Intrasubband spin-flip relaxation by one-magnon processes in Cd 1 Àx Mn x Te quantum wells E. Souto, O. A. C. Nunes, F. M. S. Lima, D. A. Agrello, and A. L. A. Fonseca Institute of Physics, University of Brası ´lia, P. O. Box 04455, 70919-970, Brası ´lia, Brazil Received 27 November 2002; revised manuscript received 20 May 2003; published 18 September 2003 The ‘‘s - d model’’ which contains a description of band electrons coupled to localized spins is used to calculate the intrasubband spin-flip lifetime due to scattering of electrons by magnons in Cd 1-x Mn x Te quantum well structures. We found that the low-temperature result  flip 1 ps agrees nicely with the low-temperature time-resolved photoluminescence measurements. Furthermore, the spin-flip lifetime broadening was found to scale with L -1 , L being the quantum well width. DOI: 10.1103/PhysRevB.68.125317 PACS numbers: 72.10.Di, 72.15.Lh, 72.25.Rb, 73.21.Hb I. INTRODUCTION During the past decade, the physics of carrier spin dynam- ics in GaAs/AlGaAs quantum wells QWs has been the fo- cus of much interest, 1–7 and its potential applications for ultrafast devices using a spin-dependent optical nonlinearity 8 as well as spin-polarized electrons. 9 Indeed, the high optical and electronic qualities of these quantum structures and their very well-known properties make them ideal candidates to explore spin-related properties. However, despite this inten- sive work the spin relaxation processes are still not fully understood. Type II-VI QWs spin properties have been the focus of much less attention. However, the possibility to incorporate magnetic ions, such as manganese, opens possibilities of spin control, which, for example, have been recently used to dem- onstrate the spin injection from a diluted magnetic semicon- ductor DMS into a GaAs light emitting diode. 10 In this emerging field of spin-dependent electronics it becomes in- creasingly important to unravel the spin relaxation processes, in particular for quantum structures containing magnetic ions. Furthermore, recent progress in the growth of DMS- based QW’s by molecular beam epitaxy allows great flexibil- ity when elaborating new structures. The interest in elec- tronic spin polarization in DMS quantum well systems has grown since then 10–14 fueled by the possibility of producing spin memory devices and spin transistors as well as exploit- ing the properties of spin coherence for quantum computa- tion. The determination of spin-flip scattering rates between s - p electrons and the 3 d electrons of the localized magnetic moments in Mn-based QW’s is extremely important for spin- tronic devices, because if the spins relax too rapidly, the distances traveled by spin-polarized currents will be too short for practical applications. Photoinduced magnetization and spin-dependent absorption experiments 15–17 in which the injection of spin-polarized carriers induces the magnetization of the magnetic ions, have confirmed the existence of spin- flip process between the carrier spin and the embedded mag- netic ion. Time-resolved measurements 18,19 of the Mn mag- netization in Cd 1 -x Mn x Te due to the creation of spin- polarized photoelectrons, pointed out a strong electron- energy dependence of the spin-relaxation rate. The time- resolved measurement is particularly interesting because it addresses the question of what spin-flip scattering mecha- nism determines the relaxation of the injected carrier spins. The data for the low-temperature time-dependent intensity for circularly polarized components of luminescence from an 86 Å Cd 1 -x Mn x Te/Cd 1 -y Mn y Te QW ( x  y ) have shown 18,19 that for low detection energies close to the ground sate, the response is virtually instantaneous indicat- ing very rapid electron-spin relaxation which has been asso- ciated with spin-orbit effects in the valence band. At higher detection energies, which are thought to reflect free-carrier behavior, the spin dynamics is very slow, corresponding to recombination in the initial nonequilibrium population of free electrons and holes. The 1.88 eV detection-energy data 18 give an orientation-decay time of 5 ps and suggests a strong free-carrier-ion–spin-spin-exchange relaxation mechanism. The data have also shown similar short spin-relaxation times in quantum wells containing no magnetic materials which indicates that the electron spin relaxation times are insensi- tive to the presence of Mn ions in the QW, a rather surprising result indeed since s - d exchange scattering should be very efficient. Latter studies 20 have revealed that these so-called nonmagnetic QW’s may exhibit magneto-optical splittings, which in some instances may be larger than those from the magnetic barriers. This effect results mainly because of mag- netic dilution at the interface and because of the fact that the magnetic susceptibility decreases as the Mn concentration becomes larger than 10–15 %. Therefore, in our opinion, the conclusions of Freeman and Awschalom 18 and Freeman et al. 19 in early studies must be reconsidered. More recently, Akimoto et al. 21 measured electron and heavy-hole spin re- laxation times in CdTe/Cd 1 -x Mn x Te QW’s ( x =0.35) by time-resolved circular dichroism. They found a steep de- crease of the electron spin relaxation time  e as the QW width decreases, which they related to the increase of the overlap between s and d orbitals. This was the first direct hint that exchange scattering acts efficiently to flip the elec- tron spin. Although the arguments given in those works 18,19 to explain the intriguing results seem perfectly sensible, nev- ertheless, the interesting diversity of results suggests a need for theoretical enquiry. Ferromagnetic ordering in p -doped diluted magnetic semiconductors has attracted much attention from both experimentalists 22 and theorists. 23 In particular carrier in- duced ferromagnetism has been observed in modulation doped p -type Cd 1 -x Mn x Te QW’s with Curie temperatures between 1 and 5 K. 24,25 It has been proven that the antifer- romagnetic coupling of the hole spin with the magnetic spin PHYSICAL REVIEW B 68, 125317 2003 0163-1829/2003/6812/1253176/$20.00 ©2003 The American Physical Society 68 125317-1