Magnetic Polarons in Concentrated and Diluted Magnetic Semiconductors

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1 Magnetic Polarons in Concentrated and Diluted Magnetic Semiconductors S. von Molnár Martech, The Florida State University, Tallahassee FL Gd 3-x v x S 4 Ref. 1 For: Spins in Solids, June 23 rd, Past support by DARPA and the Office of Naval Research, ONR N and MDA Spins in Solids 1

2 Example δm δρ(t) T C 25 K Ref. 2 The Insulator-metal transition at T C in Eu 0.95 La 0.05 S Why? Spins in Solids 2

3 Example δm δρ(t) Ref. 3 The Insulator-metal transition at T C in Eu 0.99 La 0.01 Se Spins in Solids 3

4 Extra Energy Term in Magnetic Semiconductors E S = g * µ B H + 2 J r s r S α S r α 1 2 : Value of S averaged over region occupied by electron, s 2 >> 1 Results in : Giant band splitting E S (EuS) ~ 0.5 ev Magnetic polarons Local FM order in PM host Spins in Solids 4

5 Europium Chalcogenides : EuX (X= O, S, Se, Te) Prototype System EuX : Prime example of concentrated magnetic semiconductor EuS, EuO : First ferromagnetic insulators (ideal Heisenberg ferromagnets) r J S σ r magnetism transport, optics,... doping carrier injection optical excitation } δn δm δθ p, δt C δρ(t) Example δn δθ p Ref. 4 Spins in Solids 5

6 Optical Red Shift in EuX Ref. 5 E r r = 2J s S EuS : J sf ev sf d(t 2g ) 4f Spins in Solids 6

7 Schottky Device Band-Splitting + Spin Polarization In or Sn EuS ϕ Metal Fermi Level d 1.7V 2.4V 4f states Ref. 6 Capacitance vs. Voltage of a EuS-Sn junction having T above and below the Curie temperature. Spins in Solids 7

8 Characterization: Spin Polarization Fowler-Nordheim Tunneling ϕ Metal Fermi Level Bottom of the empty conduction band in EuX ev Tunneling Metal Fermi Level I H V Ref. 7 Meservey-Tedrow Technique di/dv Al Metal contact V Insulator Ferromagnet Ref. 8 Spins in Solids 8

9 Measurement of spin polarization using Zeeman splitting E µh ev E F F H S N(E) Meservey and Tedrow (1994) ev/ Ref. 9 Spins in Solids 9

10 Results for CrO 2 Results: Zeeman splitting G (V) / G N H = 0.0 T = 0.5 T = 1.0 T = 1.5 T = 2.0 T = 2.5 T V (mv) 1.4 T =400 mk +2.5T -2.5T (µev) H (T) G (V) / G N V (mv) Spins in Solids 10

11 Lateral all electrical all sc spintronics device Detector Injector 1. Source of spin polarized electrons 2. Long spin diffusion length ( SD ) Semiconductor L< SD 3. Efficient spin injection and detection Conductivity mismatch Spins in Solids 11

12 Spin Injection: the conductivity mismatch I I R F1 R SC R F2 I R F1 R SC R F Solutions: Ref. 10 σ F > σ SC Schmidt et.al., PRB, 2000 Use injector with 100% spin polarization Non-diffusive injection Conductivity matching Spins in Solids 12

13 EuS/GaAs Heterostructure 1. EuS: ~100% spin polarization L. Esaki, P. J. Stiles and S. von Molnár, Phys. Rev. Lett. 19, (1967) Ref GaAs: ~100µm spin diffusion length J. M. Kikkawa and D. D. Awscahlom, Nature 397, (1999) Ref. 12 I V 3. What about the interface? e -? GaAs EuS Single EuS/GaAs heterojunction in both the injector and the detector modes Spins in Solids 13

14 EuS: Magnetic and transport properties EuS: a ferromagnetic insulator with T C =16.5K T< T C E F EuS: Conductivity tuning 100% spin polarization High - close to 100% spin polarization E S (EuS) ~ 0.5 ev I.J. Guilaran et al., PRB 68, (2003) Ref. 13 Spins in Solids 14

15 Zeeman splitting and the I-V characteristics 55K R(kΩ) EuS film measurements T(K) Semiconducting paramagnetic region Increased spin scattering Ferromagnetic region T >T C EuS - paramagnetic Φ Β EuS Both spin species have equal probability of tunneling through the barrier. Φ Β T<T C EuS - ferromagnetic Φ B = Φ B + Φ B Φ B =½ E S Φ B = Φ B - Φ B Spin up electrons have much higher probability of tunneling through the barrier the spin filter effect. Spins in Solids 15

