1. Dynamics of collective spin excitations in n-doped CdMnTe quantum wells M. Vladimirova, P. Barate, S. Cronenberger, D. Scalbert Groupe d'Etude des Semi-conducteurs, CNRS and University Montpellier 2, France

2. CdMnTe Te Cd Mn Diluted Magnetic Semiconductors II-VI Cd 1-x Mn x Te, Zn 1-x Mn x Te Cd 1-x Mn x Se, Cd 1-x Mn x S III-V Ga 1-x Mn x As, In 1-x Mn x As New Ga 1-x Mn x N, Zn 1-x Mn x O, Ge 1-x Mn semiconductors magnets DMS: introduced by R. GAŁAZKA in ~1970

3. Diluted Magnetic Semiconductors Paramagnetic at low Mn content Carrier-induced ferromagnetism  few K in p-doped II-VI  up to ~ 200K in III-V localized magnetic moments J=5/2 (5 d-electrons) Mn 2+ exchange interaction with s anp p-type carriers CdMnTe Te Cd Mn B CB VB More about DMS : Cibert and Scalbert, in Spin Physics in Semiconductors, ed. by M. Dyakonov, Springer 2008

4. Diluted Magnetic Semiconductor Quantum Wells CdMnTe Te Cd Mn CdZnMgTe MBE-growth  -doping 2DEG densities of carriers (2D) & Mn (3D) Coulomb interactions in 2DEG Exchange interactions between spins: carrier – Mn 2+ Possibility to study strongly polarised 2DEG in the abscence of significant orbital quantisation B hh B

5. Spin excitations of a polarized 2DEG : in-plane field Polarized 2DEG B EFEF B0B0 Z E B=B 0 q B B0B0 Z E 1 4 Spin excitations: single-particle picture Coulomb interactions q B B0B0 E Z Z*Z* Z spin wave increase single-particle spin excitations Boukari et al, PRB (2006), Perez et al, PRL 99 (2007) spin-flip wave Jusserand et al, PRL (2003) Perez, PRB (2009) spin polarization

6. Spin excitations of 2DEG coupled to Mn: transverse coupling Resonant coupling of delocalized electron and localized Mn spin-flip excitations at low concentrations Mn spin-flip Spin wave Single-particle spin-flip E B Possible spin excitations of a 2DEG embedded in a CdMnTe QW Studied by time-resolved Kerr rotation Mn e-e- E B electron x=1% x=0.2% x=0 Cd 1-x Mn x Te ? ? x ~ 0.2%

7. Time-resolved Kerr rotation MM  K ~M  Magneto-optical Kerr (Faraday) effect |↑  |0  ++ B B Under in-plane field circularly polarised light creats a coherent superposition of |↑  and |↓  states ↔ spin polarisation in the direction of the light Optical orientation Non-equilibrium spin polarisation precesses around magnetic field photo-excitation of polarised carriers transfer of spin polarisation to resident carriers (eg via trion formation) coherent rotation of an existing magnetisation (eg via a Raman process)

8. Time-resolved Kerr rotation t pump probe Wollaston Balanced photodiodes (spectrally filtered) optical bridge ~3° Characteristic frequency  Transverse spin dephasing time T 2 * Electron, hole and Mn spin contributiions in DMS electron Larmor frequency scales with magnetization Mn electron

9. Samples CdZnTe 15% Zn CB VB I 2+ 2DEG CdMnTe QW Al 2+ CdZnTe 15% Zn W ~0.2% Mn SamplesM1120M2126M1118011609B2 n e (cm -2 )1.34x10 11 2.4x10 11 2.85x10 11 2.9x10 11 E F (meV)3.15.56.56.6 x eff (%)0.240.290.250.26 W (nm)101510 12 Grenoble Warsaw

10. Observation of mixed modes in TRKR

11. Measured frequency agrees with calculated spin-wave frequency frequency of the spin wave determined by Raman scattering single-particle spin flips are not observed: S  = 0 Identification of the observed mode as a spin wave

12. Mean-field model of mixed e-Mn spin waves coupled Bloch equations for e and Mn precession q=0 electron spin wave total spin q=0 Mn spin wave total spin linearized and solved for small transverse spin fluctuations and Model for spin wave with q non zero exists but must include e-e interactions Shmakov et al, arXiv May 2010 Coupled by s-d exchange

13. Mode frequencies of mixed spin waves ++ --  -- ++ Do not couple to Mn spins ++ -- incoherent single-particle spin-flips

