1. Spin effects in diluted magnetic semiconductors M. Vladimirova, P. Barate, S. Cronenberger, F. Teppe and D. Scalbert, Groupe d'Etude des Semi-conducteurs, CNRS-Université Montpellier 2 France C. Misbah Laboratoire de Spectrométrie Physique, CNRS- Université Joseph-Fourier Grenoble, France T. Wojtowicz, J. Kossut Institute of Physics, Polish Academy of Sciences, Warszawa, Poland What is DMS : electrons, holes, magnetic ions and polarized light Manipulation of magnetic ions spins by light Pump-induced Kerr rotation technique Examples of spin effects in CdMnTe QWs : inhomogeneous Mn spin heating and mixed e-Mn spin excitations

2. Diluted magnetic semiconductors RnAtPoBiPbTlHgAuPtIrOsReWTaHfLaBaCs XeITeSbSnInCdAgPdRhRuMoNbZrYSrRb KrBrSeAsGeGaZnCuNiCoFeMnCrVTiScCaK ArClSPSiAlMgNa NeFONCBBeLi HeH VIIIVIIVIVIVIIIIII 3d II Mn 4s 2 3d 5 S=5/2 Localized spins -5/2 -3/2 -1/2 1/2 3/2 5/2 Mn 3d 5 BC BV Eg (x)~2 eV 3 eV CdMnTe N 0 concentration of cations X Mn fraction

3. Diluted magnetic semiconductors CdTe CdMnTe CdMnTe Paramagnetic n-CdMnTe Paramagnetic p-CdMnTe Ferromagnetic(T c =2K) Super exchange Localized electrons interacting with magnetic ions Carriers mediated interaction between magnetic moments ferromagnetism Antiferromagnetic clucters Magnetic polaron T. Dietl and J. Spalek, PRL 48, 355 (1982)

4. Exchange interaction “Overhauser shift” in the mean field approximation exchange integral ~meV ~  eV Exchange coupling is ferrromagnetic for electrons and antiferromagnetic for holes Out-of-equilibrium electrons depolarize Mn spins Out-of-equilibrium holes polarize Mn spins “Knight shift” Mn e-e- h+h+ B B

5. Giant Zeeman Splitting -3/2 -1/2 +1/2 +3/2 -1/2 +1/2 Energy  -  + CdMnTe electron  Magnetic field Allowed optical transitions

6. Large splitting only at low temperatures (T<10K) Nearest neighbors Mn- Mn pairs do not contribute in the effective field x → x eff; ;T →T+T 0 ~x(1-x) 12 Gai, Planel, Fishman Solid State Commun 29, 435 (1979) Modified brillouin function x → x eff; ;T →T+T 0

7. Magnetization = Mn density x Mn spin polarization Temperature dependenceMn content dependence

8. Optically excited CdMnTe QWs CB VB +3/2 -3/2 +1/2 -1/2 +1/2 s e =1/2 s h =3/2 hh lh Band diagramMagnetic field in Voigt configuration Hole Strong hh-lh splitting spin locked in the growth direction ↔ g-factor ~0 Fast spin relaxation ~few ps Electron Zeeman splitting + Exchange excitation with circularly polarized light pulse->spin precession Spin relaxation ~ few 10 ps B h

9. How does the polarized light affect Mn ions 1.Mn spin heating via mutual spin flips with optically created electrons 2.Mn spin cooling via mutual spin flips with optically created holes (bulk) 3.Impulsive coherent rotation of Mn by hole spin locked in the growth direction (QWs) 4.Magnetic polaron

10. How does the polarised light affect the Mn ions Magnetic polaron EFEF T. Dietl and J. Spalek, PRL 48, 355 (1982) Exchange energy gain : Mean field approximation is not valid at low fields N Mn ion spins e or h Electrons (holes) localized by the potential fluctuations or on donors

11. z x y B electrons holes Electrons : photocreated +2DEG -> spin precession Hole spin locked in growth direction -> impulsive coherent rotation of Mn Crooker et al PRL 77, 2814 (1996) Akimoto et al PRB 57, 7208 (1998) Impulsive coherent rotation of Mn How does the polarized light affect the Mn ions XZ is a QW plane

12. How does the polarised light affect the Mn ions Energy and polarization transfer via spin-flip scattering Ryabchenko et a, Sov. Phys. JETP 55, 951 (1982) CdMnTe 5%, exchange scattering with holes → Mn spin cooling 1)With electrons 2) With holes ,  SF  <<  SL Electron or hole spins out of equilibrium Mn spins, T S Lattice, T=2K e-Mn spin-flip time Spin-lattice relaxation Other spin relaxation mechanisms TSTS 10 N up /N down Mn e-e- h+h+ B B 2 levels system In general

