Resonant x-ray diffraction from chiral electric-polarization structures

TL;DR

This paper explains the observed circular dichroism in resonant x-ray diffraction from chiral ferroelectric superlattices as arising from charge quadrupole arrangements, providing a non-magnetic alternative to previous interpretations.

Contribution

The authors present a non-magnetic explanation for circular dichroism in resonant x-ray diffraction, attributing it to chiral charge quadrupole moments rather than polar vector rotation.

Findings

Charge quadrupole moments explain the diffraction patterns.

The model accounts for all previously reported observations.

Predictions made for second harmonic and unpolarized x-ray polarization.

Abstract

Heterostructures of PbTiO$_3$/SrTiO$_3$ superlattices have shown the formation of "polar vortices", in which a continuous rotation of ferroelectric polarization spontaneously forms. Recently, Shafer {\it{et al.}} [Proc.\ Natl.\ Acad.\ Sci.\ (PNAS) {\bf{115}}, 915 (2018)] reported strong {\it{non-magnetic}} circular dichroism (CD) in resonant soft x-ray diffraction at the Ti $L_3$ edge from such superlattices. The authors ascribe the CD to the chiral rotation of a polar vector. However, a polar vector is invisible to the parity-even electric-dipole transition which governs absorption in the soft x-ray region. A realistic, non-magnetic explanation of the observed effect is found in Templeton-Templeton scattering. Following this route, the origin of the CD in Bragg diffraction is shown by us to be the chiral array of charge quadrupole moments that forms in these heterostructures. While there is no charge quadrupole moment in the spherically symmetric $3d^0$ valence state of Ti$^{4+}$, the excited state $2p_{3/2}3d(t_{2g})$ at the Ti $L_3$ resonance is known to have a quadrupole moment. Our expressions for intensities of satellite Bragg spots in resonance-enhanced diffraction of circularly polarized x-rays, including their harmonic content, account for all observations reported by Shafer {\it{et al.}} We predict both intensities of Bragg spots for the second harmonic of a chiral superlattice and circular polarization created from unpolarized x-rays, in order that our successful explanation of existing diffraction data can be further scrutinized through renewed experimental investigations. The increased understanding of chiral dipole arrangements could open the door to switchable optical polarization.