Femtosecond demagnetization and hot-hole relaxation in ferromagnetic ${\text{Ga}}_{1-x}{\text{Mn}}_x\text{As}$

We have studied ultrafast photoinduced demagnetization in GaMnAs via two-color time-resolved magneto-optical Kerr spectroscopy. Below band gap midinfrared pump pulses strongly excite the valence band, while near-infrared probe pulses reveal subpicosecond demagnetization that is followed by an ultrafast $\left(\sim 1\text{ps}\right)$ partial recovery of the Kerr signal. Through comparison with InMnAs, we attribute the signal recovery to an ultrafast energy relaxation of holes. We propose that the dynamical polarization of holes through $p\text{−}d$ scattering is the source of the observed probe signal. These results support the physical picture of femtosecond demagnetization proposed earlier for InMnAs, identifying the critical roles of both energy and spin relaxation of hot holes.

Figure 1

(Color online) Optical transitions involved in the present experiments on GaMnAs (left) and InMnAs (right) in the ferromagnetic state where the conduction band (CB) and valence band (VB) are spin split. In GaMnAs, below-band-gap pump pulses at 0.62 eV (thick solid arrows) create holes in the VB via transitions from below the Fermi level to the midgap states (e.g., ${\text{As}}_{\text{Ga}}$ antisite defect band centered $\sim 0.5\text{eV}$ above the top of the VB) and excite the pre-existing hole population by intervalence band transitions allowed through the relaxation of the $k$-selection rule. In InMnAs, the photoelectrons in the CB are also created through direct interband transitions. The magnetization changes are probed via Kerr rotation by the reflected, time-delayed pulses at 1.6 eV (thin blue arrows).

Figure 2

(a) First 4 ps of $\Delta {\theta }_K\left(t\right)$ for GaMnAs. (b) $\Delta {\theta }_K\left(t\right)$ up to $t=120\text{ps}$. The initial signal is negative (i.e., demagnetization) and very fast, followed by a partial recovery of the MOKE angle with a time constant of $\sim 1\text{ps}$, and a slow, continuous decrease up to $\sim 100\text{ps}$.

Figure 3

(a) Magnetic-field dependence of $\Delta {\theta }_K\left(t\right)$. (b) Temperature dependence of $\Delta {\theta }_K\left(t\right)$ from 6 to 60 K. The signal decreases quickly with increasing temperature and is absent above the Curie temperature $\left(\sim 50\text{K}\right)$.

Figure 4

Photoinduced MOKE dynamics for (a) InMnAs and (b) GaMnAs under pumping with circularly (${\sigma }^{+}$ and ${\sigma }^{-}$) and linearly polarized radiations. The pump and probe photon energies are the same as those in other figures, and the magnetic field is $B>0$.

Figure 5

Illustration of the spin bottleneck effect for a (III,Mn)V semiconductor. (a) Hole spin-flip scattering event which leads to demagnetization of the localized spins (this is the dominant scattering event when holes are hot and Mn are fully polarized), with $\mu$ being the chemical potential. The band is spin split by exchange interaction with the localized spins. (b) When the spin-relaxation time of holes is finite, such scattering leads to the dynamical polarization of holes, parametrized by the spin splitting $\Delta \mu$ of the quasichemical potentials.

Figure 6

Simulation of the time dependence of the Mn spin polarization (the macroscopic magnetization) and the hole spin polarization after excitation with 140-fs-long pulse of light. The influence of the pulse is modeled as a rise of hole temperature $T_h$ from 4 to 1000 K right after the end of the pulse. Other parameters are total $p={10}^{20}{\text{cm}}^{-3}$, energy relaxation time of holes ${\tau }_E=1\text{ps}$, their spin-relaxation time ${\tau }_{\text{sr}}=10\text{fs}$, and $p\text{−}d$ exchange constant $N_0\beta =-1\text{eV}$ (with $N_0$ being the cation density), which for Mn concentration $x=0.26$ leads to the initial spin splitting of the valence band of 70 meV.