Observation of a metal-to-insulator transition with both Mott-Hubbard and Slater characteristics in Sr${}_2$IrO${}_4$ from time-resolved photocarrier dynamics

We perform a time-resolved optical study of Sr${}_2$IrO${}_4$ to understand the influence of magnetic ordering on the low energy electronic structure of a strongly spin-orbit coupled $J_{\mathrm{eff}}$ $=$ 1/2 Mott insulator. By studying the recovery dynamics of photoexcited carriers, we find that upon cooling through the Néel temperature $T_N$ the system evolves continuously from a metal-like phase with fast ($\sim$50 fs) and excitation density independent relaxation dynamics to a gapped phase characterized by slower ($\sim$500 fs) excitation density-dependent bimolecular recombination dynamics, which is a hallmark of a Slater-type metal-to-insulator transition. However our data indicate that the high energy reflectivity associated with optical transitions into the unoccupied $J_{\mathrm{eff}}$ $=$ 1/2 band undergoes the sharpest upturn at $T_N$, which is consistent with a Mott-Hubbard type metal-to-insulator transition involving spectral weight transfer into an upper Hubbard band. These findings show Sr${}_2$IrO${}_4$ to be a unique system in which Slater- and Mott-Hubbard-type behaviors coexist and naturally explain the absence of anomalies at $T_N$ in transport and thermodynamic measurements.

Figure 1

Normalized time-resolved reflectivity traces ($\Delta$$R$/$R$)${}_{\mathrm{norm}}$ of Sr${}_2$IrO${}_4$ collected in the temperature ranges (a) 4–120 K, (b) 120–210 K, (c) 210–300 K, and (d) 300–350 K. Curves are collected in 10-K intervals with a pump fluence of 15.4 $\mu$J/cm${}^2$. Inset of panel (a) shows a schematic of the low-energy electronic density of states (DOS) based on calculations.[12] The red arrow denotes the optical transition being excited by the pump pulse. Inset of panel (d) shows the $T$ $=$ 300 K trace out to 100-ps time delay.

Figure 2

Transient reflectivity traces taken at $T$ $=$ 300 K and $F$ $=$ 15.4 $\mu$J/cm${}^2$ and fitted to a (a) single and (b) double exponential decay. Transient reflectivity traces taken at $T$ $=$ 180 K and $F$ $=$ 1.9 $\mu$J/cm${}^2$ and fitted to a (c) single and (d) double exponential decay. Curves show the overall fit as well as the separate components of the fit. The fitted parameters and their associated fitting errors (in parentheses) are listed in red.

Figure 3

(a) A typical un-normalized time-resolved reflectivity transient ($\Delta$$R$/$R$) of Sr${}_2$IrO${}_4$ overlaid with a bi-exponential fit described in the text (red curve). Inset shows the Gaussian instrument time resolution (red curve) superimposed on 300-K data where decay dynamics are dominated by the fast (${\tau }_1$) component [Fig. 4b]. This shows that the fast initial decay is not resolution limited. (b) The fitted amplitude ($A$) of the fast exponential decay component measured over a range of pump fluences corresponding to $\sim$10${}^{-5}$ to $\sim$10${}^{-3}$ pump photons per iridium atom. The red line is a linear fit. (c) Temperature dependence of the fitted decay time (${\tau }_1$) of the fast exponential decay component measured over a range of pump fluences. (d) Schematic showing that the initial fast decay process is governed by energy relaxation of photoexcited electrons and holes towards the band edges via optical phonon emission. The errors in the fit parameters are smaller than the size of the symbols.

Figure 4

(a) Temperature dependence of the fit parameters $A$ and $B$, normalized to their values at $T$ $=$ 350 K, taken in the low pump fluence regime. (b) Temperature dependence of $B$/$A$ derived from data shown in (a). (c) Temperature dependence of the amplitude ratio and (d) the decay time of the slower component (${\tau }_2$) measured using three different fluences 15.4 $\mu$J/cm${}^2$, 1.9 $\mu$J/cm${}^2$, and 0.18 $\mu$J/cm${}^2$. (e) Fluence dependence of the slower decay rate measured at 4 K. Straight line is a guide to the eye showing a linear dependence at low fluences. The errors in the fit parameters are less than the size of the symbols. A schematic of the bimolecular relaxation process involving the annihilation of photoexcited empty and doubly occupied sites via emission of optical phonons or magnons is shown in the inset, which emphasizes the Mott-Hubbard character of the system. (f) Schematic showing the temperature evolution of the low-energy electronic density of states (DOS) in Sr${}_2$IrO${}_4$ based on our data. Filled and empty circles denote the photoexcited electron and hole respectively.

Figure 5

(a) Diagram illustrating the temporal equilibration between the electronic and lattice subsystems following a pump pulse. The slowest process (C) is the cooling of the equilibrated system via diffusion of hot carriers or hot phonons away from the measured sample spot. (b) Temperature dependence of the offset (C) measured using a pump fluence of 15.4 $\mu$J/cm${}^2$. A clear minimum in C is observed at $T_N$ corresponding to a rapid rise in reflectivity at 1.5 eV at $T_N$ (see inset schematic). The errors in the fit parameters are less than the size of the symbols.

Figure 6

Temperature dependence of un-normalized $\Delta R/R$ traces that are plotted over a range to emphasize the long time offset. Data are plotted from (a) $T$ $=$ 4–130 K, (b) 140–240 K, and (c) 250–350 K in increments of 10 K. (d) The value of $\Delta R/R$ at a time delay of 5 ps [red arrows in panels (a)–(c)] plotted as a function of temperature.