Relation between Kitaev magnetism and structure in $\alpha -{\mathrm{RuCl}}_3$

Raman scattering has been employed to investigate lattice and magnetic excitations of the honeycomb Kitaev material $\alpha -{\mathrm{RuCl}}_3$ and its Heisenberg counterpart ${\mathrm{CrCl}}_3$. Our phonon Raman spectra give evidence for a first-order structural transition from a monoclinic to a rhombohedral structure for both compounds. Significantly, only $\alpha -{\mathrm{RuCl}}_3$ features a large thermal hysteresis, consistent with the formation of a wide phase of coexistence. In the related temperature interval of $70–170$ K, we observe a hysteretic behavior of magnetic excitations as well. The stronger magnetic response in the rhombohedral compared to the monoclinic phase evidences a coupling between the crystallographic structure and low-energy magnetic response. Our results demonstrate that the Kitaev magnetism concomitant with fractionalized excitations is susceptible to small variations of bonding geometry.

Figure 1

(a)–(d) Comparison of Raman spectra of ${\mathrm{CrCl}}_3$ at $T=8$ and 300 K in ($xx$), ($xy$), ($RL$), and ($LL$) polarizations, respectively. ${\mathrm{A}}_g\left(i\right)$ and ${\mathrm{B}}_g\left(i\right)$ ($i=1–6$) are the phonon modes allowed in each polarization. The asterisks indicate a weak forbidden ${\mathrm{A}}_g$ mode showing up in ($xy$) and ($RL$) polarizations due to a leakage of a polarizer.

Figure 2

Temperature dependent Raman spectra of ${\mathrm{CrCl}}_3$ measured upon cooling (a) and heating (b) in ($RL$) polarization. The yellow bars mark the phonon which is present at a finite temperature interval.

Figure 3

Sketch of the eigenvectors of the (a) 209, (b) 247.9, and (c) 345.5 ${\mathrm{cm}}^{-1}$ modes in ${\mathrm{CrCl}}_3$. (d)–(i) Temperature dependence of the frequency and full width at half maximum (FWHM) of the 209, 247.9, and 345.5 ${\mathrm{cm}}^{-1}$ modes comparing cooling and warming. The vertical shaded bars indicate the magnetic and structural transition temperatures. The solid lines are fits to the anharmonic model as described in the text.

Figure 4

(a) Fit of the $T=8$ K spectrum to a sum of a Gaussian profile (cyan shaded region), two Fano lines (red and blue solid lines), and six Lorentzian profiles (colored solid lines). The red dash line represents the total sum of a fitting. Temperature dependence of the Raman spectra of $\alpha -{\mathrm{RuCl}}_3$ measured on cooling (b) and heating (c) in the in-plane ($RL$) polarization as well as on cooling (d) and heating (e) in the out-of-plane ($cc$) polarization. The yellow bars mark the phonon which disappears below $T_{\mathrm{S}}$ and the green bars indicate the activated phonons below $T_{\mathrm{S}}$.

Figure 5

Thermal hysteresis behavior of (a) the frequency, (b) the FWHM, and (c) the normalized intensity of the 116.4, 163.8, 270, 299.5, and 310 ${\mathrm{cm}}^{-1}$ modes. The shaded region indicates the coexistence of the monoclinic and rhombohedral phase. The arrows indicate the direction of the temperature sweep.

Figure 6

(a)–(d) Comparison of the magnetic Raman spectra among four different ($RL$), ($LL$), ($xx$), and ($xy$) scattering polarizations measured at $T=8$ and 300 K. A magnetic continuum of each data set is emphasized by a color shading. The yellow bar marks the phonon which shows the strongest variation of its intensity with polarization. (e) Comparison of the $T=100$ K Raman spectrum between the warming and cooling runs. (f) Temperature dependence of the integrated Raman intensity $I_{\mathrm{mid}}$ obtained in the middle energy window from 40 to 120 ${\mathrm{cm}}^{-1}$. The shaded area indicates the bosonic background and the solid red line is a fit to a temperature dependence expected for a two-fermion creation or annihilation process $[{(1-f\left({\omega }_f\right)]}^2$ with the Fermi distribution function $f\left({\omega }_f\right)$. (g) Thermal hysteresis of the total intensity obtained by the integration of a magnetic continuum up to 250 ${\mathrm{cm}}^{-1}$.

Figure 7

(a) Temperature dependence of the Raman conductivity ${\chi }^{\prime \prime }/\omega$ on cooling in ($RL$) polarization. The cyan shading is a magnetic continuum. (b) Temperature dependence of the dynamic Raman susceptibility deduced from ${\chi }^{\prime \prime }/\omega$ using the Kramers Kronig relation. Temperature dependence of the static spin susceptibility for ${\mu }_{0}H\parallel c$ is plotted together for comparison.

Figure 8

Schematic representation of eigenvector of (a) the 116.6 and (b) the 163.7 ${\mathrm{cm}}^{-1}$ modes of the monoclinic phase. The amplitude of the vibrations is represented by the arrow length. Gray balls indicate Ru ions and green balls are Cl ions. Temperature dependence of (c) the frequency, (d) the linewidth, (e) the Fano asymmetry $1/\left|q\right|$, and (f) the normalized intensity. The thin solid lines are a fit to an anharmonic phonon model and the thick solid line is the dynamic spin susceptibility taken from Fig. 7.