L.Besombes Y.Leger H. Boukari D.Ferrand H.Mariette J. Fernandez- Rossier CEA-CNRS team « Nanophysique et Semi-conducteurs » Institut Néel, CNRS Grenoble, FRANCE Department of applied physics, University of Alicante, SPAIN Optical control of an individual spin

Introduction  Ultimate semiconductor spintronic device: Single magnetic ion / individual carriers -Control of the interaction between a single magnetic atom and an individual carrier. (spin injection, spin transfer) -Manipulation of an individual spin (memory, quantum computing) II-VI Semi-Magnetic semiconductor QDs Localized carriers Magnetic doping (Mn: S=5/2) …Towards a single spin memory.

Theoretical proposals Transport: A single QD containing a Mn atom could be use as a spin filter Nano-magnetism : electrical control of the magnetism. Hawrylak et al. Phys. Rev. Lett. 95, (2005) Qu et al. Phys. Rev. B74, (2006) Memories : writing and reading of the spin state of a single Mn atom. A.O. Govorov et al., Phys. Rev. B 71, (2005)

1. Probing the spin state of a single Magnetic atom - II-VI magnetic self assembled QDs - Carriers-Mn exchange interaction - Importance of QD structural parameters on the spin detection (Shape anisotropy, valence band mixing) 2. Carrier controlled Mn spin splitting - Anisotropy of the hole-Mn interaction - Charge tunable Mn-doped QDs 3. Carriers and Mn spin dynamics Outline

 UHV-AFM image of CdTe QDs on ZnTe. QDs density: cm -2 Size: d=15nm, h=3nm (Lz<<Lx,Ly)  TEM image of CdTe QDs on ZnTe. Individual CdTe/ZnTe QDs 100  m  Micro-spectroscopy.

J z =+1 J z = -1 Jz= - 2 J z = +2 G.S. B=0 eheh eheh -- ++ e: spin 1/2 h: anisotropic (J z =  3/2) Jz= -3/2 Jz= -1/2 Jz= +3/2 Jz= +1/2 Sz= +1/2 Sz= -1/2 ++ -- e hh lh Optical selection rules: z Optical transitions in an individual QD

 Electrical control of the charge.  Transfer of holes from the surface states: p type doping of the QDs. V p-ZnTe CdTe Gated charged quantum dots

Te Cd Mn Mn remplace Cd: Mn 2+ Mn 2+ S=5/2, 2S+1=6 Cd: 3d 10 4s 2 Mn: 3d 5 4s 2 Exchange interaction: Mn - electron Mn - hole Mn doped II-VI QDs Electron: σ = 1/2 Hole: j Z = ±3/2 Mn atom: S = 5/2  nm  nm h

 The presence of a single magnetic atom completely control the emission structure. Measurement of the exchange interaction energy of the electron, hole, Mn Phys Rev Lett. 93, (2004) Emission of Mn-doped individual QDs

X X+Mn 2+ S z = ±5/2, ±3/2, ±1/2 Mn 2+ -5/2 J z = -1 eheh J z = +1 eheh -3/2 -1/2 +1/2 +3/2 +5/2 J z = -1 eheh +5/2 +3/2 +1/2 -1/2 -3/2 -5/2 Exchange constant: s-d,  >0 p-d,  <0 J z = +1 eheh Heavy hole exciton Mn 2+ Heavy-hole exciton / Mn exchange coupling

X X+Mn 2+ Heavy hole exciton Mn 2+ -- -5/2 +5/2 … ++ -5/2 … 1 photon (energy, polar) = 1 Mn spin projection  Overall splitting controlled by I e-Mn and I h-Mn. Heavy-hole exciton / Mn exchange coupling

 Magnetic field dependent PL intensity distribution. N Mn =0N Mn =1 Mn-doped individual QDs under magnetic field

eheh Mn 2+ eheh eheh B eheh ++ -- B Jz = -1 Jz = +1 g Mn =2 Mn spin conservation Mn spin polarization  Boltzmann distribution of the Mn-Exciton system: T eff =12K Polarization of the Mn spin distribution

 Resonant excitation Complex excited states fine structure Selection of Mn spin distribution and spin conservation during the lifetime of the exciton. Statistic Mn spin distribution B=0T

0 1 2 Energy (meV) Th.Exp. Effective spin Hamiltonian: Carriers-Mn exchange coupling - X-Mn Overlap - QD shape - Strain distribution

 I e-Mn in a flat parabolic potential: Exchange integrals controlled by the overlap with the Mn atom. Decrease of X-Mn overlap 1.3 meV Detection condition: Exciton-Mn overlap

Influence of the QD shape Phys Rev Lett. 95, (2005) Influence of the valence band mixing Jz=+ - 3/2 Jz=+ - 1/2 Sz= +- 1/2 e hh lh Phys Rev B. 72, (R) (2005) QD3QD1QD2 Heavy-hole + Mn Detection condition: Structural parameters

 Inhomogeneous relaxation of strain in a strained induced QD (Bir & Pikus Hamiltonian): |3/2> |1/2> |-1/2> |-3/2> |3/2> = c1 |3/2>+ c2 |-1/2> c1>>c2 |-3/2> = c3 |-3/2>+ c4 |1/2> c3>>c4 ~ ~ = 0 ~ ~ via cross components because k     E   Valence band mixing in strained induced QDs

Allows simultaneous hole-Mn spin flip Possibility to flip from j z =+3/2 to -/3/2 via light holes Effective h-Mn interaction term in the Heavy hole Subspace eheh eheh  lh : Heavy-light hole mixing efficiency XX+Mn 2+ ~ ~ Influence of valence band mixing

