Orbital dichotomy of Fermi liquid properties in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ revealed by Raman spectroscopy

We report a polarization-resolved Raman spectroscopy study of the orbital dependence of the quasiparticle properties in the prototypical multiband Fermi liquid ${\mathrm{Sr}}_2\mathrm{Ru}{\mathrm{O}}_4$. We show that the quasiparticle scattering rate displays ${\omega }^2$ dependence, as expected for a Fermi liquid. In addition, we observe a clear polarization dependence in the energy and temperature dependence of the quasiparticle scattering rate and mass, with the $d_{xz/yz}$ orbital derived quasiparticles showing significantly more robust Fermi liquid properties than the $d_{xy}$ orbital derived ones. The observed orbital dichotomy of the quasiparticles is consistent with the picture of ${\mathrm{Sr}}_2\mathrm{Ru}{\mathrm{O}}_4$ as a Hund's metal. Our study establishes Raman scattering as a powerful probe of Fermi liquid properties in correlated metals.

Figure 1

(a)–(c) Schematic representation of the two-dimensional intraorbital hopping integrals of the Ru $d$ orbitals $t_i$. (d) Schematic representation of the Fermi surface of ${\mathrm{Sr}}_2\mathrm{Ru}{\mathrm{O}}_4$ in the first Brillouin zone. (e) and (f) Sketches of the wave-vector dependence on the Fermi surface of the squared Raman vertex for intraorbital transition terms in the $B_{1g}$ and $B_{2g}$ channels, respectively. The local linewidth denotes the strength of the vertex. Note the nodes in the Raman vertex value along the diagonals and along the principal axis directions for the $B_{1g}$ and $B_{2g}$ channels, respectively. We took the values of $t_i$ as $\{t_1,t_2,t_3,t_4\}=\{88,9,80,40\}$ meV [29]. The sketches on the left of each vertex depict, for each symmetry, the polarizations of the incident and scattered beams with respect to the in-plane Ru square lattice.

Figure 2

(a) Theoretical Raman responses expected for a metal in the Drude model and for a FL in the extended Drude model. We took the small and large ${\tilde{\mathrm{\Gamma }}}_0$ to be ${\tilde{\mathrm{\Gamma }}}_0^l=8{\tilde{\mathrm{\Gamma }}}_0^s$. For the Drude model ${\mathrm{\Gamma }}_0$ is taken to be equal to ${\tilde{\mathrm{\Gamma }}}_0^s$. (b)–(d) Experimental Raman responses obtained in the $B_{1g}, B_{2g}$, and $A_{1g}$ symmetry channels, respectively, at selected temperatures. The sketches on the right depict, for each symmetry, the polarizations of the incident and scattered beams with respect to the in-plane Ru square lattice. In (d), the inset shows the $A_{1g}$ response below 7 meV.

Figure 3

(a) Energy dependence of the relaxation rate ${\mathrm{\Gamma }}_{\mu }\left(\omega \right)$ at 15 K for $B_{1g}$ and $B_{2g}$. The solid lines are quadratic fits of the experimental data at low energy. The sketches recall the shape of the Raman vertices (see Fig. 1). (b) Low-energy dependence of the mass-enhancement factor $1+{\lambda }_{\mu }$ at 15 K in $B_{1g}$ and $B_{2g}$. (c) Temperature dependence of the ${\omega }^2$ prefactor of ${\mathrm{\Gamma }}_{\mu }\left(\omega \right)$, obtained through the fits. The error bars are computed as statistical uncertainty in the quadratic fits. (d) Temperature dependence of the extrapolated zero-energy mass enhancement. (e) Temperature dependence of the Raman static susceptibility.

Figure 4

(a) Temperature dependence of the extrapolated static relaxation rate ${\mathrm{\Gamma }}_{0,\mu }$ for $B_{1g}$ and $B_{2g}$. The solid lines are quadratic fits of the low-temperature data. The arrow denotes the upper limits of the fits at 27 K. The open symbols are excluded for the computation of the fits. (b) Gurzhi scaling with $p_{B_{1g}}=1.6$ and $p_{B_{2g}}=0.85$.