JAIRO SINOVA
Research fueled by:
NERC
Challenges and Chemical Trends in Achieving a Room Temperature Dilute Magnetic
Semiconductor: A Spintronics Tango
2007: Frontiers in Chemical Physics WorkshopFebruary 22th 2007, Knoxville TN
Allan MacDonald U of Texas
Tomas JungwirthInst. of Phys. ASCR
U. of Nottingham
Joerg WunderlichCambridge-Hitachi
Bryan GallagherU. Of Nottingham
Ewelina HankiewiczU. of MissouriTexas A&M U.
Mario BorundaTexas A&M U.
Other collaborators: Jan Masek, Karel Vyborny, Bernd Kästner, Carten Timm, Laurens Molencam,
Charles Gould, Tomas Dietl, Tom Fox, Richard Campton
Xin LiuTexas A&M U.
Alexey KovalevTexas A&M U.
OUTLINEOUTLINE
Intro: Spintronics and Semiconductor Spintronics
Intro to Diluted Magnetic Semiconductors Can we have a high Tc DMS? What is the data telling us in GaMnAs:
thumbs up or down? Strategies to achieve high Tc DMSs
ELECTRONICSELECTRONICSUP TO NOW: electronics mostly based on the manipulation of the charge of the electron
Mr. Electron Two parts to hispersonality !
CHARGE
SPIN Spintronics = Controlling spin and spin flow with electric fields magnetic fields …
There is plenty of room at the bottom - Feynman,
1959
"... Up to now we have been content to dig in the ground to find minerals. ... We should consider, whether - in the great future - we can arrange atoms the way we want, the very atoms, all the way down! ... We can use not just circuits, but some system involving the quantized energy levels, or
interactions of quantized spins."
Cou
rtes
y of
Th
e A
rch
ives
, Cal
ifor
nia
In
stit
ute
of
Tec
hn
olog
y
Why semiconductors are betterWhy semiconductors are better
Bloch Wilson
allowed energyband in crystal
allowed energyband in crystal
isolated atomic levels
Pauli 1931: “One shouldn’t work with semiconductors,that is a filthy mess; who knows whether they really exist”
New New a la Feynmana la Feynman revolution in revolution in spintronics: diluted magnetic spintronics: diluted magnetic
semiconductorssemiconductors
Goal: use the storing capacity of Goal: use the storing capacity of ferromagnetism and the processing ferromagnetism and the processing capacity of semiconductors capacity of semiconductors
Does nature give us the material Does nature give us the material already? Noalready? No
Can we make it? YesCan we make it? Yes Can we understand it? Getting thereCan we understand it? Getting there Can we improve it: that is the tangoCan we improve it: that is the tango
+
Spin: used for storage
Charge: used for computation
Dilute Magnetic Semiconductors: the simple picture
5 d-electrons with L=0 S=5/2 local moment
moderately shallow acceptor (110 meV) hole
Jungwirth, Sinova, MJungwirth, Sinova, Mašek, Kučera, ašek, Kučera, MacMacDDonaldonald, , Rev. Mod. Phys. (2006)Rev. Mod. Phys. (2006), ,
http://unix12.fzu.cz/mshttp://unix12.fzu.cz/ms
- Mn local moments too dilute (near-neghbors cople AF)
- Holes do not polarize in pure GaAs
- Hole mediated Mn-Mn FM coupling
FERROMAGNETISM MEDIATED BY THE CARRIERS!!!
Ga
As
Mn
Ferromagnetic: x=1-8%
Ga1-xMnxAs
Low Temperature - MBE
courtesy of D. Basov
Inter-stitial
Anti-site
Substitutioanl Mn:acceptor +Local 5/2
moment
As anti-site deffect: Q=+2e
Interstitial Mn: double donor
BUT THINGS ARE NOT THAT SIMPLE
Tc~ 100 K, metallic
hard magnets
(III,V) DMS: man made ferromagnets (III,V) DMS: man made ferromagnets a laa la Feynman (1992-2000)Feynman (1992-2000)
anomalous Hall effectnormal: R
Hall ~ B
anomalous: RHall
~ M
•Ohno, et al PRL (1992) (InMnAs) 7.5 K•Ohno, et al APL (1996) (GaMnAs) 55 K•Ohno, Science (1998) 110 K
Curie temperature limited to ~110K.Curie temperature limited to ~110K.
