Optical Signature of a Crossover from Mott- to Slater-Type Gap in ${\mathrm{Sr}}_2{\mathrm{Ir}}_{1-x}{\mathrm{Rh}}_x{\mathrm{O}}_4$

With optical spectroscopy we provide evidence that the insulator-metal transition in ${\mathrm{Sr}}_2{\mathrm{Ir}}_{1-x}{\mathrm{Rh}}_x{\mathrm{O}}_4$ occurs close to a crossover from the Mott- to the Slater-type. The Mott gap at $x=0$ persists to high temperature and evolves without an anomaly across the Néel temperature, $T_N$. Upon Rh doping, it collapses rather rapidly and vanishes around $x=0.055$. Notably, just as the Mott gap vanishes yet another gap appears that is of the Slater-type and develops right below $T_N$. This Slater gap is only partial and is accompanied by a reduced scattering rate of the remaining free carriers, similar as in the parent compounds of the iron arsenide superconductors.

Figure 1

(a)–(f) Temperature dependent optical conductivity of ${\mathrm{Sr}}_2{\mathrm{Ir}}_{1-x}{\mathrm{Rh}}_x{\mathrm{O}}_4$ with $0\le x\le 0.15$. Inset of panel (f) shows the difference of the spectral weight integral between 10 and 300 K, $\mathrm{\Delta }S(\omega )=S(\omega ,10\mathrm{K})-S(\omega ,300\mathrm{K})$.

Figure 2

(a) Comparison of the optical conductivity at 10 K for ${\mathrm{Sr}}_2{\mathrm{Ir}}_{1-x}{\mathrm{Rh}}_x{\mathrm{O}}_4$ at different doping levels. The peak energies and oscillator strengths of the Drude peak (D) as well as the $\alpha$, $\beta$, and $M$ bands to the spectra in (a) are shown in (b) and (c), respectively. (d) Doping dependence of the normalized spectral weight for different cutoff frequencies ${\omega }_c$.

Figure 3

(a) Optical conductivity of the $x=0.07$ sample at representative temperatures well above, around, and well below $T_N\approx 180\mathrm{K}$. (b) The corresponding difference plots of the spectra of panel (a). (c) Drude-Lorentz fit of the ${\sigma }_1(\omega )$ spectrum at 10 K. (d) Temperature dependences of the Drude weight (circles) and scattering rate (triangles), as well as of the non-Drude spectral weight between 100 and 500 meV (squares).

Figure 4

(a) Temperature dependence of the low-energy spectral weight showing the progression of the gap formations at $0\le x\le 0.07$ and the coherent metallic response at $x=0.15$. Vertical dashed lines denote $T_N$. (b) Schematic diagram of the electronic states near the Fermi level ($E_F$) for ${\mathrm{Sr}}_2{\mathrm{Ir}}_{1-x}{\mathrm{Rh}}_x{\mathrm{O}}_4$. At $x=0$, a Mott gap occurs in the half-filled $J_{\mathrm{eff}}=1/2$ band whereas the $J_{\mathrm{eff}}=3/2$ is fully occupied. Rh doping of $x=0.02$ and 0.04 produces in-gap states. At $x=0.07$, the Mott gap has collapsed but the states near the Fermi level are still partially suppressed by a Slater gap that is induced by the antiferromagnetic order. Finally, at $x=0.15$, a correlated metal appears.