1. Apoio: http://www.if.ufrj.br/~rrds/rrds.html Esta apresentação pode ser obtida do site seguindo o link em “Seminários, Mini-cursos, etc.” Hole concentration vs. Mn fraction in a diluted (Ga,Mn)As ferromagnetic semiconductor Raimundo R dos Santos (IF/UFRJ), Luiz E Oliveira (IF/UNICAMP) e J d’Albuquerque e Castro (IF/UFRJ)

2. Layout Motivation Some properties of (Ga,Mn)As The model: hole-mediated mechanism New Directions

3. Motivation Spin-polarized electronic transport  manipulation of quantum states at a nanoscopic level  spin information in semiconductors Metallic Ferromagnetism: Interaction causes a relative shift of  and  spin channels

4. Spin-polarized device principles (metallic layers): Parallel magnetic layers   spins can flow Antiparallel magnetic layers   spins cannot flow [Prinz, Science 282, 1660 (1998)]

5. Impact of spin-polarized devices: Giant MagnetoResistance heads ( ! )  US$ 1 billion Non-volatile memories ( ? )  US$ 100 billion GMR RAM’s Magnetic Tunnel Junction

6.  Injection of spin-polarized carriers plays important role in device applications  combination of semiconductor technology with magnetism should give rise to new devices;  long spin-coherence times (~ 100 ns) have been observed in semiconductors

7. Magnetic semiconductors: Early 60’s: EuO and CdCr 2 S 4  very hard to grow Mid-80’s: Diluted Magnetic Semiconductors II-VI (e.g., CdTe and ZnS) II  Mn  difficult to dope  direct Mn-Mn AFM exchange interaction  PM, AFM, or SG (spin glass) behaviour  present-day techniques: doping has led to FM for T < 2K IV-VI (e.g., PbSnTe) IV  Mn  hard to prepare (bulk and heterostructures)  but helped understand the mechanism of carrier-mediated FM Late 80’s: MBE  uniform (In,Mn)As films on GaAs substrates: FM on p-type. Late 90’s: MBE  uniform (Ga,Mn)As films on GaAs substrates: FM; heterostructures

8. Spin injection into a FM semiconductor heterostructure [Ohno et al., Nature 402, 790 (1999)] polarization of emitted electrolumiscence determines spin polarization of injected holes

9. Some properties of (Ga,Mn)As Ga: [Ar] 3d 10 4s 2 4p 1 Mn: [Ar] 3d 5 4s 2 Photoemission  Mn-induced hole states have 4p character  associated with host semiconductor valence bands EPR and optical expt’s  Mn 2+ has local moment S = 5/2 [For reviews on experimental data see, e.g., Ohno and Matsukura, SSC 117, 179 (2001); Ohno, JMMM 200, 110 (1999)]

10. Phase diagram of MBE growth Regions of Metallic or Insulating behaviours depend on sample preparation (see later) [Ohno, JMMM 200, 110(1999)]

11. Open symbols: B in-plane hysteresis  FM with easy axis in plane; remanence vs. T  T c ~ 60 K x = 0.035 x = 0.053 T c ~ 110 K [Ohno, JMMM 200, 110(1999)]

12. Resistance measurements on samples with different Mn concentrations: Metal  R  as T  Insulator  R  as T   Reentrant MIT [Ohno, JMMM 200, 110(1999)]

13. Question: what is the hole concentration, p? Difficult to measure since R Hall dominated by the magnetic contribution; negative magnetoresistance (R  as B  ) Typically, one has p ~ 0.15 – 0.30 c, where c = 4 x/ a 0 3, with a 0 being the AsGa lattice parameter only one reliable measurement: x = 0.053  3.5 x 10 20 cm -3 Defects are likely candidates to explain difference between p and c: Antisite defects: As occupying Ga sites Mn complexes with As Our purpose here: to obtain a phenomenological relation p(x) from the magnetic properties