Only metallic for ~3% to 6% MnOnly metallic for ~3% to 6% Mn
High degree of compensationHigh degree of compensation
Unusual magnetization (temperature dep.)Unusual magnetization (temperature dep.)
Significant magnetization deficitSignificant magnetization deficit
1996 1998 2000 20020
40
80
120
[4][3][2]
[1]
Cu
rie
tem
per
atu
re (
K)
Time
But are these intrinsic properties of GaMnAs ??
“110K could be a fundamental limit on TC” As
GaMn
Mn Mn
Problems for GaMnAs (late 2002)
OUTLINEOUTLINE
Intro: Spintronics and Semiconductor Spintronics
DMS’s Introduction Can we have a high Tc DMS? What is the data telling us in GaMnAs:
thumbs up or down? Strategies to achieve high Tc DMSs
Can a dilute moment ferromagnet have a high Curie temperature ?
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)?
Effective magnetic couplingEffective magnetic coupling: Coulomb correlation of d-electrons & hopping AF kinetic-exchange coupling
Jpd
= + 0.6 meV nm3
Origin of coupling between localized Origin of coupling between localized moments and dilute carriersmoments and dilute carriers
MicroscopicMicroscopic: atomic orbitals & Coulomb correlation of d-electrons & hopping
Jpd
SMn
.shole
Magnetism in systems with coupled dilute moments and delocalized band electrons
(Ga,Mn)As
cou
plin
g s
tren
gth
/ F
erm
i en
erg
y
band-electron density / local-moment density
Theoretical Approaches to DMSsTheoretical Approaches to DMSs• First Principles Local Spin Density Approximation (LSDA) 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 Tight Binding models
•Phenomenological k.p Local Moment
PROS: “Unbiased” microscopic approach, correct capture of band structure and hybridization, treats disorder microscopically (combined with CPA), good agreement with LDA+U calculations
CONS: neglects coulomb interaction effects, difficult to capture non-tabulated chemical trends, hard to reach large system sizes
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)
As
GaMn
Mn Mn
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)
3/1pxT MnMF
c
Intrinsic properties of (Ga,Mn)As
Extrinsic effects: Interstitial Mn - a magnetism killerExtrinsic effects: Interstitial Mn - a magnetism killer
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.
Mn
As
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
MnGa and MnI partial concentrations
Microscopic defect formation energy calculations:No signs of saturation in the dependence of MnGa concentrationon total Mn doping
Jungwirth, Wang, et al.Phys. Rev. B 72, 165204 (2005)
As grown Materials calculation
Annealing can very significantly increases hole densities.
Low Compensatio
n
0 2 4 6 8 100
3
6
9
12
15
18
p (
x 1
020cm
-3)
Mntotal
(%)
0 2 4 6 8 100.0
0.5
1.0
1.5
p/M
n sub
Mntotal
(%)
Obtain Mnsub assuming change in
hole density due to Mn out
diffusion
Open symbols & half closed as grown. Closed symbols annealed
High compensatio
nJungwirth, Wang, et al.Phys. Rev. B 72, 165204 (2005)
Experimental hole densities: measured by ordinary Hall effect
Theoretical linear dependence of Mnsub on total Mn confirmed experimentally
Mnsub
MnIntObtain 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
Experimental partial concentrations of MnGa and MnI in as grown samples
Can we have high Tc in Diluted Magnetic Can we have high Tc in Diluted Magnetic Semicondcutors?Semicondcutors?
Tc linear in MnGa local (uncompensated) moment concentration; falls rapidly with decreasing hole density in heavily compensated samples.