13. = +  Rotation of the polarization plane in magnetic media Magneto-optical Kerr (Faraday) effect

14. Spin polarisation created by circularly polarized light probed by linearly polarized light as a function of time delay between pump and probe pulses Polarisation of the probe beam is rotated after reflection (transmission) from the polarized media tt probe K()K() sample pump Pump-induced Kerr (Faraday) rotation

15. lock-in n°2 Chopper probe pump Elasto-optical modulator Delay line PC Optical bridge lock-in n°1 T > 1.8 K 0-6 T Al 2 O 3 :Ti Millenia 100 fs-1 ps

16. CdMnTe QWs Barrier CdMg 0.27 Te (150 ML) QW - CdMn 0.0052 Te (8 nm) Buffer CdTe (6.7 µm) Substrat GaAs (100) CdMg 0.27 Te (10 nm) CdMg 0.27 Te (15 nm) CdMg 0.27 Te (0.7 µm) CdTe/CdMgTe SL ZnTe (3 nm) Iodine doped 1.9 nm 4.9 nm 10 nm QW barrier QW1QW2QW3QW4 10 3.10 10 7.10 10 10 11 Iodine doped Samples Warsaw (GaAs substrate) Grenoble (CdZnTe substrate)

17. Time-domain spin resonance X eff =0.45%

18. First example: Spatial instability of Mn spin temperature in CdMnTe QWs

19. Spontaneous magnetization patterning x eff =0.45%, T=2K, P=15W/cm 2 at high field and excitation density formation of domains with distinct Mn spin temperatures

20. High excitation density Low excitation density Domain temperature does not depend on magnetic field Domain temperature does not vary much with excitation power density

21. Summary of experimental results High excitation density G High magnetic field B Resonant excitation E exc Mn spin temperature domains Equipartition of domain areas T hot increases slightly with excitation density Two electron spin resonances in CdMnTe QW under femtosecond pulse excitation

22. Mn e Interpretation : Positive feedback loop for Mn heating e generation e recombination e diffusion Mn diffusion e-Mn spin-flip Mn spin relaxation coldhot cold x

23. Rate equations accounting for diffusion Electron diffusion and drift Mn spin diffusion Exchange potential  e Mn  + - EZEZ n+n+ n-n- 2V Spin flip rates

24. Linear stability of the steady-state homogeneous solution Time and space derivatives = 0  n + 0, N + 0 … n + = n + 0 + A + exp(  t+iqx); N + = N + 0 +B exp(  t+iqx) Calculate  (q) in the adiabatic approximation Linearly stable if  (q) < 0 for all q Unstable for q such that  (q) > 0 Relevant dimensionless parameters : FieldGeneration rateTemp-re Mn and el-n relative diffusion

25. Domain sizes! Mn diffusion defines the critical instability wavelength destroys the instability

26. Linear stability of the steady-state homogeneous solution g=1  25W/cm 2 two threshold values ! Relevant dimentionless parameters : FieldGeneration rateTemp-re Mn and el-n relative diffusion

27. Numerical solution : Hysteresys loop T bath =2K  = 10 -10 s  = 10 4 s -1  0 = 10 -4 cm 2 /s N 0  = 220 meV x = 0.0045 g = 10 18 cm -2 s -1 g=1  0.25 W/cm 2 D Mn /D=10 -9 E s =14 d=0.005

28. Second example: Collective spin-flip excitations of electron and Mn

29. Spin-flip excitation energies Anticrossing? resonance x=0.002 Electrons: Exchange and Zeeman splittings have different signs (  >0) Two coupled spin flip transitions Here exchange splitting saturatesZeeman splitting mainly, g e =-1.5 Mne-e-

30. Spin-flip Raman scattering F. J. Teran et al, PRL 91, 077201 (2003) J. König and A. H. MacDonald PRL 91, 077202 (2003) Experiments : EPR and Raman scattering Dynamics? Theory : ferromagnetism possible in n- CdMnTe QWs, Tc~0.4mK Finite spin relaxation times and interacting 2DEG susceptibility not taken into account CdMnTe QW :  ~20  eV

31. Samples CdZnTe 15% Zn CB VB I 2+ 2DEG CdMnTe QW Al 2+ CdZnTe 15% Zn 10nm 2DEG density M1120n e =0.7x10 11 cm 2 M1118n e =2.2x10 11 cm -2 LSP, Grenoble, France V. Huard et al, PRL 84, 167 (2000) ~0.2% Mn

