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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

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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)




  • Motivation

  • Some properties of (Ga,Mn)As

  • The model: hole-mediated mechanism

  • New Directions

Motiva tion


  • 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)]



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)]

Some properties of ga mn as

Some properties of (Ga,Mn)As

Ga: [Ar] 3d10 4s2 4p1

Mn: [Ar] 3d5 4s2


  • 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

The model hole mediated mechanism

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)


  • 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

    • ...





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 15040 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



We then get

Notice maximum of p(x) within the M phase

 correlate with MIT

Early predictions


[Matsukura et al., PRB 57, R2037 (1999)]


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


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 directions

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


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]

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