Dynamics of collective spin excitations in ndoped Cd
- Slides: 25
Dynamics of collective spin excitations in n-doped Cd. Mn. Te quantum wells M. Vladimirova, P. Barate, S. Cronenberger, D. Scalbert Groupe d'Etude des Semi-conducteurs, CNRS and University Montpellier 2, France
Diluted Magnetic Semiconductors magnets semiconductors I DMS: introduced by R. GAŁAZKA in ~1970 II II IV V VI VII H 3 d VIII He Li Be B C N O F Ne Na Mg Al Si P S Cl Ar K Ca Sc Ti V Cr Rb Sr Y Zr Nb Mo Cs Ba La Hf Ta W Cd. Mn. Te Te Mn Cd Mn Re Fe Co Ni Cu Zn Ga Ge As Se Br Kr Ru Rh Pd Ag Cd In Sn Sb Te I Xe Os Ir Pt Au Hg Tl Pb Bi Po At Rn II-VI Cd 1 -x. Mnx. Te, Zn 1 -x. Mnx. Te Cd 1 -x. Mnx. Se, Cd 1 -x. Mnx. S III-V Ga 1 -x. Mnx. As, In 1 -x. Mnx. As New Ga 1 -x. Mnx. N, Zn 1 -x. Mnx. O, Ge 1 -x. Mn
Diluted Magnetic Semiconductors Te Mn 2+ localized magnetic moments J=5/2 (5 d-electrons) exchange interaction with s anp p-type carriers B Mn Cd Cd. Mn. Te CB VB • Paramagnetic at low Mn content • Carrier-induced ferromagnetism More about DMS : Cibert and Scalbert, in Spin Physics in Semiconductors, ed. by M. Dyakonov, Springer 2008 few K in p-doped II-VI up to ~ 200 K in III-V
Diluted Magnetic Semiconductor Quantum Wells d-doping Te B Mn Cd Cd. Mn. Te • densities of carriers (2 D) & Mn (3 D) • Coulomb interactions in 2 DEG Cd. Zn. Mg. Te MBE-growth B 2 DEG • Exchange interactions between spins: carrier – Mn 2+ • Possibility to study strongly polarised 2 DEG in the abscence of significant orbital quantisation hh
Spin excitations of a polarized 2 DEG : in-plane field Polarized 2 DEG E B=B 0 EF spin polarization Z B 0 Spin excitations: single-particle picture B E B=B 0 4 Z B 0 Coulomb interactions increase single-particle spin excitations 1 B E Boukari et al, PRB (2006), Perez et al, PRL 99 (2007) Z* spin wave spin-flip wave Z Jusserand et al, PRL (2003) Perez, PRB (2009) q B 0 B q
Spin excitations of 2 DEG coupled to Mn: transverse coupling Resonant coupling of delocalized electron and localized Mn spin-flip excitations at low concentrations Possible spin excitations of a 2 DEG embedded in a Cd. Mn. Te QW Cd 1 -x. Mnx. Te E x=1% E electron Single-particle spin-flip Mn ? e. Spin wave x=0. 2% Mn spin-flip Mn ? x ~ 0. 2% B x=0 B electron Studied by time-resolved Kerr rotation
Time-resolved Kerr rotation Optical orientation B |↑ B Non-equilibrium spin polarisation precesses around magnetic field s+ |0 Under in-plane field circularly polarised light creats a coherent superposition of |↑ and |↓ states ↔ spin polarisation in the direction of the light • 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) Magneto-optical Kerr (Faraday) effect QK~M M
Time-resolved Kerr rotation (spectrally filtered) t Mn probe ~3° pump electron Wollaston optical bridge Balanced photodiodes in DMS electron Larmor frequency scales with magnetization Characteristic frequency w Transverse spin dephasing time T 2* Electron, hole and Mn spin contributiions
Samples ~0. 2% Mn Cd. Zn. Te 15% Zn I 2+ Cd. Mn. Te QW CB 2 DEG VB Al 2+ W Grenoble Warsaw Samples M 1120 M 2126 M 1118 011609 B 2 ne (cm-2) 1. 34 x 1011 2. 85 x 1011 2. 9 x 1011 EF (me. V) 3. 1 5. 5 6. 6 xeff (%) 0. 24 0. 29 0. 25 0. 26 W (nm) 10 15 10 12
Observation of mixed modes in TRKR
Identification of the observed mode as a spin wave 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
Mean-field model of mixed e-Mn spin waves Coupled by s-d exchange q=0 electron spin wave q=0 Mn spin wave total spin coupled Bloch equations for e and Mn precession 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, ar. Xiv May 2010