Define MnDefine Mneffeff = Mn = Mnsubsub-Mn-MnIntInt
NO INTRINSIC LIMIT NO EXTRINSIC LIMIT
There is no observable limit to the amount of substitutional Mn we can put in
OUTLINEOUTLINE
Intro: Spintronics and Semiconductor Spintronics
DMS’s Introduction Can we have a high Tc DMS? What is the data telling us in GaMnAs:
thumbs up or down? Strategies to achieve high Tc DMSs
0 1 2 3 4 5 6 7 8 9 100
20
40
60
80
100
120
140
160
180
TC(K
)
Mntotal
(%)
8% Mn
Open symbols as grown. Closed symbols annealed
High compensatio
n0 1 2 3 4 5 6 70
20
40
60
80
100
120
140
160
180
TC(K
)
Mneff
(%)
Linear increase of Tc with Mneff = Mnsub-MnInt
Tc as grown and annealed samples
● 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
OUTLINEOUTLINE
Intro: Spintronics and Semiconductor Spintronics
DMS’s Introduction Can we have a high Tc DMS? What is the data telling us in GaMnAs:
thumbs up or down? Strategies to achieve high Tc DMSs
- 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 MBEStrategy 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 A
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)
Getting to higher Tc: Strategy B
conc. of wide gap component0 1
latti
ce c
onst
ant (
A)
5.4
5.7
(Al,Ga)As
Ga(As,P)
(Al,Ga)As & Ga(As,P) hosts
d5 d5
local moment - hole spin-spin coupling Jpd S . s
Mn d - As(P) p overlap Mn d level - valence band splitting
GaAs & (Al,Ga)As
(Al,Ga)As & Ga(As,P)GaAs
Ga(As,P)
MnAs
Ga
Smaller lattice const. more importantfor enhancing p-d coupling than larger gap
Mixing P in GaAs more favorable
for increasing mean-field Tc than Al
Factor of ~1.5 Tc enhancement
p-d coupling and Tc in mixed
(Al,Ga)As and Ga(As,P)
Mašek, et al. PRB (2006)Microscopic TBA/CPA or Microscopic TBA/CPA or
LDA+U/CPALDA+U/CPA
(Al,Ga)As
Ga(As,P)
Ga(As,P)
10% Mn
10% Mn
5% Mn
theory
theory
No reduction of MnI in (Al,Ga)As
Mixing P in GaAs more favorable forsuppressing Mnint formation
higher in (Al,Ga)As
and Ga(As,P)
than in GaAs
smaller interstitial space
only in Ga(As,P) theory
Mni formation in mixed (Al,Ga)As and Ga(As,P)
Using DEEP mathematics to find a new material
3=1+2
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)?
IIIIII = I + II = I + II Ga = Li + Zn Ga = Li + Zn
GaAs and LiZnAs are twin SC
Wei, Zunger '86;Bacewicz, Ciszek '88;Kuriyama, et al. '87,'94;Wood, Strohmayer '05
Masek, et al. PRB (2006)
LDA+U says that Mn-doped are also twin DMSs
Additional interstitial Li in
Ga tetrahedral position - donors
n-type Li(Zn,Mn)As
No solubility limit for group-II Mn
substituting for group-II Zn
theory
Electron mediated Mn-Mn coupling n-type Li(Zn,Mn)As -
similar to hole mediated coupling in p-type (Ga,Mn)As
L
As p-orb.
Ga s-orb.As p-orb.
EF
Comparable Tc's at comparable Mn and carrier doping and
Li(Mn,Zn)As lifts all the limitations of Mn solubility, correlated local-moment and carrier densities, and p-type only in (Ga,Mn)As
Li(Mn,Zn)As just one candidate of the whole I(Mn,II)V family
SUMMARYSUMMARY
No intrinsic limit to Tc: need to think in No intrinsic limit to Tc: need to think in terms of effective Mn concentrationterms of effective Mn concentration
Should use knowledge gained in (Ga,Mn)As Should use knowledge gained in (Ga,Mn)As to create new to create new a la cartea la carte materials materials
Using multiple theoretical approaches and Using multiple theoretical approaches and knowing what each is best and when IS the knowing what each is best and when IS the theory silver bullettheory silver bullet
Alloying P can help TcAlloying P can help Tc 3=2+13=2+1
BEFORE 2000
CONCLUSION:CONCLUSION:directors cutdirectors cut
BUT it takes MANY to do the spintronics tango!!
Texas A&M U., U. Texas, U. Buffalo, Nottingham, U.
Wuerzburg, U. Notre Dame, U. of Tennessee, U. of Maryland,
UCSB, Penn State, ….
