Spin effects in diluted magnetic semiconductors

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 2France  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 BC Eg (x)~2 eV BV 3 eV Mn 3d5 II I II III IV V VI VII VIII H He Li Be B C N O F Ne Na Mg Al Si P S Cl Ar 3d K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr Rb Sr Y Zr Nb Mo Ru Rh Pd Ag Cd In Sn Sb Te I Xe Cs Ba La Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn CdMnTe 5/2 Mn 4s23d5 3/2 1/2 -1/2 -3/2 -5/2 S=5/2 Localized spins N0 concentration of cations X Mn fraction

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

4. Exchange interaction B B h+ e- Mn Mn ~meV ~meV exchange integral in the mean field approximation “Overhauser shift” 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”

5. Giant Zeeman Splitting +1/2 -1/2 +3/2 +1/2 -1/2 -3/2 Energy s + s - p CdMnTeelectron Magnetic field Allowed optical transitions

6. Nearest neighbors Mn-Mn pairs do not contribute in the effective field Large splitting only at low temperatures (T<10K) x → xeff; ;T→T+T0 ~x(1-x)12 x → xeff; ;T→T+T0 Modified brillouin function Gai, Planel, Fishman Solid State Commun 29, 435 (1979)

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

8. Optically excited CdMnTe QWs B Band diagram Magnetic field in Voigt configuration CB +1/2 hn se=1/2 -1/2 • 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 VB +3/2 -3/2 sh=3/2 hh +1/2 lh -1/2

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

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

11. B z y x How does the polarized light affect the Mn ions Impulsive coherent rotation of Mn • 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) holes electrons XZ is a QW plane

12. B B h+ e- Mn Mn How does the polarised light affect the Mn ions Energy and polarization transfer via spin-flip scattering TS 2 levels system In general Electron or hole spins out of equilibrium 0 1 Nup/Ndown e-Mn spin-flip time Other spin relaxation mechanisms • With electrons • With holes t,tSF<< tSL Mn spins, TS Spin-lattice relaxation Lattice, T=2K Ryabchenko et a, Sov. Phys. JETP 55, 951 (1982) CdMnTe 5%, exchange scattering with holes→ Mn spin cooling

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

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

15. 100 fs-1 ps Delay line Elasto-optical modulator Al2O3:Ti Chopper Optical bridge probe pump Millenia lock-in n°1 T > 1.8 K 0-6 T lock-in n°2 PC

16. CdMnTe QWs barrier QW1 QW2 QW3 QW4 QW barrier 10 nm 4.9 nm 1.9 nm CdMg0.27Te (15 nm) Iodine doped CdMg0.27Te (10 nm) Iodine doped QW - CdMn0.0052Te (8 nm) Barrier CdMg0.27Te (150 ML) CdTe/CdMgTe SL CdMg0.27Te (0.7 µm) 1010 3.1010 7.1010 1011 Buffer CdTe (6.7 µm) ZnTe (3 nm) Substrat GaAs (100) • Samples • Warsaw (GaAs substrate) • Grenoble (CdZnTe substrate)

17. Time-domain spin resonance Xeff=0.45%

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

19. Spontaneous magnetization patterning xeff=0.45%, T=2K, P=15W/cm2 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 • Two electron spin resonances in CdMnTe QW under femtosecond pulse excitation High excitation density G Mn spin temperature domains High magnetic field B • Equipartition of domain areas • Thot increases slightly with excitation density Resonant excitation Eexc

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

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

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

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

26. Linear stability of the steady-state homogeneous solution g=1  25W/cm2 Relevant dimentionless parameters : Mn and el-n relative diffusion Field Generation rate Temp-re two threshold values !

27. Numerical solution : Hysteresys loop Es=14 d=0.005 Tbath=2K t = 10-10 s g = 104 s-1 w0 = 10-4 cm2 /s N0a = 220 meV x = 0.0045 g =1018 cm-2 s-1 g=1  0.25 W/cm2 DMn/D=10-9

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

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

30. Spin-flip Raman scattering CdMnTe QW : 2d~20meV • 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 F. J. Teran et al, PRL 91, 077201 (2003) J. König and A. H. MacDonald PRL 91, 077202 (2003)

31. Samples CdZnTe 15% Zn CdMnTe QW CdZnTe CB 15% Zn 2DEG 2+ I VB 2+ Al 10nm ~0.2% Mn 2DEG density M1120 ne=0.7x1011 cm 2 M1118 ne=2.2x1011 cm-2 V. Huard et al, PRL 84, 167 (2000) LSP, Grenoble, France

32. M1118 (ne=2.2x1011cm-3)

33. M1120 (ne=0.7x1011cm-3)

34. Summary M1120 (ne=0.7x1011cm-3)

35. Mean field model B z y x Coupled Bloch equations Knight field Overhauser 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

36. Mean field model B z y x coupled oscillators : wMn, we, coupling energy • K,D depend on B, T, ne, NMn • gMn << ge Strong vs weak coupling anticrossing Relaxation rate changes

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

38. Summary M1120 (ne=0.7x1011cm-3) te=20 ps, tMn=2ns 2d=20meV tMP=40ps We should suppose that electron spins are fully polarized D=1.2 meV K=0.3meV

39. Summary M1118 (ne=2.2x1011cm-3) te=20 ps, tMn=2ns 30meV tMM=40ps 2DEG : spin polarization is 3 times stronger than expected from Fermi distribution K=0.4 meV, D=1.2 meV Electron spins are almost fully polarized

40. Thank you !

42. Strong vs weak coupling gMn << ge • The transition SC->WC is controlled by ge SC WC • SC : At resonance mixed modes have the same relaxation rate • WC : Strong modification of relaxation times geSC<geWC

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

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

45. Magnetic polaron at spin-flip resonance Resonance condition EeSF=EMnSF B=0 EeSF=EMnSF=0 2d N-1 degenerate states N degenerate states EeSF>>EMnSF R. Fiederling et al, PRB 58, 4785 (1998) <Sz> ~5/2-> 2d~eMP

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

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

48. TRKR at resonance few 10 ps ? Hole spin relaxarion ~few ps Free Mn precession ~ few ns M1118 ne=2.2x1011 cm-3 Questions • Mn : non interacting modes or electron-free spatial regions? • Relative contribution of Mn and electron spin polarization in TRKR signal

49. Conclusions • Measuring the dynamics of collective electron – Mn spin flip excitations : Rabi oscillation between pure electron and Mn states • Manipulating 2DEG : hn ->hh -> Mn ->2DEG • Coupled modes splitting can be used as a tool to measure the 2DEG susceptibility : strong enhancement of 2DEG polarization is observed Perspectives • Relative contribution of e- and Mn2+ spins in the TRKR signal • How one can increase the coupling and obtain longer spin relaxation times? Reduce inhomogeneous broadening!

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