Non-Loudon-Fleury Raman scattering in spin-orbit coupled Mott insulators

Abstract

We revisit the theory of magnetic Raman scattering in Mott insulators with strong spin-orbit coupling, with a major focus on Kitaev materials. We show that Kitaev materials with bond-anisotropic interactions are generally expected to show both one- and two-magnon responses. It is further shown that, in order to obtain the correct leading contributions to the Raman vertex operator $\mc{R}$, one must take into account the precise, photon-assisted microscopic hopping processes of the electrons and that, in systems with multiple hopping paths, $\mc{R}$ contains terms beyond those appearing in the traditional Loudon-Fleury theory. Most saliently, a numerical implementation of the revised formalism to the case of the three-dimensional hyperhoneycomb Kitaev material $\beta$-Li${}_2$IrO${}_3$ reveals that the non-Loudon-Fleury scattering terms actually dominate the Raman intensity. In addition, they induce a qualitative modification of the polarization dependence, including, e.g., the emergence of a sharp one-magnon peak at low energies which is not expected in the traditional Loudon-Fleury theory. This peak is shown to arise from microscopic photon-assisted tunneling processes that are of similar type with the ones leading to the symmetric off-diagonal interaction $\Gamma$ (known to be present in many Kitaev materials), but take the form of a bond-directional magnetic dipole term in the Raman vertex. These results are expected to apply across all Kitaev materials and mark a drastic change of paradigm for the understanding of Raman scattering in materials with strong spin-orbit coupling and multiple exchange paths.

16 pages, 9 figures

References in corpus (18)

• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• $\alpha$-RuCl3: a Spin-Orbit Assisted Mott Insulator on a Honeycomb Lattice
• Inelastic Light Scattering From Correlated Electrons
• Models and Materials for Generalized Kitaev Magnetism
• Scattering Continuum and Possible Fractionalized Excitations in $\alpha$-RuCl${}_3$
• Magnetic order in $\alpha$-RuCl${}_3$: a honeycomb lattice quantum magnet with strong spin-orbit coupling
• Non-coplanar and counter-rotating incommensurate magnetic order stabilized by Kitaev interactions in $\gamma$-Li2IrO3
• Raman Scattering Signatures of Kitaev Spin Liquids in A${}_2$ IrO${}_3$ Iridates
• Unconventional magnetic order on the hyperhoneycomb Kitaev lattice in $\beta$-Li2IrO3: full solution via magnetic resonant x-ray diffraction
• Importance of anisotropic exchange interactions in honeycomb iridates. Minimal model for zigzag antiferromagnetic order in Na${}_2$IrO${}_3$
• Raman spectroscopic signature of fractionalized excitations in the harmonic-honeycomb iridates $\beta$- and $\gamma$-Li${}_2$IrO${}_3$
• Theory of Magnetic Phase Diagrams in Hyperhoneycomb and Harmonic-honeycomb Iridates
• Raman scattering study of vibrational and magnetic excitations in Sr${}_{2-x}$La${}_x$IrO${}_4$
• Floquet engineering of Mott insulators with strong spin-orbit coupling
• How to detect weak emergent broken-symmetries of the Kagome antiferromagnet from Raman spectroscopy
• Raman scattering in a Heisenberg {\boldmath $S=1/2$} antiferromagnet on the triangular lattice
• Field dependence of the magnetic spectrum in anisotropic and Dzyaloshinskii-Moriya antiferromagnets: II. Raman spectroscopy
• Unconventional magnetic field response of the hyperhoneycomb Kitaev magnet $\beta -{\text{Li}}_2{\text{IrO}}_3$