Transcript Making semiconductors magnetic: new materials properties, devices, and future Ohio State University

Making semiconductors magnetic:
new materials properties, devices, and future
JAIRO SINOVA
Texas A&M University
Institute of Physics ASCR
Texas A&M L. Zarbo
Institute of Physics ASCR
Tomas Jungwirth, Vít Novák, et al
Ohio State University
Oct 2nd 2009
Hitachi Cambridge
Jorg Wunderlich, A. Irvine, et al
University of Nottingham
Bryan Gallagher, Tom Foxon,
Richard Campion, et al.
NRI
SWAN
OUTLINE
• Motivation
• Ferromagnetic semiconductor materials:
–
–
–
–
(Ga,Mn)As - general picture
Growth, physical limits on Tc
Related FS materials (searching for room temperature)
Understanding critical behavior in transport
• Ferromagnetic semiconductors & spintronics
– Tunneling anisotropic magnetoresistive device
– Transistors (4 types)
ENGINEERING OF QUANTUM MATERIALS
Technologically motivated and scientifically fueled
Generates new physics:
•Tunneling AMR
•Coulomb blockade AMR
•Nanostructure magnetic
anisotropy engineering
Incorporate magnetic
properties with
semiconductor tunability
(MRAM, etc)
Understanding complex phenomena:
•Spherical cow of ferromagnetic systems
(still very complicated)
•Engineered control of collective
phenomena
More knobs than usual in semiconductors: density,
strain, chemistry/pressure, SO coupling engineering
Ferromagnetic semiconductor research :
strategies
1. Create a material that marriages the tunability of semiconductors
and the collective behavior of ferromagnets; once created search
for room temperature systems
2. Study new effects in this new material and utilize in metal-based
spintronics
3. Develop a three-terminal gated spintronic device to progress from
sensors & memories to transistors & logic
(Ga,Mn)As
GENERAL PICTURE
Ferromagnetic semiconductors
Need true FSs not FM inclusions in SCs
Ga
GaAs - standard III-V semiconductor
As
+
Group-II Mn - dilute magnetic moments & holes
Mn
(Ga,Mn)As - ferromagnetic semiconductor
Mn
What happens when a Mn is placed in Ga sites:
Mn–hole spin-spin interaction
Ga
As
Mn
As-p
Mn-d
hybridization
5 d-electrons with L=0
 S=5/2 local moment
intermediate
acceptor (110 meV)
 hole
Hybridization  like-spin level repulsion  Jpd SMn
 shole interaction
In addition to the Kinetic-exchange coupling, for a single Mn ion, the coulomb
interaction gives a trapped hole (polaron) which resides just above the valence band
DOS
Transition to a ferromagnet when Mn concentration increases
GaAs:Mn – extrinsic p-type semiconductor
EF
spin 
~1% Mn
<< 1% Mn
>2% Mn
Energy
spin 
onset of ferromagnetism near MIT
As-p-like holes localized on Mn acceptors
valence band As-p-like holes
Ga
Ga
As
As
Mn
Mn
Ga
Mn
Mn
As
Mn
FM due to p-d hybridization (Zener local-itinerant kinetic-exchange)
(Ga,Mn)As GROWTH
high-T growth
•Low-T MBE to avoid precipitation
•High enough T to maintain 2D growth
 need to optimize T & stoichiometry
for each Mn-doping
•Inevitable formation of interstitial Mndouble-donors compensating holes and
moments
 need to anneal out but without loosing MnGa
optimal-T growth
Polyscrystalline
20% shorter bonds
Interstitial Mn out-diffusion limited by surface-oxide
O
GaMnAs-oxide
x-ray photoemission
GaMnAs
MnI++
Olejnik et al, ‘08
10x shorther annealing with etch
Optimizing annealing-T another key factor
Rushforth et al, ‘08
(Ga,Mn)As
GENERAL THEORY
HOW DOES ONE GO ABOUT
UNDERSTANDING SUCH SYSTEMS
1.
One could solve the full many body S.E.: not possible AND not fun
2.
