From magnetic polarons to magnetic quantum dots. Jacek Kossut, Institute of Physics of the Polish Academy of Sciences

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1 From magnetic polarons to magnetic quantum dots Jacek Kossut, Institute of Physics of the Polish Academy of Sciences 1

2 Diluted magnetic semiconductors Magnetic Polarons Self-assembled dots of CdMnTe: Formation Microluminscence line width Magneto microluminescence Modelling MnTe dots Single Mn in a dot 2

3 Diluted magnetic semiconductors (DMS) Substitute nonmagnetic atom in a compound semiconductor with a TM or RE Mn in II-VI semicondutors: isoelectronic impurity Mn in III-V semiconductors: acceptor when in substitutional position Mn-Mn exchange coupling: antiferromagnetic (in III-V s and highly p-type doped II-VI s: possiblity of effective ferromagnetism) Two fairly independent systems of electrons: localized d and contributing to the valence and conduction (i.e., delocalized) s and p S=5/2 For high dilution: paramagnetism 3

4 Diluted Magnetic Semiconductors (e.g., Cd 1-x Mn x Te) r r E = J ( j S) sp d for conduction electrons (direct exchange): J = 0.2 ev for valence band holes (hybridization): J ~ - 1 ev Giant spin splitting E = xj < S > spin x < S > ~ M ( B, T ) z z = * Espin g µ BB g * ~ 200 4

5 Example of proportionality of the spin splitting and the magnetization in CdMnTe, after Gaj et al.,

6 Twardowski et al.,ssc,

7 conduction n-dms DMS n-dms valence 7

8 Magnetic polarons Yanase, Kasuya, von Molnar (MS: EuS) Nawrocki, Golnik, Gaj, Ginter, Wolff, Heiman, Warnock (early exp. On II-VI DMS) Dietl, Spalek, Wolff, Thibblin (theory, role fluctuation) Yakovlev, Kavokins (low dimensions.) Benoit a la Guillaume, Bhattacharjee. 8

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10 U. Thibblin, thesis 10

11 Raman scattering 11

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13 Mean field approximation not sufficient Role of thermal fluctuation of magnetization within the polaron (finite size of the polaron) Suppression of spin fluctuation by an external magnetic field reduction of polaron binding energy 13

14 Are MP s stable? Not really Primary localization needed in most of the cases (donor or acceptor bound magnetic polarons) Lower dimensionality helps (just like it helps in binding electrons to donors) Excitons can dress up in a cloud of magnetization 14

15 Free energy functional F( a) = H ( a) TS( a) H = E + U + H + H + H e.g., k f SS sp d 2 U = e / r or size quantization, H f = Zeeman H sp d depends on ψ (r) 2 15

16 Mean field approximation 0 2ε p tanh = 0 2kBT ε T p H = 0 2 α χ 32 π a ( gµ ) B 0 or strong fields ( >> ε, k T ) = 2ε = p = 0 ( =0) k T 12 ( ε k T ) ε p B p B 0 1/ 2 p B 16

17 Dietl and Spałek, PRL 48, 355 (1982) 17

18 Self-assembled dots 18

19 Effect of elastic strain during growth of lattice mismatched materials 19

20 Cross section TEM of CdTe self-assembled QD in ZnTe matrix 20

21 a ZnTe =6.10 Å; a CdTe =6.48 Å ZnTe-CdTe lattice mismatch a/a: 6% a/a decreases slightly upon addition of Mn a MnTe (cubic)=6.28 Å 21

22 Formation of quantum dots Cd 0.2 Zn 0.8 Te 0.7µm CdTe 4µm GaAs SI Tinjod F, Gilles B, Moehl S, Kheng K, Mariette H. Applied Physics Letters, vol.82, no.24, 16 June 2003, pp

23 High resolution TEM image of self-assembled CdTe/ZnTe quantum dots 23

24 PL i µ-pl from CdTe/ZnTe SAD Intensity au. mikro-pl Broad PL spectrally similar to intra-mn PL SAD signatures: linewidth about 150ueV Intermittency PL E[eV] 24

