Transcript Diluted Magnetic Semiconductors

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:
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Motivation
Some properties of (Ga,Mn)As
The model: hole-mediated mechanism
New Directions
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
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 < 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
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
[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
Interaction
between hole spin
and Mn local
moment is AFM,
giving rise to an
effective FM
coupling between
Mn spins
= Mn, S =5/2
= hole, S =1/2 (itinerant)
[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
Mean-field approximation
Nearly free holes moving under a magnetic field, h, due to the Mn
moments:
 2
 
2
  h  k   k  k ,   1

2 
 2m *
Hole sub-system is polarized: m  mI  n R I   n R I 
Pauli paramagnetism:
1
m  p 3h
Now, the field h is related to the Mn magnetization, M :
h  J pd  r  R I  M R I   J pd Mc
I
Mn concentration
Assuming a uniform
Mn magnetization
We then have
m  A J pd M x p
1
3
A depends on m* and on several
constants
The Mn local moments also feel the polarization of the holes:
 J pd S  
 m 
M  nMn g BM  nMn g B SBS 
 2k BT  
Brillouin function
m  A J pd M x p
1
3
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,
m* J
2
pd
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
2
2
3 2
( m * me ) J pd  2.4  10
eV nm 
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/Mn
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:
F  p1/3, increases to the right, towards VB
(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
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/Processes
1. Heterostructures
(Ga,Mn)As/(Al,Ga)As/(Ga,Mn)As  spindependent 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
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
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]