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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)

Layout

• Motivation

• Some properties of (Ga,Mn)As

• The model: hole-mediated mechanism

• New Directions

MotivationSpin-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)]

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

GMR RAM’s

Magnetic Tunnel Junction

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 < 2KIV-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

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

polarization of emitted electrolumiscence determines spin polarization of injected holes

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 moment S = 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

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

[Ohno, JMMM 200, 110(1999)]

Open symbols: B in-plane• hysteresis FM with easy axis in plane; • remanence vs. T Tc ~ 60 K

x = 0.035

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/ a0

3, 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

= 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)]

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

Mn hole

1,2*2 kkk

22

h

m

Mean-field approximation

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

Hole sub-system is polarized: III nnmm RR

Pauli paramagnetism:

hpm 31

Now, the field h is related to the Mn magnetization, M :

McJMJh pdII

Ipd RRr

Assuming a uniformMn magnetization

Mn concentration

We then have

31pxMJAm pd

A depends on m* and on several constants

The Mn local moments also feel the polarization of the holes:

m

Tk

SJSBgngnM pd

SB

BMnBMn 2M

Brillouin function

Linearizing for M 0, provides the self-consistency condition to obtain Tc:

31pxMJAm pd

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,

2* pdJm

which can then be fitted by experimental data.

Setting S = 5/2, we can write an expression for p(x):

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

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

• 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

Fitting procedure

222 104.2)*( 3nmeVpde Jmm

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

1h/MnNotice maximum of p(x) within the M phase correlate with MIT

Early predictions

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

log!

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 p1/3, increases to the right, towards VB

Picture supported by recent photoemission studies

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

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)]

New directions

I. New Materials/Geometries/Processes1. Heterostructures

(Ga,Mn)As/(Al,Ga)As/(Ga,Mn)As spin-dependent scattering, interlayer coupling, and tunnelling magnetoresistance

2. (InyGa1-y)1-x MnxAs has Tc ~ 120 K, apparently without decrease as x increases

3. (Ga,Mn) N has Tc ~ 1000 K !!!!!4. Effects of annealing time on (Ga,Mn)As

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

250 oC annealing

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

II. Improvements on the model/approximations1. Give up uniform Mn approximation

averaging over disorder configurations (e.g., Monte Carlo simulations)

2. More realistic band structures3. Incorporation of defect structures4. Correlation effects in the hole sub-system

[for a review on theory see, e.g., Konig et al., cond-mat/0111314]