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26 How to introduce Mn? 26

27 Introduction of Mn ++ into the dots: three ways in the literature S. Mackowski et al., Appl. Phys. Lett. 83, 3575 (2003). 4ML CdTe Mn-layer ZnTe Open Mn effusion cell for several seconds before CdTe deposition Due to high T, Mn diffuses into QD s G. Bacher et al., Phys. Rev. Lett. 89, (2002). DMS barriers and diffusion CdSe ZnMnSe Observe magnetoptic effects due to QD s or barriers? 1 2 L. Besombes et al., Phys. Rev. Lett. 93, (2004) CdTe ZnMnTe ZnTe Remote Mn layer grown several ML prior to QD layer Diffusion Strong dilution. Dots with single Mn observe 3 27

28 Besombes et al., PRL (2004) H int = I e σs I h j S I e-h σj 28

29 microluminescence 29

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31 M.Dobrowolska, S. Mackowski 31

32 APERTURES IN NONTRANSPARENT MASKS 700 nm and 150 nm apertures in a metallic mask for microluminescence studies Maćkowski, Pulizzi (Warsaw, Nijmegen cooperation) 32

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34 For magnetic polarons: T. Dietl, JMMM 38,34 (1983) Fluctuation of spin degree of freedom => broad lines! for polarons for dots: ε p Γ = Mn B 2ε p k B T 2 J = χ( T, B) π a g µ χ( T, B) M = B ε d = 2 J χ( T, B) 2 2 2V g µ d Mn B 34

35 Structure of the sample CdTe CdMnTe CdTe CdTe 2ML CdMnTe 2ML CdTe 2ML cap layer 4µm substrate 100 nm ZnCdTe 0.7µm Zn = 80 % CdTe GaAs Mn=1% Composition of the barrier: Avoidance of the influence of the intra Mn transition at 2.1eV PL at energies above the intra Mn transition is strongly affected. (Decrease of the intensity) Decrease of the barrier potential with the increasing amount of Cd in the ZnCdTe barrier Decrease of the lattice mismatch, which is the driving force for the QDs formation Zn 0.8 Cd 0.2 Te - good choice 35

36 Quantum dots CdTe/CdZnTe Different Zn composition in the barrier P L - s p e c t r a Intra Mn transition!! T = 8 K Non resonant excitation: Ar-laser 476 nm ( 2.6 ev ) Z n = % Z n = 8 5 % intensity au. Z n = 7 1 % Z n = 6 0 % cap layer 100nm CdZnTe 4µm CdTe Z n = 4 8 % substrate GaAs E [ e V ] 36

37 Role of intra-mn transition in PL measurements J. Seufert et al.., Phys. Rev. Lett. 88, , (2002) If QD PL above intra-m transition (2.1eV), there occurs an effecive energy transfer from excitons to 3d electrons of Mn. This leads to a considerable shartening of the luminescence lifetimeτ<20 ps and considerable weakening of excitonic PL intensity from QDs. Moreover, the intensity is stronly magnetic fielddependent On the other hand, formation of magnetic polarons inhanced if excitonic PL below intra-mn transitions 37

38 Typical size of a quantum dot HR TEM image 2nm 20nm S. Kret, P. DłuŜewski, to be published estimated the number of cation sites in this QD: ~4400 Therefore the number of Mn-ions: N = Mn 1 3 N Mn = 15 38

39 Semimagnetic quantum dots CdMnTe / CdZnTe CdTe 2ML CdMnTe 2ML CdTe 2ML Sample:032404B T=1.7K exc. power 40µW T cap layer 4µm substrate 100nm CdZnTe 0.7µm CdTe GaAs intensity au E[eV] -6T 39

40 Microluminescence of CdMnTe/CdZnTe QDs QDs CdMnTe: Mn=1% / CdZnTe: Zn=80% T=1.6K, Faraday configuration, magnetic field perpendicular to the growth axis. 1.0 polarization B [T] 40

41 Shift of PL lines with the magnetic field E 0 =1.8293eV 30 E s = 38.7meV + 2.9meV= 41.6meV E[eV] E E[meV] meV B[T] B[T] 41

42 Shift of peak position vs magnetic field σ + σ - T eff = 3.91K T real = 1.5K E B = 4.8 mev E [mev] Ε Β = 4.8 mev B [T] 42