Mode frequencies of mixed spin waves w- w+ d w+ w- t- t+ incoherent single-particle spin-flips Do not couple to Mn spins
Determination of electron spin polarization from the gap § a, w, h, known parameters of QW § ne determined by PL and Raman § D, d, ge determined from TRKR Theory from Attaccalite et al PRL 2002 Spin polarization strongly enhanced with respect to non-interacting Fermi gas
Existence of a third long-living spin excitation mixed modes third mode
Long-living mode identified as pure Mn precession g=2 not explainable in framework of MFA N Mn ions coupled to electrons N+1 modes
Spin precession modes mixed modes antisymmetric Mn mode • 2 coupled modes : correspond to the rigid spin approx beyond MFA: Vladimirova et al, PRB 2008 • N-1 vibration modes where total transverse Mn spin polarization is zero but individual spins precess while electron spin remains parallel to the field
Conclusions Summary of what is known • Jusserand et al PRL 2003 (Raman): single-particle and collective spin excitations in a polarized 2 DEG • Gomez et al, PRB 2010 (Raman): Damping of spin waves q 2 • 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: c 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 2 DEG in Cd. Mn. Te QWs
Aknowledgements 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
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
What about Larmor theorem Out of resonance Larmor theorem is satisfied Anticrossing = Larmor theorem breakdown ? e- -Mn 2+ exchange interaction is spin rotation invariant resonance B electron S NO Mn J Larmor theorem can not be applied in our case because the transverse part of the exchange interaction a. Sx. Jx+a. Sy. Jy is not rotation invariant S Electron in the effective field created by Mn spins = longitudinal part of the exchange interaction ~a. Sz. Jz Collective properties of 2 DEG are important even in the homogeneous case
First observation of mixed e-Mn modes: spin-flip Raman scattering Cd 0. 998 Mn 0. 002 Te QW : d ~20 me. V Experiments : Teran et al, PRL (2003) • EPR and Raman scattering • Dynamics? Theory : König, Mac. Donald PRL (2003) • collective spin excitations Ø HP-boson partition function • Finite spin relaxation times not taken into account
A (maybe) better model: one electron coupled to N Mn e 2 coupled modes : correspond to the rigid spin approx N+1 modes N-1 vibration modes blue oscillator does not move For spins this corresponds to : • total transverse Mn spin polarization is zero but individual spins precess • electron spins remains parallel to the field Beyond MFA : two-coupled (mixed modes) + N-2 uncoupled (pure) modes Vladimirova et al, PRB 2008
Time-resolved Kerr rotation Static polar MOKE/Faraday effects q. F q. K e= M e 1 j. Q e 1 M 0 -j. Q e 1 M e 1 0 0 0 e 1 Propagation along z : n± +jk± = e 11/2 (1±QM/2) Faraday rotation : q. F = p(n+-n-)L/l= pn. LRe(Q)M/l Kerr rotation : q. K = Im(Q/(n(n 2 -1)))M Time-resolved MOKE/Faraday effects M created or modified by a pump pulse M Ipump n ± = n ± n 2 Ipump optical Kerr effect • 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) M≠ 0 in all cases spins precess with the same phase in a transverse magnetic TRKR probes : field • Collective spin excitation (interacting spins) • Individual spins excited in phase (noninteracting spins)
СB Eg (x) 2 e. V VB 3 e. V Mn 3 d 5
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