Critical phenomena and femtosecond ordering dynamics associated with electronic and spin-ordered phases in ${\text{YVO}}_3$ and ${\text{GdVO}}_3$

We present a systematic study of the electronic- and spin-excitation dynamics associated with the sequence of spin- and orbital-ordering phase transformations in the complex vanadates ${\text{YVO}}_3$ and ${\text{GdVO}}_3$ with ultrafast optical pump-probe reflectance spectroscopy. Relaxation dynamics occurs on a different time scale for each of the ordering transitions, which enables us to unambiguously associate the critical behavior in the dynamics with the observed ordering phenomena. Spin-ordering dynamics is observed on two time scales: ${\tau }_r\simeq 2\text{ps}$ (rise time) and ${\tau }_s\simeq 300–3000\text{ps}$ (decay time), observed below $T_N$ in both compounds. In contrast, the relaxation dynamics associated with orbital ordering occurs in ${\text{YVO}}_3$ on a time scale of ${\tau }_o\simeq 20–50\text{ps}$. From the temperature dependence of the dynamics, we observe that in both the G-type and C-type orbitally ordered (OO) phases of ${\text{YVO}}_3$ spin order develops in a second-order mean-field fashion with the Nèel temperature of the C-OO phase found from our data $T_N^C=83\pm 7\text{K}$. In ${\text{GdVO}}_3$ we identify the emergence of a new ordered phase within the phase-separated state below 60 K. A new response component with a lifetime of $\sim 60\text{ps}$ is observed below 60 K together with other anomalies in the $\Delta R/R\left(\Delta t\right)$ data. This new phase is not resolved in x-ray diffraction and is not present in ${\text{YVO}}_3$.

Figure 1

(Color online) Polarized photoinduced reflectivity transients of ${\text{YVO}}_3$ and ${\text{GdVO}}_3$ crystals at four temperatures, corresponding to distinct regions of the phase diagrams [see Figs. 2a, 3a]. The components of the responses are marked according to Eq. (1).

Figure 2

(Color online) Phase diagram of ${\text{YVO}}_3$ (a) and temperature dependencies of the amplitude $B$ (b) and the lifetime ${\tau }_s$ (c) of SO relaxation, and (d) of the $\sim 40\text{ps}$ component amplitude $C$ in the ${\mathbf{E}}_{probe}\parallel a$ (△) and ${\mathbf{E}}_{probe}\parallel c$ (▲) $\Delta R/R$ responses. The solid lines in panels (b) and (d) are the fits of the data to Eq. (2).

Figure 3

(Color online) (a) Phase diagram of ${\text{GdVO}}_3$ with a dependence of a stable C-OO phase volume fraction (Ref. 8). (b) Temperature dependencies of the rise-time amplitude $A$ (○), the relaxation amplitude $B$ (●), and (c) the lifetime of SO. Temperature dependencies of the 5 ps component amplitude (on warming, ▲, and on cooling, △) and 60 ps component amplitude (◼) are shown in (d).

Figure 4

Perturbation and relaxation of the orbital (ovals) and spin (arrows) order with the corresponding time scales in $R{\text{VO}}_3$.