Combining phenomenological models (low degrees of freedom) and approximations
and comparison to other computational technieques while checking against
experiments
“This is the art of condensed matter science, an intricate tango
between theory and experiment whose conclusion can only be
guessed at while the dance is in progress”
A.H.M et al., in “Electronic Structure and Magnetism in Complex Materials”
(2002).
Theoretical Approaches to DMSs
• First Principles LSDA
Jungwirth, Sinova, Masek, Kucera, MacDonald,
Rev. of Mod. Phys. 78, 809 (2006)
PROS: No initial assumptions, effective Heisenberg model can be
extracted, good for determining chemical trends
CONS: Size limitation, difficulty dealing with long range interactions, lack of
quantitative predictability, neglects SO coupling (usually)
• Microscopic TB models
PROS: “Unbiased” microscopic approach, correct capture of band
structure and hybridization, treats disorder microscopically (combined with
CPA), very good agreement with LDA+U calculations
CONS: neglects (usually) coulomb interaction effects, difficult to capture
non-tabulated chemical trends, hard to reach large system sizes
•k.p  Local Moment
PROS: simplicity of description, lots of computational ability, SO coupling
can be incorporated,
CONS: applicable only for metallic weakly hybridized systems (e.g.
optimally doped GaMnAs), over simplicity (e.g. constant Jpd), no good for
deep impurity levels (e.g. GaMnN)
coupling strength / Fermi energy
Magnetism in systems with coupled dilute moments
and delocalized band electrons
band-electron density / local-moment density
(Ga,Mn)As
Which theory is right?
Impurity bandit vs Valence Joe
KP Eastwood
Fast principles Jack
How well do we understand (Ga,Mn)As?
In the metallic optimally doped regime GaMnAs is well described by a disordered-valence
band picture: both dc-data and ac-data are consistent with this scenario.
The effective Hamiltonian (MF) and weak scattering theory (no free parameters) describe
(III,Mn)V metallic DMSs very well in the optimally annealed regime:
• Ferromagnetic transition temperatures 
 Magneto-crystalline anisotropy and coercively 
 Domain structure 
 Anisotropic magneto-resistance 
 Anomalous Hall effect 
 MO in the visible range 
 Non-Drude peak in longitudinal ac-conductivity 
• Ferromagnetic resonance 
• Domain wall resistance 
• TAMR 
•Transport critical behaviour 
•Infrared MO effects 
TB+CPA and LDA+U/SIC-LSDA calculations describe well chemical trends, impurity
formation energies, lattice constant variations upon doping
EXAMPLE: MAGNETO-OPTICAL EFFECTS IN THE INFRARED
Tc LIMITS AND
STRATEGIES
Problems for GaMnAs (late 2002)

Curie temperature limited to ~110K.

Only metallic for ~3% to 6% Mn

High degree of compensation
Mn Mn

Unusual magnetization (temperature dep.)

Significant magnetization deficit
“110K could be a fundamental limit on TC”
As
Mn
Ga
But are these intrinsic properties of GaMnAs ??
Can a dilute moment ferromagnet have a high Curie temperature ?
EXAMPLE OF THE PHYSICS TANGO
The questions that we need to answer are:
1. Is there an intrinsic limit in the theory models (from
the physics of the phase diagram) ?
2. Is there an extrinsic limit from the ability to create the
material and its growth (prevents one to reach the
optimal spot in the phase diagram)?
Intrinsic properties of (Ga,Mn)As
TcMF  xMn p1/ 3
COMBINATION OF THEORY APPROACHES PREDICTS:
Tc linear in MnGa local moment concentration; falls
rapidly with decreasing hole density in more than 50%
compensated samples; nearly independent of hole
density for compensation < 50%.
Jungwirth, Wang, et al. Phys.
Rev. B 72, 165204 (2005)
Extrinsic effects: Interstitial Mn - a magnetism killer
Interstitial Mn is detrimental to magnetic order:
compensating double-donor – reduces carrier density
couples antiferromagnetically to substitutional Mn even in
low compensation samples
Blinowski PRB ‘03, Mašek, Máca PRB '03
Mn
As
Yu et al., PRB ’02:
~10-20% of total Mn concentration is
incorporated as interstitials
Increased TC on annealing corresponds to
removal of these defects.
