No Arabic abstract
Chiral properties of the two phases - collinear motif (below Morin transition temperature, TM=250 K) and canted motif (above TM) - of magnetically ordered hematite ({alpha}-Fe2O3) have been identified in single crystal resonant x-ray Bragg diffraction, using circular polarized incident x-rays tuned near the iron K-edge. Magneto-electric multipoles, including an anapole, fully characterize the high-temperature canted phase, whereas the low-temperature collinear phase supports both parity-odd and parity-even multipoles that are time-odd. Orbital angular momentum accompanies the collinear motif, while it is conspicuously absent with the canted motif. Intensities have been successfully confronted with analytic expressions derived from an atomic model fully compliant with chemical and magnetic structures. Values of Fe atomic multipoles previously derived from independent experimental data, are shown to be completely trustworthy.
Rutile-type RuO2 likely supports a simple antiferromagnetic structure which can be verified by x-ray Bragg diffraction. Three magnetic motifs that do not break translation symmetry are explored in calculations of amplitudes suitable for diffraction enhanced by tuning the primary x-ray energy to a ruthenium atomic resonance. Coupling to x-ray helicity through a charge-magnetic interference is common to all motifs, together with magnetic and charge intensities in quadrature in the rotated channel of polarization. Necessary conditions for these diffraction phenomena are a centrosymmetric crystal structure, null magnetic propagation vector, and absence of a linear magnetoelectric effect. Published x-ray diffraction data for RuO2 was analysed by the authors against a magnetic motif that does not satisfy the conditions. A polarized neutron study of antiferromagnetic domains can be achieved with a sample that meets the stated crystal and magnetic symmetries.
Magnetic spiral structures can exhibit ferroelectric moments as recently demonstrated in various multiferroic materials. In such cases the helicity of the magnetic spiral is directly correlated with the direction of the ferroelectric moment and measurement of the helicity of magnetic structures is of current interest. Soft x-ray resonant diffraction is particularly advantageous because it combines element selectivity with a large magnetic cross-section. We calculate the polarization dependence of the resonant magnetic x-ray cross-section (electric dipole transition) for the basal plane magnetic spiral in hexaferrite Ba0.8Sr1.2Zn2Fe12O22 and deduce its domain population using circular polarized incident radiation. We demonstrate there is a direct correlation between the diffracted radiation and the helicity of the magnetic spiral.
Resonant angle scanned x-ray photoelectron diffraction (RXPD) allows the determination of the atomic and magnetic structure of surfaces and interfaces. For the case of magnetized nickel the resonant L2 excitation with circularly polarized light yields electrons with a dichroic signature from which the dipolar part may be retrieved. The corresponding L2MM and L3MM Auger electrons carry different angular momenta since their source waves rotate the dichroic dipole in the electron emission patterns by distinct angles.
Resonant Bragg diffraction of soft, circularly polarized x-rays has been used to observe directly the temperature dependence of chiral-order melting in a motif of Mn ions in terbium manganate. The underlying mechanism uses the b-axis component of a cycloid, which vanishes outside the polar phase. Melting is witnessed by the first and second harmonics of a cycloid, and we explain why the observed temperature dependence is different in the two harmonics. Our direct observation of melting is supported by a solid foundation of evidence, derived from extensive studies of the azimuthal-angle dependence of intensities with both linear and circular polarization.
The sensitivity of Circularly polarized X ray Resonant Magnetic Scattering (CXRMS) to chiral asymmetry has been demonstrated. The study was performed on a 2D array of Permalloy (Py) square nanomagnets of 700 nm lateral size arranged in a chess lattice of 1000 nm lattice parameter. Previous X ray Magnetic Circular Dichroism Photoemission Electron microscopy (XMCD-PEEM) images on this sample showed the formation of vortices at remanence and a preference in their chiral state. The magnetic hysteresis loops of the array along the diagonal axis of the squares indicate a non-negligible and anisotropic interaction between vortices. The intensity of the magnetic scattering using circularly polarized light along one of the diagonal axes of the square magnets becomes asymmetric in intensity in the direction transversal to the incident plane at fields where the vortex states are formed. The asymmetry sign is inverted when the direction of the applied magnetic field is inverted. The result is the expected in the presence of an unbalanced chiral distribution. The effect is observed by CXRMS due to the interference between the charge scattering and the magnetic scattering.