14. The model: hole-mediated mechanism = Mn, S =5/2 = hole, S =1/2 (itinerant) Interaction between hole spin and Mn local moment is AFM, giving rise to an effective FM coupling between Mn spins [Dietl et al., PRB 55, R3347 (1997)]

15. Simplifying the model even further: neither multi-band description nor spin-orbit  parabolic band for holes hole and Mn spins only interact locally (i.e., on-site) and isotropically – i.e., Heisenberg-like – since Mn 2+ has L = 0 no direct Mn-Mn exchange interactions no Coulomb interaction between Mn 2+ acceptor and holes no Coulomb repulsion among holes  no strong correlation effects... 0 Mn hole

16. Mean-field approximation Nearly free holes moving under a magnetic field, h, due to the Mn moments:  Hole sub-system is polarized: Pauli paramagnetism:

17. Now, the field h is related to the Mn magnetization, M : Assuming a uniform Mn magnetization Mn concentration We then have A depends on m* and on several constants

18. The Mn local moments also feel the polarization of the holes: Brillouin function Linearizing for M  0, provides the self-consistency condition to obtain T c :

19. Now, there are considerable uncertainties in the experimental determination of m* and on J pd [e.g., 55  10 to 150  40 meV  nm 3 ]. But, within this MFA, these quantities appear in a specific combination, which can then be fitted by experimental data. Setting S = 5/2, we can write an expression for p(x):

20. In most approaches x (c or n) and p are treated as independent parameters [Schliemann et al., PRB 64, 165201 (2001)]

21. Only reliable estimate for p is 3.5  10 20 cm -3, when x = 0.053. For this x, one has T c = 110 K We get Fitting procedure Results for p (x): Note approximate linear behaviour for T c (x) between x = 0.015-0.035  p(x) constant in this range

22. We then get 1h/Mn Notice maximum of p(x) within the M phase  correlate with MIT Early predictions [Matsukura et al., PRB 57, R2037 (1999)] log!

23. Assume impurity band: (a)Low density: unpolarized holes,  F below mobility edge (b)Slightly higher densities: holes polarized, but  F is still below the mobility edge (c)Higher densities:  F reaches maximum and starts decreasing, but exchange splitting is larger  still metallic (d)Much higher densities:  F too low and exchange splitting too small   F returns to localized region  F  p 1/3, increases to the right, towards VB

24. Picture supported by recent photoemission studies [Asklund et al., cond-mat/0112287]

25. Magnetiztion of the Mn ions 1.Maxima decrease as T increases 2.Operational “window” shrinks as T increases Simple model is able to: predict p(x); discuss MIT; M(x) [RRdS, LE Oliveira, and J d’Albuquerque e Castro, JPCM (2002)]

26. New directions I.New Materials/Geometries/Processes 1.Heterostructures (Ga,Mn)As/(Al,Ga)As/(Ga,Mn)As  spin- dependent scattering, interlayer coupling, and tunnelling magnetoresistance 2.(In y Ga 1-y ) 1-x Mn x As has T c ~ 120 K, apparently without decrease as x increases 3.(Ga,Mn) N has T c ~ 1000 K !!!!! 4.Effects of annealing time on (Ga,Mn)As

27.  T c grows with annealing time, up to 2hrs; for longer times, T c decreases   M as T  0 only follows T 3/2 (usual spin wave excit’ns) for annealing times longer than 30min 250 o C annealing  All samples show metallic behaviour below T c   xx decreases with annealing time, up to 2 hrs, and then increases again [Potashnik et al., APL (2001)]

28. Two different regimes of annealing times (~2 hrs): FM enhanced Metallicity enhanced lattice constant suppressed  changes in defect structure: As antisites and correlation with Mn positions? Mn-As complexes? More work needed to ellucidate nature of defects and their relation to magnetic properties

29. II.Improvements on the model/approximations 1.Give up uniform Mn approximation  averaging over disorder configurations (e.g., Monte Carlo simulations) 2.More realistic band structures 3.Incorporation of defect structures 4.Correlation effects in the hole sub-system [for a review on theory see, e.g., Konig et al., cond-mat/0111314]