MnGa and MnI partial concentrations
As grown
Materials
calculation
Jungwirth, Wang, et al.
Phys. Rev. B 72, 165204 (2005)
Microscopic defect formation energy calculations:
No signs of saturation in the dependence of MnGa concentration
on total Mn doping
Experimental hole densities: measured by ordinary Hall effect
Open symbols & half closed as grown. Closed symbols annealed
18
p/Mnsub
1.5
20
-3
p (x 10 cm )
15
12
1.0
Low
Compensation
0.5
0.0
0
2
9
4
6
Mntotal(%)
8
Obtain Mnsub
assuming
change in hole
density due to
Mn out diffusion
10
6
3
0
0
2
4
6
Mntotal(%)
8
10
High
compensation
Jungwirth, Wang, et al.
Phys. Rev. B 72, 165204 (2005)
Annealing can vary significantly increases hole densities.
Experimental partial concentrations of MnGa and MnI in as grown samples
Theoretical linear dependence of Mnsub on total Mn confirmed
experimentally
Mnsub
MnInt
Obtain Mnsub &
MnInt assuming
change in hole
density due to
Mn out diffusion
Jungwirth, Wang, et al.
Phys. Rev. B 72, 165204 (2005)
SIMS: measures total Mn concentration.
Interstitials only compensation assumed
Can we have high Tc in Diluted Magnetic Semicondcutors?
NO INTRINSIC LIMIT
Tc linear in MnGa local (uncompensated)
moment concentration; falls rapidly with
decreasing hole density in heavily
compensated samples.
NO EXTRINSIC LIMIT
There is no observable limit to
the amount of substitutional
Mn we can put in
Define Mneff = Mnsub-MnInt
Closed symbols annealed
140
TC(K)
TTC(K)
(K)
120
C
TC(K)
100
120
100
100
100
80
80
80
60
40
20
0
0
1
2
3
4
5
6
Mntotal(%)
7
8
80
60
60
1.7%Mn
Mn Linear increase of Tc
1.7%
2.2%
Mn Mn = Mn -Mn
1.7%Mn
2.2%
eff
sub
Int
3.4%
Mn
2.2%
Mn
3.4% Mn
4.5%Mn
Mn 180
4.5%
3.4%
Mn
5.6%Mn
Mn 160
5.6%
4.5%
Mn
6.7%Mn
Mn 140
6.7%
5.6%
Mn
9%
Mn
9%Mn
Mn
6.7%
Mn 120
8%
9% Mn 100
TC(K)
180
180
Tc as grown and annealed samples
180
160
160
160
140
180
140
140
160 Open symbols as grown.
120
120
60
40
40
40
20
20
20
0 10
90
0
1
1
0 0
0
1
80
60
40
20
22
33
2
3
0
04 4
15 5 26
●
●
As-Grown
As-Grown
Annealed
As-Grown
Annealed
High
Annealed
compensation
7
6 37 7 4 8 85 9 9610 10
Mn
(%)
Mneff(%)
(%)
total
4Mn
5
6
7
8
9
10
total
Mn
●
with
(%)
Concentration of uncompensated Mntotal
Ga
moments has to reach ~10%. Only 6.2%
in the current record Tc=173K sample
Charge compensation not so important
unless > 40%
No indication from theory or experiment
that the problem is other than
technological - better control of growth-T,
stoichiometry
188K!!
Tc limit in (Ga,Mn)As
remains open
180
160
140
120
2008
Olejnik et al
“... Ohno’s ‘98 Tc=110 K is the fundamental
upper limit ..” Yu et al. ‘03
TC(K)
100
80
60
40
20
“…Tc =150-165 K independent of
xMn>10% contradicting Zener kinetic
exchange ...” Mack et al. ‘08
0
0
1
2
3
4
5
`
“Combinatorial” approach to growth
with fixed growth and annealing T’s
6
Mntotal(%)
7
8
9
10
Getting to higher Tc: Strategy A
- Effective concentration of uncompensated MnGa moments has to increase
beyond 6% of the current record Tc=173K sample. A factor of 2 needed
 12% Mn would still be a DMS
- Low solubility of group-II Mn in III-V-host GaAs makes growth difficult
Low-temperature MBE
Strategy A: stick to (Ga,Mn)As
- alternative growth modes (i.e. with proper
substrate/interface material) allowing for larger
and still uniform incorporation of Mn in zincblende GaAs
More Mn - problem with solubility
Getting to higher Tc: Strategy B
Find DMS system as closely related to (Ga,Mn)As as possible with
• larger hole-Mn spin-spin interaction
• lower tendency to self-compensation by interstitial Mn
• larger Mn solubility
• independent control of local-moment and carrier doping (p- & n-type)
Other (III,Mn)V’s DMSs
Kudrnovsky et al. PRB 07
Weak hybrid.