32. M1118 (n e =2.2x10 11 cm -3 )

33. M1120 (n e =0.7x10 11 cm -3 )

34. Summary M1120 (n e =0.7x10 11 cm -3 )

35. Mean field model Coupled Bloch equations Overhauser field Knight field Relaxation terms We consider small deviations of the magnetization from z-axis and look for the dynamics of the transverse component of the magnetization B z x y

36. Mean field model B z x y coupled oscillators :  Mn,  e  coupling energy Strong vs weak coupling  K,  depend on B, T, n e, N Mn   Mn <<  e anticrossing Relaxation rate changes

37. + Initial conditions : photocreated electrons and holes +impulsive coherent rotation of Mn Solution of Bloch equations B  +,  -, eigen frequencies of the mixed modes B z x y

38. Summary M1120 (n e =0.7x10 11 cm -3 ) 2  =20  eV K=0.3  eV We should suppose that electron spins are fully polarized t MP =40ps t e =20 ps, t Mn =2ns  =1.2 meV

39. Summary M1118 (n e =2.2x10 11 cm -3 ) 30  eV Electron spins are almost fully polarized 2DEG : spin polarization is 3 times stronger than expected from Fermi distribution t e =20 ps, t Mn =2ns K=0.4  eV,  =1.2 meV t MM =40ps

40. Thank you !

42. Strong vs weak coupling SCWC SC : At resonance mixed modes have the same relaxation rate WC : Strong modification of relaxation times  e SC <  e WC  Mn <<  e The transition SC->WC is controlled by  e

43. Dynamics of coupled spins Strong coupling Weak coupling Rabi period

44. Magnetic polaron EFEF T. Dietl and J. Spalek, PRL 48, 355 (1982) Exchange energy gain : Mean field approximation is not valid at low fields N Mn ion spins e-e- Electrons localized by the potential fluctuations

45. Magnetic polaron at spin-flip resonance E e SF >>E Mn SF B=0 E e SF =E Mn SF =0 R. Fiederling et al, PRB 58, 4785 (1998) 22 Resonance condition E e SF =E Mn SF N degenerate states N-1 degenerate states ~5/2-> 2  ~  MP

46. Magnetic polaron /Mean field Magnetic polaron 2DEG if = 1/2 If if < 1/2 N Mn ion spins e-e- (N=N Mn /N e )  provides the information on the electron spin polarization

47. Time-resolved Kerr rotation B tt pump probe K  SyK  Sy + - z x y 100 fs pulses spectrally filtered -> ~ ps resolution Excitation power 250  W, resonant with hh exciton Pump-probe ratio 2:1 S y may include electron, Mn, hole or mixed mode contribution

48. TRKR at resonance Hole spin relaxarion ~few ps Free Mn precession ~ few ns M1118 n e =2.2 x 10 11 cm -3 Mn : non interacting modes or electron-free spatial regions? Relative contribution of Mn and electron spin polarization in TRKR signal Questions ? few 10 ps

49. Conclusions Measuring the dynamics of collective electron – Mn spin flip excitations : Rabi oscillation between pure electron and Mn states Manipulating 2DEG : h ->hh -> Mn ->2DEG Coupled modes splitting can be used as a tool to measure the 2DEG susceptibility : strong enhancement of 2DEG polarization is observed Relative contribution of e - and Mn 2+ spins in the TRKR signal How one can increase the coupling and obtain longer spin relaxation times? Reduce inhomogeneous broadening! Perspectives

50. n-CdMnTe QWs CdZnTe 15% Zn CB VB I 2+ 2DEG CdMnTe QW Al 2+ CdZnTe 15% Zn 10nm In-plane localization potential EFEF EFEF 0.2% Mn this work F. Teran and this work

51. Microcavities with DMS Magnetic tuning of exciton mode microcavity with 2 DMS QWs Reflectivity spectra for  + polarization +8 T -8 T 0 T H. Ulmer-Tuffigo et al, Superlattices and Microstructures 22, 383 (1997)

52. QW in a microcavity: N round trips of light in the cavity A. Kavokin et al, PRB 56, 1087 (1997)   ~ 3° in (In,Ga)As/GaAs QW microcavity @ 11.25T   ~ 140° in CdMnTe QW microcavity @ 1T M. Haddad et al, SSC 111, 61 (1999) Microcavities with DMS QW : Enhanced Faraday rotation