[en] Optical activity (OA) was only recently discovered in the x-ray range. It is caused mainly by the electric dipole-electric quadrupole E1E2 interference terms which mix multipole moments of opposite parity and exist only in structures with odd space parity. OA related phenomena can be either even or odd with respect to time reversal: natural OA is concerned with time-reversal even effects whereas non-reciprocal OA refers to time-reversal odd contributions. Various types of x-ray dichroisms related to either natural or non-reciprocal OA have been detected and are reviewed in the present paper. Extra emphasis is put on two different non-reciprocal effects that were observed in selected magnetoelectric materials: (i) x-ray magnetochiral dichroism (XMχ D) and (ii) the non-reciprocal x-ray magnetic linear dichroism. Edge-selective OA sum rules have recently been established which show that the effective operator of XMχ D is the orbital anapole moment at the absorbing centre

[en] We discuss how measurements of x-ray circular intensity differentials (XCIDs) could be used to probe the Voigt-Fedorov vector part of optical activity (OA) due to electric dipole-electric quadrupole (E 1E 2) interferences. The first experiment was carried out on a single crystal of zincite (hexagonal ZnO: class 6mm). XCID spectra were recorded in the x-ray resonant diffraction regime near the Zn K edge using the (300) reflection at Bragg angles near 45 deg. In the x-ray range, the effective operator responsible for the vector part of OA can be assigned to the vector product LxΩ_L-Ω_LxL∝n, in which L and Ω_L are time-reversal odd operators associated with the orbital angular momentum and the orbital anapole respectively, whereas n is a true time-reversal even electric dipole. This is consistent with the pyroelectric properties of zincite crystals