16 Schottky device: GaAs/EuS; Injection from EuS into GaAs I 0 *exp(-φ Β /E 00 ) I(V, T) = I0(exp( ΦB(T)/E00))exp(V/E00) 5x x x x x Tribovic et al.(2005) Ref T(K) Field emission Current rises due to the barrier lowering Thermionic field emission Φ (T) = ln(i (T)/I (T )) E B 0 0 C 00 Normalized Φ B Φ S=7/2 Brillouin function T(K) = ( ± ) ev B Brillouin fit to the insulating EuS T C : Field emission is probing the depletion region of the EuS barrier Transport across EuS/GaAs HJ dominated by depletion region of EuS Spins in Solids 16

17 Example I-M transition in EuO Penny et al. (1972) See also Oliver et al. (1970) Shapira et al. (1973) Ref. 15 Ref. 16 Ref.17 Low concentration (Eu excess, accidental) I F(H A ) Spins in Solids 17

18 Example n = cm -3 Ref. 17 M-I Transition Insulating EuTe Antiferromagnet Spins in Solids 18

19 Example Gd 3-x v x S 4 v = vacancy AF insulator x=1/3 F.M. metal x=0 #2 n = cm -3 #3 n = cm -3 Large negative MR E C E F ρ = ρ 0 e ( E E ) kt C F E C -E F H ; E C -E F H=0 60 K Ref. 18 Spins in Solids 19

20 Magnetic Polarons Ubiquitous in all magnetic semiconductors e.g. CdMnTe, GaMnAs,, (LaCa)MnO 3... Ref. 3 The paramagnetic polaron [A.F. is much the same] Gedanken experiment ; T > T N (T C ) electron (hole) Donor (acceptor) e - captured aligns neighboring spins Carrier motion impeded External field or magnetic order (internal field) will align spins outside of red circle. Spins in Solids 20

21 Evidence for magnetic polarons n 1 > n 2 n 2 > n 3 n 3 ~ cm -3 n 3 0 Ref. 1 A.F + F.M = M 0 gives minimum size of polaron Constant slope means incomplete saturation M s = 190 emu/gm Spins in Solids 21

22 Stability of polaron If no impurity present Ref. 19 F R Polaron solution for R If coulomb trap exists F R Polaron stable at r P, Increases with H I-M r P (H=0) r P (H>0) For PM, FM (EuS): T = T - θ ~ 3 K For AF (EuTe): T ~ T < T N More recently (1999) Khomskii and collaborators (Ref. 20) Spins in Solids 22

23 Magnetic polarons ABO 3 A: B: La Sr Mn Mn /Pr / Ca... O 2 Ref. 21 LaMnO 3 x La 3 M Mn 3 Mn O 1 x x 1 x x 3 AF insulator FM metal de Gennes (1960) Ref. 22 Spin canting with increasing x Magnetic Polarization! Spins in Solids 23

24 Example La 0.67 Ca 0.33 MnO 3 Magnetoresistance T C 270 K Ref. 23 CMR Spins in Solids 24

25 Lattice magnetic polaron Coupling to lattice degrees of freedom essential Millis, et al. (1995) Ref. 24 Röder, et al. (1996) Ref. 25 Percolation Snyder, et al. (1996) Ref. 26 Two-fluid model Jaime et al. (1999) Ref. 27 Theory Gor kov & Kresin (1998, 2000) Refs. 28,29 Noise Spectroscopy Raquet et al. (2000) Ref. 30 Merithew et al. (2000) Ref. 31 FM AF FM FM FM Insulator Metal Spins in Solids 25

26 Spectroscopic Scanning Tunneling Microscopy Fäth et al. (1999) Ref. 32 La 2/3 Ca 1/3 MnO 3 Generic spectroscopic images (0.61 µm x 0.61 µm) of the local electronic structure taken just below T C. From left to right and top to bottom. 0, 0.3, 1, 3, 5, 9 Tesla Spins in Solids 26

27 Dilute Magnetic Semiconductors Take a well-known semiconductor and introduce a magnetic species substitutionally into the lattice CdTe dilute magnetic system Cd 1-x Mn x Te Also: Hg 1-x Mn x Te Hg 1-x Fe x Te Zn 1-x Mn x Te Hg 1-x-y Cd x Mn y Te Pb 1-x Mn x S etc. Magnetic behavior is tunable by varying the concentration x Spin-spin interactions; ion-conduction band (valence band) ion-ion Spins in Solids 27

28 Awschalom (1986) Ref. 33 Spins in Solids 28

29 Awschalom (1989) Ref. 34 Spins in Solids 29

30 M A B C E g E Response (Static) A) Sample transparent B) Region of polaron formation (slightly below E g Bound exciton) C) Above band gap constant signal but smaller than in B C) Magnetism occurs via spin flip exchange (Krenn, Zawadzki, Bauer, 1985) e, h Mn 2+ N Mn >> n e, n h Mn polarization << 1 τ ~ sec Spins in Solids 30