Allows simultaneous hole-Mn spin flip Effective h-Mn interaction term in the Heavy hole Subspace eheh eheh  lh : Heavy-light hole mixing efficiency Exp. Th. Emission of “non-radiative” exciton states Possibility to flip from j z =+3/2 to -/3/2 via light holes ~ ~ Phys Rev B. 72, (R) (2005) Influence of valence band mixing

X-Mn in transverse B field «0» B // Faraday B┴B┴ Voigt Voigt: Complex fine structure… Suppression of the hole Mn exchange interaction Faraday: Zero field structure is conserved 001 «+1 »«-1 » Phys Rev B. 72, (R) (2005)

1. Probing the spin state of a single Magnetic atom - II-VI magnetic self assembled QDs - Carriers-Mn exchange interaction - Importance of QD structural parameters on the spin detection (Shape anisotropy, valence band mixing) 2. Carrier controlled Mn spin splitting - Anisotropy of the hole-Mn interaction - Charge tunable Mn-doped QDs 3. Carriers and Mn spin dynamics

Increase of the excitation density Increase of the number of carriers in the QD. Formation of the biexciton (binding energy 11meV) Similar fine structure for the exciton and the biexciton. eheh X X2X2 eheh Biexciton in a Mn-doped QD

 Optical control of the magnetization: - One exciton splits the Mn spin levels - With two excitons, the exchange interaction vanishes… X 2 (J=0) X, J=±1 G.S. σ + σ - Phys Rev B. 71, (R) (2005) Carrier controlled Mn spin splitting

Charge tunable sungle Mn-doped QDs allow us to probe independantly the interactions between electron and Mn or hole and Mn eheh eheh Phys Rev Lett. 97, (2006) Gated charged Mn-doped quantum dots

I e-Mn = 40 μeV I h-Mn (X+)= 95 μeV I h-Mn (X)= 150 μeV I h-Mn (X-)= 170 μeV ♦ The hole confinement is influenced by the Coulomb attraction X+, Mn X, Mn X-, Mn Mn h e Increasing the hole-Mn overlap by injecting electrons in the QD X+, Mn hardly resolved eheh eheh Variation of hole-Mn exchange interaction

J=3 J=2 Final state: 1 e + 1 Mn Isotropic e-Mn interaction Anisotropic h-Mn interaction Initial state: 1 h + 1 Mn eheh eheh  Negatively charged exciton in a Mn doped QD

J=3 J=2 ♦ Optical transitions between: Proportional to the overlap: Eigenstates of H e-Mn J z =-1 Optical recombination of the charged exciton

J=3 J=2 Energy Probability 1 Optical recombination of the charged exciton

J=3 J=2  Energy Probability 1 Optical recombination of the charged exciton

J=3 J=2  Energy Probability 1 e-Mn: isotropic h-Mn: anisotropic Optical recombination of the charged exciton

J=3 J=2 Final state: 1 e + 1 Mn Initial state: 1 h + 1 Mn eheh (+3/2,-1/2) (-3/2,+1/2)  Phys Rev Lett. 97, (2006) Charged exciton in a single QD: Influence of VBM

J=3 J=2 Final state: 1 e + 1 Mn Initial state: 1 h + 1 Mn eheh (+3/2,-1/2) (-3/2,+1/2)  Charged exciton in a single QD: Influence of VBM

♦ X-, Mn♦ X+, Mn e, Mn h, Mn e, Mn ♦ Reversed initial and final states J=3 J=2 Negatively / Positively charged Mn-doped QDs

Heisenberg STST Q=-1Q=0Q=+1 Free hh Ising MzMz Mn+1h= Nano-Magnet Energy Gated controlled magnetic anisotropy

1. Probing the spin state of a single Magnetic atom - II-VI magnetic self assembled QDs - Carriers-Mn exchange interaction - Importance of QD structural parameters on the spin detection (Shape anisotropy, valence band mixing) 2. Carrier controlled Mn spin splitting - Anisotropy of the hole-Mn interaction - Charge tunable Mn-doped QDs 3. Carriers and Mn spin dynamics

Spin dynamics vs photon statistics 1 photon (σ, E) 1 Mn spin state 1 Mn atom S z If S z (t=0) = -5/2 t 0 1 ~1/6 -5/2 ? P (S z = -5/2) -- -5/2 +5/2 … ++ -5/2 … Photon statistics ?

Correlation measurement on single QDs Use of a SIL to increase the signal Select a QD with a large splitting to spectrally isolate a Mn spin state Single emitter statistics : Antibunching: The QDs cannot emit two photons with a given energy at the same time Whole PL autocorrelation

Single Mn spin dynamics Auto Correlation on one line in one polarization One Mn spin projection XX+Mn 2+ E τ X-Mn Photon bunching at short delay 8 ns t  +, -5/2)

Auto Correlation on one line in one polarization σ + One Mn spin projection XX+Mn 2+ E τ X-Mn Single Mn spin dynamics Mixing between Mn spin relaxation time and X-Mn spin relaxation time 2 x P 0 P0P0 3 x P 0 Power dependence

Single Mn spin dynamics -- -5/2 +5/2 … ++ -5/2 … Direct evidence of the spin transfer Polarization Cross-Correlation σ + One Mn spin projection σ - Influence of magnetic field?...To be continued…

 Optical probing of a single carrier/single magnetic atom interaction. - The exchange coupling is controlled by the carrier / Mn overlap. - BUT, real self assembled QDs:- Shape anisotropy - Valence band mixing …. Store information on a single spin?  Hole-Mn complex is highly anisotropic but non-negligeable effects of heavy-light hole mixing  Charged single Mn-doped QDs: Change the magnetic properties of the Mn with a single carrier. Summary  Photon statistics reveals a complex spin dynamics.