Mean-field but
low TcMF
InSb
Strong hybrid.
Delocalized holes
long-range coupl.
d5
Impurity-band holes
short-range coupl.
Large TcMF but
low stiffness
GaP
(Al,Ga,In)(As,P) good candidates, GaAs seems close to the optimal III-V host
Steps so far in strategy B:
• larger hole-Mn spin-spin interaction : DONE BUT DANGER IN
PHASE DIAGRAM
• lower tendency to self-compensation by interstitial Mn: DONE
• larger Mn solubility ?
• independent control of local-moment and carrier doping (p- & n-type)?
Using DEEP mathematics to find a new material
3=1+2
III = I + II  Ga = Li + Zn
GaAs and LiZnAs are twin SC
LDA+U says that Mn-doped
are also twin DMSs
It can be n and p doped!!!
EF
As p-orb.
L
Ga s-orb.
No solubility limit
for group-II Mn
substituting for
group-II Zn !!!!
As p-orb.
Masek, et al. PRB (2006)
UNDERSTANDING
CRITICAL BEHAVIOUR
IN TRANSPORT
Towards spintronics in (Ga,Mn)As: FM & transport
Dense-moment MS
F<< d-
Dilute-moment MS
F~ d-
Eu - chalcogenides
Critical contribution to resistivity at Tc
~ magnetic susceptibility
Broad peak near Tc disappeares with
annealing (higher uniformity)???

When density of carriers is smaller than
density of local moments what matters
is the long range behavior of Γ (which
goes as susceptibility)
uncor  small
When density of carriers is similar to
density of local moments what matters
is the short range behavior of Γ (which
goes as the energy)
Tc
(k ~ k F ~ 1 / d )
EuCdSe
(k ~ kF ~ 0) ~ 
Ni
d / dT ~ d / dT ~ cv
Tc
d/dT singularity at Tc – consistent with kF~d-
Optimized materials with x=4-12.5% and
Tc=80-185K
Annealing sequence
Remarkably universal
both below and above
Tc
V. Novak, et al “Singularity in temperature derivative of resistivity in
(Ga,Mn)As at the Curie point”, Phys. Rev. Lett. 101, 077201 (2008).
OUTLINE
• Motivation
• Ferromagnetic semiconductor materials:
–
–
–
–
(Ga,Mn)As - general picture
Growth, physical limits on Tc
Related FS materials (searching for room temperature)
Understanding critical behavior in transport
• Ferromagnetic semiconductors & spintronics
– Tunneling anisotropic magnetoresistive device
– Transistors (4 types)
AMR
TMR
~ 1% MR effect
~ 100% MR effect
Exchange split & SO-coupled bands:
 ~ v g ( M vs. I )
TAMR

 ~ TDOS ( M )
Au
Exchange split bands:
 ~ TDOS ()  TDOS ()
discovered in (Ga,Mn)As Gold et al. PRL’04
TAMR in metal structures
experiment
ab intio theory
Shick, et al, PRB '06, Park, et al, PRL '08
Park, et al, PRL '08
Also studied by Parkin et al., Weiss et al., etc.