31 InMnAs Characterization: Magnetism Magnetization Measurements by SQUID: 1. Is the material single phase? InMnAs Munekata et al von Molnár et al Ref. 35, Determination of T C : M vs. (H,T), Arrott plots Spins in Solids 31

32 (In, Mn)As, (Ga, Mn)As InMnAs 1.3% Mn, T C 10K H. Ohno et al. (1992) Ref. 37 Low temperature MBE for more Mn incorporation GaMnAs 5% Mn, T C 110K H. Ohno et al. (1998) Ref. 38 R R Hall sheet resistivity: 0 S R M ( R M H = B + ρ Hall = 0B + Rs ) d d RH M 1 R because S = crsheet "Skew c R d sheet Scattering" Spins in Solids 32

33 Characterization: Magnetism Magneto-Optical Characterization Faraday rotation : Rapid Measurement of Magnetization and T C Magneto-optical absorption : Exchange Constant Ref. 39 E = λ x <S> x = x = x = and x <S> M The splitting of the free exciton line vs. magnetization for GaMnAs Extrapolation : for x ~ 0.05 E ~ 0.3 ev Spins in Solids 33

34 Large Polarons p-type (In, Mn)As Ohno et al. (1992) Ref. 37 χ R0 + cρ ; B = µ H µ R H = 0 0 T 1/3 Weak localization (Imry, 1982) + Mag. Field dependence Large Bound Magnetic Polaron Diameter > 10 nm; contains large # of Mn, and holes!! Spins in Solids 34

35 Oiwa et al. (1998), Iye et al. (1999) Ref. 40 Magnetic field dependence due to J pd σ p S Mn Spins in Solids 35

36 Dilute Magnetic Oxides Wide band gap semiconductors (~3eV) ZnO, TiO 2, SnO 2 doped with transition metal (TM) impurities If FM, T c > room temperature even at low dopant concentration If FM, moment per ion decreases as impurity concentration increases Giant moments reported at low impurity concentration Lack of reproducibility between groups Disorder dependence: more disorder, higher moment Magnetic Polaron Percolation? Secondary Phases/Contamination? Spins in Solids 36

37 Bound Magnetic Polarons Coey et al., Nature Mat.4, 173 (2005) Ref. 41 Electron trapped in defect site forms polaron with orbit r H =ε(m/m*)a 0 Magnetic impurities within orbit are coupled High dielectric constant ε implies large polaron radius and large moment Nearest neighbour pairs couple AFM due to superexchange This could explain lower moment observed as TM concentration increases (more nn pairs) Spins in Solids 37

38 TiO 2 :Co Ref. 38 Cobalt clusters form at reduced growth pressure. Linear log(r) vs T -1/2 characteristic of hopping transport in multiphase systems. X-ray analysis shows epitaxial structure of rutile. Spins in Solids 38

39 New Developments: (Cd,Mn)Te 2DES Size stable (ferro) magnetic clusters J. Jaroszynski et al. (cond-mat/ , 2006) Ref. 42 Spins in Solids 39

40 New Developments: La 1-x Sr x CoO 3 Small Angle Neutron Scattering (SANS) I-M transition at x~.18 Small q Large q constant radius magnetic cluster critical scattering: Tc Two phase GMR and ln ρ~t -1/2 Wu et al. (2005) Ref. 43 For x=0 defect induced Magnetic Exciton Giblin et al. (2005) Ref. 44 Spins in Solids 40

41 Magnetic Polaron Percolation Overlapping polarons align forming FM clusters Effective polaron radius depends on temperature (for details Kaminski, Das Sarma PRL ) Ref. 45 Below T c material is FM Magnetic properties depend both on impurity concentration and defect concentration May explain observed lack of reproducibility and dependence on film quality Spins in Solids 41

42 Secondary Phases/Contamination Reports of secondary magnetic phases forming in oxides (eg. Kundaliya et al. (2004). Nature Mat 3 709, Colis et al. (2005). Chem Phys Lett 415, Refs. 46,47 Reports of segregation of magnetic TM impurities (eg. Kim et al. (2002). Appl. Phys Lett , Kennedy et al. (2004). Appl Phys Lett ) Refs. 48,49 Reports of contamination from stainless steel tweezers (e.g. Abraham et al. (2005). Appl Phys Lett ) Ref. 50 Reports of contamination from furnace during annealing Must be cautious in drawing conclusions Very Recent Findings GaN:Gd a) For Gd concentration ~10 16 cm cm -3 => FM, T c > room temperature b) Low Gd concentration, magnetic moment/gd ~ 4000 µ B EVEN WHEN INSULATING Dahr et al. (2005a) Ref. 51 Polarization of GaN marix and percolation to achieve FM Dahr et al. (2005b) Ref. 52 c) Band Structure calculation propose polarization of donor electrons Dalpain and Wei (2005) Ref. 53 Spins in Solids 42

43 Conclusions Magnetic polarons are ubiquitous to concentrated and diluted magnetic semiconductors Spins in Solids 43