Diluted Magnetic Semiconductors

1
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 dAlbuquerque 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

• 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 60s EuO and CdCr2S4
• very hard to grow
• Mid-80s 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 lt 2K
• IV-VI (e.g., PbSnTe) IV ? Mn
• hard to prepare (bulk and heterostructures)
• but helped understand the mechanism of
  carrier-mediated FM
• Late 80s MBE ? uniform (In,Mn)As films on GaAs
  substrates FM on p-type.
• Late 90s 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 expts
• ? 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)
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
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

1. Low density unpolarized holes, ?F below mobility
   edge
2. Slightly higher densities holes polarized, but
   ?F is still below the mobility edge
3. Higher densities ?F reaches maximum and starts
   decreasing, but exchange splitting is larger ?
   still metallic
4. 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
Magnetiztion of the Mn ions
Simple model is able to predict p(x) discuss
MIT M(x)
RRdS, LE Oliveira, and J dAlbuquerque 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
  excitns) 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