43 (a) (b) energy shift [mev] 2.0 Magneto-optical data (a) shift of the energy position (b) spectral width QD I T=3.6K E=4.8eV E (a) energy shift [mev] (b) QD II T=1.6K E=0.9eV E FWHM [mev] FWHM [mev] B[T] B[T] 43

44 Mn ++ (2) S=5/2 (1) ψ 2 = 1 V = r 0 Model of a Spin Molecule const (3) e - outside inside QD QD 3 r r sd i i = 1 Hˆ = J S s Electron wave f. Exchange int. For cond. band 3 α E( J, S) = 2 ( J ( J + 1) S( S + 1) ) J S 2 V i= 1 S 6 ˆ α r r r r α r r H = ( S S r 1 + S2 + S3) s = S s V V ˆ α r ( ) 1 H ˆ r r = 2 J S s ˆ r J = S + s, Ĵ V Total Mn spin ff = ψ ( r) u( r) α = Hˆ = α S r r is ψ ( Ri ) 2 Envelope f. and S r u( r) J sd u( r) = ± commute with Ĥ S= N, N 1,... Mn 2 Mn 2 Bloch f. 44

45 I initial state Model of a Spin Molecule electron hole ˆ α r r β r rr r r H ˆ ˆ ˆ I = S s + S j + gµ BBS + geµ BBs + ghhµ BBj V 3V ˆ α r r β H = S s + Sˆ ˆj ˆ ˆ ˆ I Z + gµ B S + g µ B s + g µ B j V 3V B Z Z e B Z Z hh B II Final state rr H = gµ BS ˆ F B H = gµ B Sˆ ˆ F B Z Z Z Z Z e - hh 45

46 ghsl g(s) Model of a Spin Molecule 10 Mn ++ g(s) combinatiroal factor how many ways to achieve a given total Mn spin J=S+1/ DensityDOS of states energy Intensity a.u. J=S-1/2 S total spin N cat =2500 T=10K B=0T Total Energy [mev] Energy [mev] energy@mevd Density of states The energy calculated from H I, density of states defined by g(s) PLspectrum E I I = exp( ) g( S ) S, m, j, j, s, m σ ± S, m kt s z e Energy of the transition given by the difference E I -E F 46 s 2

47 COMPARISON FOR SAMPLE II experiment modelling Intensity au. B=6T B=6T N Mn =4 N kat =2000 T=5K B=0T B=0T E[eV]

48 Sample II - comparison experiment modelling N Mn =12 B=4T B=3T B=2T B=1T Intensity au. B=4T B=3T N kat =4000 T=5K 0.6 B=2T 0.4 B=1T B=0T B=0T E[eV]

49 Splitting [mev] E[eV] 49

50 Sample I: x Mn =0.03±0.003 PL-intensity a.u. 7T 6T 5T 4T 3 T 2T 1T PL-intensity a.u. 7T 6T 5T 4T N M n = 1 50; N ca t = 56 00; x= ; J d -d = 1.9K T = 3K 3T 2T 1T E [ev ] E [m ev ] (a) Magnetic field dependence of an individual diluted magnetic QD from sample I (b) simulation in terms of the muffin tin model: N cat =5600; N Mn = 150; T=3K; J d-d =1.9K N cat =6280 x=0.033 N cat =1100 x= energy shift [mev] x= position at B=0T 5 50

51 CdTe/ZnTe QD with one Mn at 4 T sigma minus sigma plus Intensity (arb. u.) Energy (ev) 51

52 More topics Charged dots (Leger et al.) Inter-Mn interactions (Hawrylak et al..) Playing with sp-d interaction strength 52

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54 One Mn per (charged) dot [Leger et al. PRL 97, (2006)] 54

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57 The influence of the NNN ion-ion interaction? E[eV] B c =2.8 T J NNN =0.8k B B[T] 57

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59 Magnetoluminescence from CdMnTe Quantum Dots Piotr Wojnar, and Grzegorz Karczewski Institute of Physics, Polish Academy of Sciences, Warsaw, Jan Suffczyński, Katarzyna Kowalik and Andrzej Golnik Institute of Experimental Physics, Warsaw University, Warsaw 59

60 acknowledgements SANDiE FP-6 Network Foundation for Polish Science Ministry of Scientific Research and Higher Education MP 60