DMS DEVICES
Gating of highly doped (Ga,Mn)As:
p-n junction FET
(Ga,Mn)As/AlOx FET with large gate voltages, Chiba et al. ‘06
p-n junction depletion estimates
-3
carrier density [ 10 cm ]
10
8
19
0V
3V
5V
10V
6
4
2
0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
GaMnAs layer thickness [nm]
~25% depletion feasible at low voltages
Olejnik et al., ‘08
Increasing  and decreasing AMR and Tc with depletion
Vg = 0V
Vg = 3V
24.5
-3
 [10 cm]
19.4
24.0
19.2
19.0
23.5
18.8
23.0
18.6
20
22
24
26
28
30
32
34
22.5
T [K]
-6
d/dT [10 
AMR
100
Tc Tc
0
0
-100
-100
-200
-300
-200
20
22
24
26
28
T [K]
30
32
34
Persistent variations of magnetic
properties with ferroelectric gates
Stolichnov et al.,
Nat. Mat.‘08
62K
65K
depletion
accumulation
dR/dT
200
100
30
40
50
60
T (K)
70
80
90
100
Electro-mechanical gating with piezo-stressors
exy = 0.1%
exy = 0%
Strain & SO 
Rushforth et al., ‘08
Electrically controlled magnetic anisotropies via strain
(Ga,Mn)As spintronic single-electron transistor
Wunderlich et al. PRL ‘06
Huge, gatable, and hysteretic MR
Single-electron transistor
Two "gates": electric and magnetic
Single-electron charging energy controlled by Vg and M
Source
QQ
ind0 = (n+1/2)e
Q VD
Drain
QQ0 ind = ne
Gate
VG
eE2/2C
C
n-1
Q
U   dQ 'VD (Q ' ) 
0
Q ( M )
e
(Q  Q0 ) 2
 ( M ) C
U
& Q0  CG [VG  VM ( M )] & VM 
2C
e
CG
electric
& magnetic
control of Coulomb blockade oscillations
n
n+1
[110]

n+2
[010] M
F
[100]
[110]
[010]
SO-coupling (M)
Theory confirms chemical potential anisotropies in (Ga,Mn)As
& predicts CBAMR in SO-coupled room-Tc metal FMs
Nonvolatile programmable logic
Variant p- or n-type FET-like transistor in one single nano-sized CBAMR device
V DD
VA
ON
OFF
ON
VB
ON
OFF
OFF
ON
1
VB
ON
OFF
10 Vout
10
ON
OFF
1
0
VA
1
0
1
0
0
1
0
OFF
ON
OFF
“OR”
A
0
1
0
1
B
0
0
1
1
Vout
0
1
1
1
Nonvolatile programmable logic
Variant p- or n-type FET-like transistor in one single nano-sized CBAMR device
V DD
0
1
OFF
ON
1
0
VA
VB
ON
OFF
Vout
VB
VA
“OR”
A
0
1
0
1
B
0
0
1
1
Vout
0
1
1
1
Device design
Physics of SO & exchange
Materials
FSs and metal FS
with strong SO
Chemical potential
 CBAMR
SET
FSs
Tunneling DOS
 TAMR
Tunneling device
metal FMs
Resistor
Group velocity & lifetime
 AMR
Conclusion
No intrinsic or extrinsic limit to Tc so far: it is a materials growth issue
In the metallic optimally doped regime GaMnAs is well described by a disordered-valence
band picture: both dc-data and ac-data are consistent with this scenario.
The effective Hamiltonian (MF) and weak scattering theory (no free parameters) describe
(III,Mn)V metallic DMSs very well in the optimally annealed regime:
• Ferromagnetic transition temperatures 
 Magneto-crystalline anisotropy and coercively 
 Domain structure 
 Anisotropic magneto-resistance 
 Anomalous Hall effect 
 MO in the visible range 
 Non-Drude peak in longitudinal ac-conductivity 
• Ferromagnetic resonance 
• Domain wall resistance 
• TAMR 
•Transport critical behaviour 
•Infrared MO effects 
BUT it is only a peace of the theoretical mosaic with many remaining challenges!!
TB+CPA and LDA+U/SIC-LSDA calculations describe well chemical trends,
impurity formation energies, lattice constant variations upon doping
Tomas Jungwirth
Inst. of Phys. ASCR
U. of Nottingham
Hideo Ohno
Tohoku Univ.
