Magnetization dynamics and the ${\text{Mn}}^{3+}$ $d\text{−}d$ excitation of hexagonal ${\text{HoMnO}}_3$ single crystals using wavelength-tunable time-resolved femtosecond spectroscopy

We analyze the photo-induced carrier and magnetization dynamics in antiferromagnetic (AFM) ${\text{HoMnO}}_3$ single crystals, delineated by wavelength-dependent femtosecond spectroscopy. The emergence of long-range and short-range magnetic order are unambiguously revealed in association with an abnormal blueshift of ${\text{Mn}}^{3+}$ $3d$ level around the Néel temperature and the slope variation in the temperature-dependent transient reflectivity change $\left(\Delta R/R\right)$ near the Néel transition, respectively. Furthermore, the disturbance (in ps time scale) of the AFM ordering and its reordering time (in a few 100 ps time scale) are clearly identified in the negative $\Delta R/R$.

Figure 1

The temperature-dependent susceptibility $\chi \left(T\right)$ of $h\text{-HMO}$ with a magnetic field of 100 Oe applied along $c$ axis. The inset shows the inverse susceptibility. The dashed line: the Curie-Weiss high-temperature extrapolation.

Figure 2

(Color online) The temperature-dependent $\Delta R/R$ measured at (a) $\lambda =800\text{nm}$ and (b) $\lambda =740\text{nm}$. The inset shows three primary features of dynamics in the $\Delta R/R$ curves.

Figure 3

(Color online) (a) The normalized amplitude of $\Delta R/R$ as a function of temperature at various wavelengths $\left(\lambda \right)$ taken from Fig. 2 at zero delay time. The insets illustrate the splitting of the ${\text{Mn}}^{3+}$ energy levels in the local environment ${\text{MnO}}_5$ for photon energy above and below $E_{dd}$ $\left(T_1>T_2\right)$ (b) The energy gap $E_{dd}$ as a function of $T_0$. $E_{dd}$ is estimated from the wavelengths in (a) and the error bars are the bandwidth of laser spectrum at various center wavelengths. The dashed line is a guide to the eye emphasizing the linear behavior at high-temperature range. (c) The slope of the temperature-dependent normalized amplitude of $\Delta R/R$ in (a) (the gray thick lines) as a function of $T_0$ at various wavelengths. (Dashed line is a guide to the eye emphasizing the behavior of slope.)

Figure 4

(Color online) (a) The $\Delta R/R$ curves at various temperatures ($T=290\text{K}$, 180 K, and 75 K). Dashed lines (red) and dash-dotted lines (green) show temperature of electrons $\left(T_e\right)$ and lattice $\left(T_l\right)$, respectively, due to the energy transfer by electron-lattice relaxation. The short-dashed lines (blue) show the temperature of spin system $\left(T_s\right)$ due to spin-lattice coupling. The inset shows the reordering time $\left({\tau }_r\right)$ of the disordered magnetization.

Figure 5

(Color online) The temperature-dependent ${\tau }_d$ for various wavelengths. The dashed line is a guide to emphasizing the behavior of ${\tau }_d$.