Optically induced instability of spin precession in magnetic quantum wells F. Teppe, M. Vladimirova, and D. Scalbert Groupe d’Etude des Semi-Conducteurs, UMR 5650 CNRS-Universite ´, Montpellier 2, Place Euge `ne Bataillon, 34095 Montpellier Cedex, France T. Wojtowicz and J. Kossut Institute of Physics, Polish Academy of Sciences, Al. Lotniko ´w 32/46, 02-668 Warszawa, Poland Received 18 September 2002; published 22 January 2003 Dynamic phase separation in CdMnTe quantum wells under femtosecond pulse excitation leads to formation of hot and cold spin domains. Using Fourier spectroscopy of the time-resolved magneto-optical Kerr effect we determine the temperatures and the total areas of each kind of domain. The instability is shown to be triggered by the magnetic field above a threshold value. DOI: 10.1103/PhysRevB.67.033304 PACS numbers: 78.66.Hf, 05.45.-a, 75.50.Pp, 78.47.+p In a great variety of natural phenomena the nonlinearity in stochastic systems far from equilibrium is responsible for a complex behavior and auto-organization. 1 Among such sys- tems one can mention chemical reactions, where local- density fluctuations are amplified by autocatalytic mecha- nism, or biological systems, where the feedback loop is controlled by generation of ferments. In magneto-optics, a complex behavior of magnetization vector can be expected in diluted magnetic semiconductors DMS’s, 2 that is, semi- conductors, alloyed with transition metals, e.g., manganese. Indeed, under optical excitation the spins of magnetic ions are heated via spin flips with electron spins due to s -d ex- change interaction, and this heating is more efficient in hotter spin regions. 3 Thus in such a system any local fluctuation of ions spin temperature is amplified by the positive feedback loop. Therefore one expects the inhomogeneity of spin tem- perature that eventually results in dynamic phase separation. In this paper, we show that such phase separation does occur in CdMnTe quantum wells QW’s subjected to the magnetic field in Voigt geometry under femtosecond pulse excitation, resonant with the QW fundamental optical transition. Using the time-resolved magneto-optical Kerr technique 4 we pro- vide a direct evidence of hot and cold domains formation and determine both temperatures and total areas of these do- mains, as well as the magnetic-field intensity threshold for domain formation. Finally, the effect of optical excitation intensity and photon energy is discussed. Our experimental technique exploits the well-known magneto-optical Kerr effect in a pump-probe geometry to detect the spin polarization in the sample excited by 100-fs circularly polarized laser pulses. The Kerr rotation is then monitored by a weak probe pulse. The repetition rate of the laser pulses is set to 82 MHz and the pump to probe intensity ratio 2:1 is chosen to optimize the signal. We use a triple modulation scheme, where the helicity of the pump beam is modulated at f =50 kHz, and the intensities of pump and probe are modulated at low frequencies f pump =147 Hz and f probe =176 Hz, respectively. The signal is detected at fre- quencies f ( f pump + f probe ) where it is less affected by the low-frequency noise. To minimize the inhomogeneous exci- tation effects the laser beams are weakly focused onto a spot of 200- m diameter. The sample is immersed in a bath of superfluid helium at 1.8 K. The sample under scrutiny is an iodine modulation-doped CdMnTe/CdMgTe QW grown on GaAs substrate with a thick CdTe buffer layer. The details on the structure and op- tical properties of similar samples may be found elsewhere. 5 The QW electron-density modulation in the range of 10 10 – 10 11 cm -2 is obtained by changing the thickness of the io- dine doping layer along a fixed direction in the plane of the sample. The residual electron density 10 10 cm -2 was esti- mated from photoluminescence experiments using the method proposed in Ref. 6. The QW width is 80 Å and the effective Mn concentration x eff =0.42% was deduced from the electron-spin splitting of the conduction band. Spin do- mains are observed in the QW irrespective of the doping level and follow the same general trends. Most of the results reported hereafter are obtained on the nominally undoped piece of the sample. Figure 1 shows a series of spectra, obtained by Fourier FIG. 1. Fast Fourier transform spectra of the time-resolved magneto-optical Kerr signal at 1.8 K. The intensity of line U is divided by a factor 5. The lines H, M, and C are assigned to electron spins precessing in spatial regions of the QW with different Mn spin temperatures see text. The lines visualizing their evolution are guides to the eye. PHYSICAL REVIEW B 67, 033304 2003 0163-1829/2003/673/0333044/$20.00 ©2003 The American Physical Society 67 033304-1