Polar magnetism and chemical bond in α-RuCl3

Abstract

The micaceous black allotrope of ruthenium trichloride is the subject of many recent experimental and theoretical studies. Even so, its structural and magnetic properties remain undecided; monoclinic, trigonal and rhombohedral space groups for the crystal structure have been proposed on the basis of various types of experiments. The magnetic structure is often discussed in the context of the Kitaev state, but inevitably they are inconclusive discussions in the absence of structural and magnetic space groups. Johnson et al infer a candidate for the magnetic structure (Cc2/m) from results gathered in an extensive set of experiments on an untwined sample of α-RuCl3 (Johnson et al 2015 Phys. Rev. B 92 235119). The proposed zigzag antiferromagnetic ground state of Ru ions does not respond to bulk magnetic probes, with optical rotation and all forms of dichroism prohibited by symmetry. Experimental techniques exploited by Johnson et al included x-ray and magnetic neutron diffraction. Properties of the candidate magnetic structure not previously explored include polar magnetism that supports Ru Dirac multipoles, e.g. a ruthenium anapole that is also known as a toroidal dipole. In a general case, Dirac dipoles are capable of generating interactions between magnetic ions, as in an electrical Dzyaloshinskii–Moryia interaction (Kaplan and Mahanti 2011 Phys. Rev. B 83 174432; Zhao et al 2021 Nat. Mater. 20 341). Notably, the existence of Dirac quadrupoles in the pseudo-gap phases of cuprate superconductors YBCO and Hg1201 account for observed magnetic Bragg diffraction patterns. Dirac multipoles contribute to the diffraction of both x-rays and neutrons, and a stringent test of the magnetic structure Cc2/m awaits future experiments. From symmetry-informed calculations we show that, the magnetic candidate permits Bragg spots that arise solely from Dirac multipoles. Stringent tests of Cc2/m can also be accomplished by performing resonant x-ray diffraction with signal enhancement from the chlorine K-edge. X-ray absorption spectra published for α-RuCl3 possess a significant low-energy feature (Plumb et al 2014 Phys. Rev. B 90 041112(R)). Many experimental studies of other Cl-metal compounds concluded that identical features hallmark the chemical bond. Using a monoclinic Cc2/m structure, we predict the contribution to Bragg diffraction at the Cl K-edge absorption. Specifically, the variation of intensity of Bragg spots with rotation of the sample about the reflection vector. The two principal topics of our studies, polar magnetism and the chemical bond in the black allotrope of ruthenium trichloride, are brought together in a minimal model of magnetic Ru ions in Cc2/m.