L. Paolasini

Femtoscale Magnetically Induced Lattice Distortions in Multiferroic TbMnO3

Ferroelectric order in a multiferroic compound is probably caused by small displacements of ions in its crystal lattice. Magneto-electric multiferroics exemplified by TbMnO3 possess both magnetic and ferroelectric long-range order. The magnetic order is mostly understood, whereas the nature of the ferroelectricity has remained more elusive. Competing models proposed to explain the ferroelectricity are associated respectively with charge transfer and ionic displacements. Exploiting the magneto-electric coupling, we used an electric field to produce a single magnetic domain state, and a magnetic field to induce ionic displacements. Under these conditions, interference between charge and magnetic x-ray scattering arose, encoding the amplitude and phase of the displacements. When combined with a theoretical analysis, our data allow us to resolve the ionic displacements at the femtoscale, and show that such displacements make a substantial contribution to the zero-field ferroelectric moment.

ID20: a beamline for magnetic and resonant X-ray scattering investigations under extreme conditions.

A new experimental station at ESRF beamline ID20 is presented which allows magnetic and resonant X-ray scattering experiments in the energy range 3-25 keV to be performed under extreme conditions. High magnetic field up to 10 T, high pressure up to 30 kbar combined with low temperatures down to 1.5 K are available and experiments can be performed at the M-edges of actinide elements, L-edges of lanthanides and K-edges of transition metals.

Circularly polarized X rays as a probe of noncollinear magnetic order in multiferroic TbMnO3.

Nonresonant x-ray magnetic scattering has been used to study the magnetic structure of multiferroic TbMnO3 in its ferroelectric phase. Circularly polarized x rays were combined with full polarization analysis of the scattered beam to reveal important new information on the magnetic structure of this canonical multiferroic. An applied electric field is shown to create essentially a single magnetic domain state in which the cycloidal order on the Mn sublattice rotates either clockwise or anticlockwise depending on the sign of the field. It is demonstrated how this technique provides sensitivity to the absolute sense of rotation of the Mn moments and to components of the ordering on the Tb sublattice and phase shifts that earlier neutron diffraction experiments could not resolve.

Disentangling multipole resonances through a full x-ray polarization analysis

Complete polarization analysis applied to resonant x-ray scattering at the Cr K edge in K2CrO4 shows that incident linearly polarized x rays can be converted into circularly polarized x rays by diffraction at the Cr pre-edge (E=5994eV) . The physical mechanism behind this phenomenon is a subtle interference effect between purely dipole (E1-E1) and purely quadrupole (E2-E2) transitions, leading to a phase shift between the respective scattering amplitudes. This effect may be exploited to disentangle two close-lying resonances that appear as a single peak in a conventional energy scan, in this way allowing one to single out and identify the different multipole order parameters involved.

Linear polarization scans for resonant X-ray diffraction with a double-phase-plate configuration

An in-vacuum double-phase-plate diffractometer for performing polarization scans combined with resonant X-ray diffraction experiments is presented. The use of two phase plates enables the correction of some of the aberration effects owing to the divergence of the beam and its energy spread. A higher rate of rotated polarization is thus obtained in comparison with a system with only a single retarder. Consequently, thinner phase plates can be used to obtain the required rotated polarization rate. These results are particularly interesting for applications at low energy (e.g. 4 keV) where the absorption owing to the phase plate(s) plays a key role in the feasibility of these experiments. Measurements by means of polarization scans at the uranium M(4) edge on UO(2) enable the contributions of the magnetic and quadrupole ordering in the material to be disentangled.

X-ray scattering study of the order parameters in multiferroic TbMnO3

We report on an extensive investigation of the multiferroic compound TbMnO3 using x-ray scattering techniques. Nonresonant x-ray magnetic scattering NRXMS was used to characterize the domain population of the single crystal used in our experiments. This revealed that the dominant domain is overwhelmingly A type. The temperature dependence of the intensity and wave vector associated with the incommensurate magnetic order was found to be in good agreement with neutron scattering data. X-ray resonant scattering experiments were performed in the vicinity of the Mn K and Tb L3 edges in the high-temperature collinear phase, the intermediate temperature cycloidal and ferroelectric phase, and the low-temperature phase. In the collinear phase, where according to neutron diffraction only the Mn sublattice is ordered, resonant E1-E1 satellites were found at the Mn K edge associated with A-type but also F-type peaks. Detailed measurements of the azimuthal dependence of the F-type satellites and their absence in the NRXMS experiments leads us to conclude that they are most likely nonmagnetic in origin. We suggest instead that they may be associated with an induced charge multipole. At the Tb L3 edge, resonant A- and F-type satellites were observed in the collinear phase again associated with E1-E1 events. We attribute these to a polarization of the Tb 5d states by the ordering of the Mn sublattice. On cooling into the cycloidal and ferroelectric phase, a new set of resonant satellites appear corresponding to C-type order. These appear at the Tb L3 edge only. In addition to a dominant E1-E1 component in the - channel, a weaker component is found in the preedge with - polarization and displaced by −7 eV with respect to the E1-E1 component. Comprehensive calculations of the x-ray scattering cross section were performed using the FDMNES code. These calculations show that the unrotated - component of the Tb L3 C-type peaks appearing in the ferroelectric phase contains a contribution from a multipole that is odd with respect to both space and time, known in various contexts as the anapole. Our experiments thus provide tentative evidence for the existence of a type of anapolar order parameter in the rare-earth manganite class of mulitferroic compounds.

Strong coupling of Sm and Fe magnetism in SmFeAsO as revealed by magnetic x-ray scattering

The magnetic structures adopted by the Fe and Sm sublattices in SmFeAsO have been investigated using element-specific x-ray resonant and nonresonant magnetic scattering techniques. Between 110 and 5 K, the Sm and Fe moments are aligned along the c and a directions, respectively, according to the same magnetic representation Gamma(5) and the same propagation vector (1 0 1/2). Below 5 K, the magnetic order of both sublattices changes to a different magnetic structure, and the Sm moments reorder in a magnetic unit cell equal to the chemical unit cell. Modeling of the temperature dependence for the Sm sublattice, as well as a change in the magnetic structure below 5 K, provides clear evidence of a surprisingly strong coupling between the two sublattices, and indicates the need to include anisotropic exchange interactions in models of SmFeAsO and related compounds.

Experimental evidence of anapolar moments in the antiferromagnetic insulating phase of V 2 O 3 obtained from x-ray resonant Bragg diffraction

We have investigated the antiferromagnetic insulating phase of the Mott-Hubbard insulator vanadium sesquioxide

Valence instability of YbCu2Si2through its magnetic quantum critical point

({\text{V}}_{2}{\text{O}}_{3})

Circularly Polarised X-ray Scattering Investigation of Spin-Lattice Coupling in TbMnO3 in Crossed Electric and Magnetic Fields

by resonant x-ray Bragg diffraction at the vanadium