Influence of spin and orbital fluctuations on Mott-Hubbard exciton dynamics in ${\mathrm{LaVO}}_3$ thin films

Recent optical conductivity measurements reveal the presence of Hubbard excitons in certain Mott insulators. In light of these results, it is important to revisit the dynamics of these materials to account for excitonic correlations. We investigate time-resolved excitation and relaxation dynamics as a function of temperature in perovskite-type ${\mathrm{LaVO}}_3$ thin films using ultrafast optical pump-probe spectroscopy. ${\mathrm{LaVO}}_3$ undergoes a series of phase transitions at roughly the same critical temperature $T_C\cong 140$ K, including a second-order magnetic phase transition ($\mathrm{PM}\stackrel{}{\to }\mathrm{AFM}$) and a first-order structural phase transition, accompanied by $C$-type spin order and $G$-type orbital order. Ultrafast optical pump-probe spectroscopy at 1.6 eV monitors changes in the spectral weight of the Hubbard exciton resonance which serves as a sensitive reporter of spin and orbital fluctuation dynamics. We observe dramatic slowing down of the spin, and orbital dynamics in the vicinity of $T_C\cong 140$ K, reminiscent of a second-order phase transition, despite the (weakly) first-order nature of the transition. We emphasize that since it is spectral weight changes that are probed, the measured dynamics are not reflective of conventional exciton generation and recombination, but are related to the dynamics of Hubbard exciton formation in the presence of a fluctuating many-body environment.

Figure 1

(a) Diagram of the $C$-type spin and $G$-type orbital order configuration in ${\mathrm{LaVO}}_3$. The spins on $d_{zx}$ and $d_{yz}$ orbitals, shown as white arrows, are slightly canted from the $c$ axis. (b) Depiction of the density of states near the Fermi level, showing the photoexcitation process at 1.6 eV from the lower Hubbard band (LHB) to the upper Hubbard band (UHB) as a solid red arrow, corresponding to peak HE in the optical conductivity. An electron from a $t_{2g}$ orbital in the LHB on vanadium atom ${\mathrm{V}}_1$ is promoted to a $t_{2g}$ orbital in the UHB on ${\mathrm{V}}_2$. The dashed arrow depicts the single-particle excitation with well-separated quasiparticles, corresponding to peak B in the optical conductivity. (c) Depiction of the $c$-axis optical conductivity evolution with temperature, reproduced from [21]. Peak HE corresponds to the excitonic resonance in the vicinity of the MH gap, and peak B an excitation from $\mathrm{LHB}\stackrel{}{\to }\mathrm{UHB}$ (consisting of well-separated quasiparticles). The ratio of peak HE to peak B grows drastically below the ordering temperature at $T_C=140$ K, indicating the importance of spin and orbital order upon the exciton spectral weight. The red dotted line indicates the laser photoexcitation energy. (d) Motion of a “double occupancy” on the spin and orbitally ordered lattice. Each hopping process creates a trace of disordered spins and orbitals.

Figure 2

Photoinduced differential reflectivity traces in the high-temperature phase ($T\ge 140$ K), for long (a) and short (b) pump-probe delays, and in the low-temperature phase ($T\le 135$ K) for long (c) and short (d) pump-probe delays. The black curves are exponential fits to the data, of the form given in Eq. (1).

Figure 3

Photoinduced reflectivity traces near the critical temperature for long (a) and short (b) pump-probe delays with considerably smaller temperature steps in comparison to Fig. 2. Black curves are multiexponential fits to the data. (c) Pump-probe scan at 136 K, showing the four separate components of the response as given in Eq. (1).

Figure 4

Time constants and amplitudes extracted from the exponential fits, for (a) the Hubbard exciton component ${\tau }_{\mathrm{HE}}$ emerging at 140 K, and (b) the ${\tau }_{\mathrm{slow}}$ component assigned to the recovery of spin and orbital order. The lines are guides to the eye. The inset plots ${\tau }_{\mathrm{HE}}$ and ${\tau }_{\mathrm{slow}}$ on the same axis, normalized at 139 K for comparison. (c) and (d) depict the critical behavior and power-law fit [of the form given in Eq. (2), in red] for ${\tau }_{\mathrm{HE}}$ and $A_{\mathrm{HE}}$, respectively. The insets show the same data on a log-log scale with the reduced temperature. (e) and (f) present the power-law fits for ${\tau }_{\mathrm{slow}}$ and $A_{\mathrm{slow}}$, respectively.

Figure 5

Exciton dynamics near $T_C$ on an AFM spin and antiferro-orbitally ordered background. Each arrow represents the spin and orbital occupation at a separate lattice site. (1) After photoexcitation, the holon and DO are bound as a Hubbard exciton. Hopping of the bound pair $\left[\left(1\right)\stackrel{}{\to }\left(2\right)\right]$ preserves spin and orbital order. Hopping of the individual holon or DO along the $c$ axis $\left[\left(2\right)\stackrel{}{\to }\left(3\right)\right]$ results in orbital disorder, while hopping along the $a$ or $b$ axis $\left[\left(3\right)\stackrel{}{\to }\left(4\right)\right]$ produces both spin and orbital disorder. At temperatures near $T_C$ and at times $t>{\tau }_{\mathrm{HE}}$ after photoexcitation, spin and orbital fluctuations [depicted in (4)] disrupt the local order and the individual holon and DO are able to move farther apart $\left[\left(4\right)\stackrel{}{\to }\left(5\right)\right]$. This destabilizes the HE (5) and reduces spectral weight at the HE peak.

Figure 6

(a) Time-dependent Ginzburg-Landau simulations for a generic first-order phase transition, as a function of temperature near $T_C({\alpha }_0=0.25,\beta =-0.35,\gamma =1,T_C=138$ K). The results qualitatively match the experimental data, with a similar slowing down of dynamics approaching $T_C$. (b) The simulated ${\tau }_{\mathrm{slow}}$ is plotted in red alongside the experimental values, showing a remarkable correspondence. (c) The free energy given by Eq. (3) as a function of the order parameter $m$. Note that the free energy never completely flattens at $T_C$, instead retaining three discrete minima.