Allan MacDonald
U of Texas
Laurens Molenkamp
Wuerzburg
Tomesz Dietl
Institute of Physics,
Polish Academy of
Sciences
Joerg Wunderlich
Cambridge-Hitachi
Ewelina Hankiewicz
Fordham Univesrsity
Bryan Gallagher
U. Of Nottingham
Other collaborators: John Cerne, Jan Masek, Karel Vyborny, Bernd
Kästner, Carten Timm, Charles Gould, Tom Fox, Richard Campion,
Laurence Eaves, Eric Yang, Andy Rushforth, Viet Novak
k.p  Local Moment - Hamiltonian
· Model Anderson Hamiltonian:
(s - orbitals: conduction band; p - orbitals: valence band)
ELECTRONS
+ (Mn d - orbitals: strong on-site Hubbard int. local moment)
+ (s,p - d hybridization)
Mn
ELECTRONS-Mn
· Semi-phenomenological Kohn-Luttinger model for
heavy, light, and spin-orbit split-off band holes
· Local exchange coupling:
Mn: S=5/2; valence-band hole: s=1/2; Jpd > 0
   
 J pd  rj  RI s j  SI
I , j v
Large S:
treat classically
Tc LIMITS AND
STRATEGIES
Can we have high Tc in Diluted Magnetic Semicondcutors?
NO IDENTIFICATION OF AN INTRINSIC LIMIT
NO EXTRINSIC LIMIT
Tc linear in MnGa local (uncompensated)
moment concentration; falls rapidly with
decreasing hole density in heavily
compensated samples.
(lines – theory, Masek et al 05)
Relative Mn concentrations obtained through
hole density measurements and saturation
moment densities measurements.
Qualitative consistent picture
within LDA, TB, and k.p
Define Mneff = Mnsub-MnInt
Closed symbols annealed
140
TC(K)
TTC(K)
(K)
120
C
TC(K)
100
120
100
100
100
80
80
80
60
40
20
0
0
1
2
3
4
5
6
Mntotal(%)
7
8
80
60
60
1.7%Mn
Mn Linear increase of Tc
1.7%
2.2%
Mn Mn = Mn -Mn
1.7%Mn
2.2%
eff
sub
Int
3.4%
Mn
2.2%
Mn
3.4% Mn
4.5%Mn
Mn 180
4.5%
3.4%
Mn
5.6%Mn
Mn 160
5.6%
4.5%
Mn
6.7%Mn
Mn 140
6.7%
5.6%
Mn
9%
Mn
9%Mn
Mn
6.7%
Mn 120
8%
9% Mn 100
TC(K)
180
180
Tc as grown and annealed samples
180
160
160
160
140
180
140
140
160 Open symbols as grown.
120
120
60
40
40
40
20
20
20
0 10
90
0
1
1
0 0
0
1
80
60
40
20
22
33
2
3
with
0
04 4
15 5 26
As-Grown
As-Grown
Annealed
As-Grown
Annealed
High
Annealed
compensation
7
6 37 7 4 8 85 9 9610 10
Mn
(%)
Mneff(%)
(%)
total
4Mn
5
6
7
8
9
10
total
Mntotal(%)
●
●
●
Concentration of uncompensated MnGa moments has to reach ~10%. Only 6.2%
in the current record Tc=173K sample
Charge compensation not so important unless > 40%
No indication from theory or experiment that the problem is other than
technological - better control of growth-T, stoichiometry
III = I + II  Ga = Li + Zn
GaAs and LiZnAs are twin SC
LDA+U says that Mn-doped
are also twin DMSs
n and p type doping through
Li/Zn stoichiometry
No solubility limit
for group-II Mn
substituting for
group-II Zn !!!!
Masek, et al. PRB (2006)
Tc limit in (Ga,Mn)As
remains open
180
160
140
Tc=110 K is the fundamental upper limit ..”
Yu et al. ‘03
100
TC(K)
Indiana & California (‘03): “ .. Ohno’s ‘98
120
80
Nottingham & Prague
(’08): Tc up to 185K
so far
60
40
California (‘08): “…Tc =150-165 K
20
independent of xMn>10% contradicting
Zener kinetic exchange ...”
Mack et al. ‘08
“Combinatorial” approach to growth
with fixed growth and annealing T’s
0
0
1
2
3
4
5
6
Mntotal(%)
7
?
8
9
10