It IS true that it takes two to tango
2000-2004
2006NEW DMSs ,Heterostructures
NEXT
MAGNETIC ANISOTROPY
M. Abolfath, T. Jungwirth, J. Brum, A.H. MacDonald, Phys. Rev. B 63, 035305 (2001)
Condensation energy dependson magnetization orientation
<111>
<110>
<100>
compressive strain tensile strain
experiment:
Potashnik et al 2001Lopez-Sanchez and Bery 2003Hwang and Das Sarma 2005
Resistivity temperature dependence of metallic GaMnAs
I
M
Anisotropic Magnetoresistance
exp.
T. Jungwirth, M. Abolfath, J. Sinova, J. Kucera, A.H. MacDonald, Appl. Phys. Lett. 2002
GaMnAsAuAlOx Au
Tunneling anisotropic Tunneling anisotropic magnetoresistance (TAMR)magnetoresistance (TAMR)
Bistable memory device with a single magnetic layer only
Gould, Ruster, Jungwirth, et al., PRL '04
Giant magneto-resistance
(Tanaka and Higo, PRL '01)
[100]
[010]
[100]
[010]
[100]
[010]
ANOMALOUS HALL EFFECT
T. Jungwirth, Q. Niu, A.H. MacDonald, Phys. Rev. Lett. 88, 207208 (2002)
anomalous velocity:
M0M=0
JpdNpd<S> (meV)
Berry curvature:
AHE without disorder
The valence band picture of IR absorption
F = dRe[()] = e2p / 2m
opt
mopt
independent of
(within 10%):· density· disorder· magnetic state
GaAsm
op 0.24 m
e
infrared absorption accurate density measurement
hole density: p=0.2, 0.3, ....., 0.8 nm-3
exp.
J. Sinova, et al. Phys. Rev. B 66, 041202 (2002).
x=5%
Exps: Singley et al Phys. Rev. Lett. 89, 097203 (2002)Hirakawa, et al Phys. Rev. B 65, 193312 (2002)
FINITE SIZE EXACT DIAGONALIZATION STUDIESFINITE SIZE EXACT DIAGONALIZATION STUDIES
S.-R. E. Yang, J. Sinova, T. Jungwirth, Y.P. Shim, and A.H. MacDonald, PRB 67, 045205 (03)
6-band K-L model
parabolic band model
p=0.33 nm-3, x=4.5%, compensation from anti-sites
p=0.2 nm-3, x=4.0%, compensation from anti-sites
6-band K-L model
GaAs
GaAs
f-sum rule accurate within 10 %
● Energy dependence of Jpd
● Localization effects
● Contributions due to impurity states: Flatte’s approach of starting from isolated impurities
● Systematic p and xeff study (need more than 2 meff data points)
Possible issues regarding IR absorption
Keeping Keeping ScoreScore
The effective Hamiltonian (MF) and weak scattering theory (no free parameters) describe (III,Mn)V shallow acceptor metallic DMSs very well in the regime that is valid:
• 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
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
OUTLINEOUTLINE Intro: Spintronics and Semiconductor Spintronics DMS’s Intro:
III-V Semiconductors: the basic picture Perhaps Pauli was right: the messy reality Discovery and cool down of expectations
Can we have a high Tc DMS? Origin of the coupling between local moments and delocalized
carriers Basic phase diagram Theoretical approaches: no silver bullet but a good arsenal Is there an intrinsic limitation from theory Extrinsic limitations
What is the data telling us in GaMnAs: thumbs up or down? Strategies to achieve high Tc DMSs
Strategy A: focus on GaMnAs Strategy B: use what we have learned from DMSs to search for other
materials Increasing coupling strength but still sallow levels Mathematical strategy: decompose 3
d4
d
Weak hybrid.Delocalized holeslong-range coupl.
Strong hybrid.Impurity-band holesshort-range coupl.
d 5 d 4 no holes
InSb, InAs, GaAs Tc: 7 173 K
(GaN ?)
GaP Tc: 65 K
Similar hole localization tendencies
in (Al,Ga)As and Ga(As,P)
Scarpulla, et al. PRL (2005)
d5
Limits to carrier-mediated
ferromagnetism in (Mn,III)V