Local Chiral-Symmetry Breaking in Globally Centrosymmetric Crystals

Abstract

A thorough tensor analysis of the Bragg-forbidden reflection (00.3)(h) in corundum systems having a global center of inversion, such as V2O3 and alpha-Fe2O3, shows that anomalous x-ray resonant diffraction can access chiral properties related to the dipole-quadrupole (E1-E2) channel via an interference with the pure quadrupole-quadrupole (E2-E2) process. This is also confirmed by independent ab initio numerical simulations. In such a way, it becomes possible to detect chiral quantities in systems where dichroic absorption techniques are ineffective.

Detection of electromagnetic multipoles by x-ray spectroscopies

“…Notice that when we relax the approximation of frozen orbitals, only an actual calculation can tell us whether the polarization still persists or not: a posteriori this is confirmed by the signals obtained through numerical abinitio simulations in Refs. [ 5,11]. These same quantities are detectable also by means of RXS, where the local transition amplitudes are added with a phase factor that can compensate the possible vanishing effect due to the global symmetry, as shown in Ref.…”

“…Similarly, in the E1-E2 channel, XNCD was found to be sensitive to the mean value of the tensor F (2+) (E1 − E2). 5 It is interesting to note that this latter has been interpreted in the past 6,11,16 as the expectation value of the physical quantity l z t z , while from the previous table it comes out that this term measures the quadrupole of g, which is time-reversal even and parity-odd. Quantitatively, the former identification is not incorrect, as the expectation values of the operators l z t z and r z g z between states with ∆l = ±1 are proportional to each other.…”

“…These same quantities are detectable also by means of RXS, where the local transition amplitudes are added with a phase factor that can compensate the possible vanishing effect due to the global symmetry, as shown in Ref. [ 11] for the quadrupole of g in the corundum phase of V 2 O 3 and, e.g., in Ref. [ 19] for the magnetic moment in the antiferromagnetic insulating phase of V 2 O 3 .…”

“…24 7) Non-magnetic (axial) toroidal quadrupole, as discussed above, was found with XNCD in α-LiIO 3 , 5 and in V 2 O 3 by means of RXS. 11 8) Electric octupole (F (3+) (E1 − E2)) has been predicted in Ref. [ 16] for K 2 CrO 4 on the basis of symmetry arguments.…”

“…1(a) represents the untwisted situation, where the local symmetry is not lower than C 3v and no local F (2+) (E1 − E2) term is allowed, as forbidden by the vertical mirror plane (see, eg, Ref. [ 11]). In Fig.…”