost all studied cases,
any contribution to the resonant part of the atomic fac-
tor, magnetic or non-magnetic, is dominant. In [8], res-
onant diffraction of synchrotron radiation was studied
in the GdB
4
crystal, where both magnetic and non-mag-
netic resonant reflections were observed. Magnetic and
non-magnetic contributions to the tensorial atomic fac-
tor were dominant at low temperatures and at room
temperature, respectively. Interference of both contri-
butions which were considered to be additive was also
observed. The problem of the additivity of the contribu-
tions to resonant scattering of x-ray radiation, which
were caused by several anisotropic factors, was dis-
cussed in [9–11]; it was shown that, apart from additive
contributions, the resonant atomic factor can contain an
additional contribution called the combined one [10].
This name arose by analogy with the case of combined
interaction in Mössbauer spectroscopy. In the case of
combined interaction during Mössbauer radiation dif-
fraction, i.e., the simultaneous presence of magnetic
and quadrupole hyperfine splittings, the appearance of
forbidden reflections is possible, which would be
absent in the presence of each separately [12–13]. Nev-
ertheless, the presence of the combined contribution to
resonant reflections in resonant diffraction of synchro-
tron radiation has not yet been detected. This can be
caused by various factors, among which are the preva-
lence of the non-magnetic contribution for resonant
scattering at the absorption K-edge and, on the contrary,
the magnetic contribution at the L-edge, as well as
rather broad resonances (~1–10 eV).
In this paper, we discuss the problem of the appear-
ance of combined effects in purely resonant reflections
when any of anisotropic factors is dominant. The effect
of the combined contribution to resonant scattering on
the azimuthal dependence of purely resonant reflec-
tions experimentally measured in [14] was considered
by the example of the HoFe
2
crystal.
TENSORIAL ATOMIC FACTOR
IN THE PRESENCE OF SEVERAL
ANISOTROPIC FACTORS
In the dipole–dipole approximation, the tensorial
atomic factor is phenomenologically described by the
second-rank symmetric tensor whose components res-
onantly depend on the incident radiation energy. This
tensor can be divided into the isotropic, symmetric, and
antisymmetric parts. The presence of the anisotropic
Resonant Scattering of X-Ray Radiation in Magnetic Crystals
with Non-Cubic Local Anisotropy
A. A. Antonenko
a
, E. N. Ovchinnikova
a
,
V. E. Dmitrienko
b
, and S. P. Collins
c
a
Moscow State University, Moscow, 119992 Russia
e-mail: ovtchin@mail.ru
b
Shubnikov Institute of Crystallography, Russian Academy of Sciences, Leninskii pr. 59, Moscow, 117333 Russia
c
Diamond Light Source, Chilton, Didcot, Oxfordshire OX11 0DE, United Kingdom
Received June 26, 2007
Abstract—Features of resonant diffraction of synchrotron radiation in magnetic crystals in which the local
symmetry of resonant atom positions is lower than cubic are considered. It was shown that the simultaneous
presence of two anisotropic factors can cause asymmetry of the azimuthal dependence of purely resonant reflec-
tions. The observed azimuthal dependence of the 002 reflection in the HoFe
2
crystal was numerically simulated.
DOI: 10.1134/S1027451008040113