We have investigated the antiferromagnetic insulating phase of the Mott-Hubbard insulator V$_2$O$_3$ by resonant x-ray Bragg diffraction at the vanadium K-edge. Combining the information obtained from azimuthal angle scans, linear incoming polarizati
on scans and by fitting collected data to the scattering amplitude derived from the established chemical I2/a and magnetic space groups we provide evidence of the ordering motif of anapolar moments (which results from parity violation coupling to an electromagnetic field). Experimental data (azimuthal dependence and polarization analysis) collected at space-group forbidden Bragg reflections are successfully accounted within our model in terms of vanadium magnetoelectric multipoles. We demonstrate that resonant x-ray diffraction intensities in all space-group forbidden Bragg reflections of the kind $(hkl)_m$ with odd $h$ are produced by an E1-E2 event. The determined tensorial parameters offer a test for ab-initio calculations in this material, that can lead to a deeper and more quantitative understanding of the physical properties of V$_2$O$_3$.
We have performed a resonant x-ray scattering (RXS) study near the Co K edge on a single crystal of Ca3Co2O6. In the magnetically ordered phase a new class of weak reflections appears at the magnetic propagation vector tau (1/3,1/3,1/3). These new re
flections allow direct access to the dipolar-quadrupolar E1E2 scattering channel. The theoretical possibility of observing isolated E1E2 electromagnetic multipoles has attracted a lot of interest in the recent years. Unfortunately in many system of interest, parity even and parity odd tensor contributions occur at the same positions in reciprocal space. We demonstrate that in Ca3Co2O6 it is possible to completely separate the parity even from the parity odd terms. The possibility of observing such terms even in globally centrosymmetric systems using RXS has been investigated theoretically; Ca3Co2O6 allows a symmetry based separation of this contribution.
We have employed resonant x-ray magnetic scattering to specifically probe the magnetic order of the rare-earth ions in multiferroic $mathrm{TbMn_2O_5}$. Two energy resonances were observed, one originated from the E1-E1 dipolar transition and the oth
er from the E2-E2 quadrupolar transition. These resonances directly probe the valence 5d band and the partially occupied 4f band, respectively. First, full polarization analysis, which is a measurement of the scattered polarization as a function of incident polarization, confirmed a spin polarization of the terbium valence states (probed by the E1-E1 transition) by the $mathrm{Mn^{4+}}$ spin density in the commensurate phase. Second, full polarization analysis data were collected in the low-temperature incommensurate and commensurate phases when tuned to the E2-E2 resonance. By employing a least-squares fitting procedure, the spin orientations of the terbium ion sublattice were refined.
