Spin-lattice coupling induced chiral phonons and their signature in Raman Circular Dichroism

Abstract

Recent Raman experiments on the Kitaev material $α$-RuCl$_3$ have reported a finite Raman circular dichroism (RCD), revealing chiral phonon behaviour not expected from lattice symmetry alone. To explain this observation, we develop a diagrammatic framework for the spin-phonon coupled Kitaev model. We demonstrate that bare phonons contribute no RCD, but coupling to the chiral spin excitation continuum under an applied magnetic field renormalizes the phonon propagator, mixing real polarization eigenvectors into complex superpositions with finite angular momentum. This interaction-induced modification generates a nonzero RCD accompanied by characteristic Fano line shapes in the Raman response, reflecting interference between discrete phonons and the continuum. The resulting signal grows with magnetic field strength, consistent with experiment, and directly tracks the field-induced chirality of the spin sector. More broadly, our results establish RCD as a powerful probe of interaction-induced chiral phonons in correlated quantum materials.

Figures (6)

• Figure 1: Experimental setup and Raman circular Dichroism (a) $\bar{z} (\sigma^+\sigma^-)z$ geometry of the Raman scattering experiment. In the monoclinic structure of $\alpha$-RuCl$_3$ the crystallographic $\bf c$-axis is tilted relative to the laboratory $\bf z$-axis Mai2019, reducing the point group symmetry from $D_{3d}$ to $C_{2h}$. Application of a magnetic field along the crystallographic $\bf a$-axis further lowers the symmetry to the magnetic point group $2^\prime/m^\prime$. Nearest-neighbor (NN) Majorana hopping amplitudes are indicated by the colored bonds, while the black star denotes the next-nearest-neighbor (NNN) Majorana hopping generated by the time-reversal symmetry breaking Zeeman term. (b) Comparison between experimental RCD spectra at $B = 12.5$T (open circles, dashed lines as guides to the eye) and theoretical predictions at $\kappa$ = 0.18 (solid lines), highlighting the amplitude difference and frequency splitting between the $I^{+-}$ and $I^{-+}$ scattering channels. The comparison is carried out using the parameters listed in Tab. \ref{['tab:thyvsexp_parameters']}. At zero magnetic field, the absence of chiral excitations results in a vanishing RCD signal, indicated by a dashed black line.
• Figure 2: Linear and circular phonon modes. TRS enforces real $A_g$ and $B_g$ phonon modes at the $\Gamma$-point, while the hybridization with the chiral-spinon continuum renormalizes the phonon modes into complex combinations with opposite angular momentum.
• Figure 3: Diagramatic Raman scattering (a) Photon-spin vertex with spin-photon coupling constant $\nu$. (b) Photon-phonon vertex with phonon-photon coupling constant $\mu_{\Gamma}$. (c) Spin-phonon coupling vertex with spin-phonon coupling constant $\lambda_\Gamma$. (d) Magnetic Raman scattering. (e) Phonon scattering with renormalized phonon and renormalized vertex and its contribution in (f)-(h). (f) Phonon Raman scattering with renormalized phonon (g) left and (h) right Fano diagram. Note, that each vertex per diagram comes with a sum over the different irreps.
• Figure 4: Raman response of a spin–phonon coupled Kitaev spin liquid. Rows show the separate contributions from spinons (a–c), phonons (d–f), Fano interference (g–i), and the total response (j–l). Columns correspond to the intensities $I^{+-}(\Omega)$ in the $\overline{z}(\sigma^+\sigma^-)z$ geometry, $I^{-+}(\Omega)$ in the $\overline{z}(\sigma^-\sigma^+)z$ geometry, and their difference $I^{\mathrm{RCD}}(\Omega) = I^{+-}(\Omega) - I^{-+}(\Omega)$. Insets in the upper-left corners show the corresponding Feynman diagrams. Numerical evaluation uses a $600\times600$$\mathbf{k}$-mesh and 200 energy intervals over $\Omega\in[ 0,12J]$ with $J=10~\text{meV}$, the phonon broadening parameter in $i\Omega\to\Omega+i\delta$ is $\delta=0.04$.
• Figure 5: Polarization bubble $\Pi_{\Gamma,\Gamma^\prime}(\Omega,0)$ Imaginary part red gradient solid, real part red gradient dashed. (a) Diagonal component of the polarization bubble (b) off-diagonal component of the polarization bubble. Note $\Pi_{A_g A_g}(\Omega,q) = \Pi_{B_g B_g}(\Omega,q)$ and $\Pi_{A_g B_g}(\Omega,\bm q) = - \Pi_{B_g A_g}(\Omega,\bm q)$. At $\kappa=0$ the off-diagonal polarization bubble vanishes. The gray line indicates the energy of the bare $E_g$ doublet.