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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:

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

- 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

Spin-polarized device principles (metallic layers):

Parallel magnetic layers

spins can flow

Antiparallel magnetic layers

spins cannot flow

[Prinz, Science 282, 1660 (1998)]

GMR RAM’s

Magnetic Tunnel Junction

- Impact of spin-polarized devices:
- Giant MagnetoResistance heads ( ! ) US$ 1 billion
- Non-volatile memories ( ? ) US$ 100 billion

- 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

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

Spin injection into a FM semiconductor heterostructure

polarization of emitted electrolumiscence determines spin polarization of injected holes

[Ohno et al., Nature 402, 790 (1999)]

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)]

Phase diagram of MBE growth

[Ohno, JMMM 200, 110(1999)]

Regions of Metallic or Insulating behaviours depend on sample preparation (see later)

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)]

- Resistance measurements on samples with different Mn concentrations:
- Metal R as T
- Insulator R as T

- Reentrant MIT

[Ohno, JMMM 200, 110(1999)]

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

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)

- 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

Mean-field approximation

Nearly free holes moving under a magnetic field, h, due to the Mn moments:

Hole sub-system is polarized:

Pauli paramagnetism:

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

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:

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 15040 meV nm3].

But, within this MFA, these quantities appear in a specific combination,

which can then be fitted by experimental data.

In most approaches x (c or n) and p are treated as independent parameters

[Schliemann et al., PRB 64, 165201 (2001)]

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

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)]

Assume impurity band:

Fp1/3, 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

Picture supported by recent photoemission studies

[Asklund et al., cond-mat/0112287]

- 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)]

- 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

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)]

- 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

- 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]