14. Determination of electron spin polarization from the gap  , w, , known parameters of QW  n e determined by PL and Raman  ,  e determined from TRKR Theory from Attaccalite et al PRL 2002 Spin polarization strongly enhanced with respect to non-interacting Fermi gas

15. Existence of a third long-living spin excitation mixed modes third mode

16. Long-living mode identified as pure Mn precession not explainable in framework of MFA g=2 N Mn ions coupled to electrons  N+1 modes

17. Spin precession modes mixed modes antisymmetric Mn mode beyond MFA: Vladimirova et al, PRB 2008 2 coupled modes : correspond to the rigid spin approx N-1 vibration modes where total transverse Mn spin polarization is zero but individual spins precess while electron spin remains parallel to the field

18. Conclusions Summary of what is known Jusserand et al PRL 2003 (Raman): single-particle and collective spin excitations in a polarized 2DEG Gomez et al, PRB 2010 (Raman): Damping of spin waves  q2 Teran et al PRL 2003 (Raman+EPR): mixed e-Mn modes due to s-d exchange Vladimirova et al, PRB 2008 (TRKR) : Dynamics of mixed e-Mn modes: influence of spin lifetime on the gap between mixed modes existence of uncoupled Mn modes Perez et al, PRL 2007 (Raman), Boukari et al, PRB 2007 (PL): Spin susceptibility enhancement due to e-e (or h-h) interactions Barate et al, PRB 2010 (TRKR) e-e interactions strongly enhance the gap between mixed e-Mn modes:  enhancement mixed modes are spin waves (q=0) TRKR probes collective spin modes (individual spin-flip not seen) Perspectives Dynamics of spin waves with q≠0 (FWM) Study of high mobility 2DEG in CdMnTe QWs

19. F. Perez Institut des Nanosciences de Paris, CNRS and University Paris 6, France H. Boukari, J. Cibert Institut Néel, CNRS and Université Joseph Fourier, Grenoble, France T. Wojtowicz, J. Kossut Institute of Physics, Warsaw, Poland A.P. Dmitriev Ioffe Institute, Sankt-Petersburg, Russia Aknowledgements

20. Existence of a third long-living spin excitation The third mode is only observed in the samples where Mn spin resonance show up at low field

21. B S J What about Larmor theorem Out of resonance Larmor theorem is satisfied e - -Mn 2+ exchange interaction is spin rotation invariant Anticrossing = Larmor theorem breakdown ? Mn electron J resonance Larmor theorem can not be applied in our case because the transverse part of the exchange interaction  S x J x +  S y J y is not rotation invariant Collective properties of 2DEG are important even in the homogeneous case B S Electron in the effective field created by Mn spins = longitudinal part of the exchange interaction ~  S z J z NO

22. First observation of mixed e-Mn modes: spin-flip Raman scattering Experiments : Teran et al, PRL (2003) EPR and Raman scattering Dynamics? Theory : König, MacDonald PRL (2003) collective spin excitations  HP-boson partition function Finite spin relaxation times not taken into account Cd 0.998 Mn 0.002 Te QW :  ~20  eV

23. A (maybe) better model: one electron coupled to N Mn 2 coupled modes : correspond to the rigid spin approx For spins this corresponds to : total transverse Mn spin polarization is zero but individual spins precess electron spins remains parallel to the field N+1 modes N-1 vibration modes blue oscillator does not move e Beyond MFA : two-coupled (mixed modes) + N-2 uncoupled (pure) modes Vladimirova et al, PRB 2008

24. Time-resolved Kerr rotation 11 11 11 jQ  1 M -jQ  1 M 0 0 00  = Static polar MOKE/Faraday effects M Time-resolved MOKE/Faraday effects M created or modified by a pump pulse M  I pump n ± = n ± n 2 I pump optical Kerr effect M≠0  in all cases spins precess with the same phase in a transverse magnetic field Propagation along z : n ± +jk ± =  1 1/2 (1 ± QM/2) Faraday rotation :  F =  (n + -n - )L/  nLRe(Q)M/ Kerr rotation :  K = Im(Q/(n(n 2 -1)))M FF KK Collective spin excitation (interacting spins) Individual spins excited in phase (non- interacting spins) TRKR probes : photo-excitation of polarized carriers transfer of spin polarization to resident carriers (eg via trion formation) coherent rotation of an existing magnetization (eg via a Raman process)

25. Mn 3d 5 СBСB VB E g (x)  2 eV 3 eV