Apoio:

1. Esta apresentação pode ser obtida do site http://www.if.ufrj.br/~rrds/rrds.html 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) Apoio:

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

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 CdCr2S4 • 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 polarization of emitted electrolumiscence determines spin polarization of injected holes [Ohno et al., Nature 402, 790 (1999)]

9. Some properties of (Ga,Mn)As Ga: [Ar] 3d10 4s2 4p1 Mn: [Ar] 3d5 4s2 Photoemission • Mn-induced hole states have 4p character associated with host semiconductor valence bands EPR and optical expt’s •  Mn2+ has local momentS = 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 [Ohno, JMMM 200, 110(1999)] Regions of Metallic or Insulating behaviours depend on sample preparation (see later)

11. x = 0.035 • Open symbols: B in-plane • hysteresis  FM with easy axis in plane; • remanence vs. T  Tc ~ 60 K x = 0.053 Tc ~ 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 RHall dominated by the magnetic contribution; negative magnetoresistance (R as B ) • Typically, one has p ~ 0.15 – 0.30 c , where c = 4 x/ a03, with a0 being the AsGa lattice parameter • only one reliable measurement: x = 0.053  3.5 x 1020 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 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)] = Mn, S =5/2 = hole, S =1/2 (itinerant)

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 Mn2+ has L = 0 • no direct Mn-Mn exchange interactions • no Coulomb interaction between Mn2+ acceptor and holes • no Coulomb repulsion among holes  no strong correlation effects • ... 0 hole Mn

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 : Mn concentration Assuming a uniform Mn magnetization 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 Tc:

19. Setting S = 5/2, we can write an expression for p(x): Now, there are considerable uncertainties in the experimental determination of m* and on Jpd [e.g., 55 10 to 15040 meV nm3]. But, within this MFA, these quantities appear in a specific combination, which can then be fitted by experimental data.

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

21. Fitting procedure • Only reliable estimate for p is 3.5  1020 cm-3, when x = 0.053. • For this x, one has Tc = 110 K • We get Results for p (x): Note approximate linear behaviour for Tc(x) between x = 0.015-0.035 p(x) constant in this range

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

23. Assume impurity band: Fp1/3, increases to the right, towards VB • Low density: unpolarized holes, F below mobility edge • Slightly higher densities: holes polarized, but F is still below the mobility edge • Higher densities: F reaches maximum and starts decreasing, but exchange splitting is larger  still metallic • Much higher densities: F too low and exchange splitting too small  F returns to localized region

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

25. Maxima decrease as T increases • Operational “window” shrinks as T increases Magnetiztion of the Mn ions 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 • New Materials/Geometries/Processes • Heterostructures (Ga,Mn)As/(Al,Ga)As/(Ga,Mn)As  spin-dependent scattering, interlayer coupling, and tunnelling magnetoresistance • (InyGa1-y)1-x MnxAs has Tc ~ 120 K, apparently without decrease as x increases • (Ga,Mn) N has Tc ~ 1000 K !!!!! • Effects of annealing time on (Ga,Mn)As

27. 250 oC annealing • Tc grows with annealing time, up to 2hrs; for longer times, Tc decreases • M as T 0 only follows T 3/2 (usual spin wave excit’ns) for annealing times longer than 30min • All samples show metallic behaviour below Tc • 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. Improvements on the model/approximations • Give up uniform Mn approximation  averaging over disorder configurations (e.g., Monte Carlo simulations) • More realistic band structures • Incorporation of defect structures • Correlation effects in the hole sub-system [for a review on theory see, e.g., Konig et al., cond-mat/0111314]