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Jairo Sinova (TAMU)
Making semiconductors magnetic: A new approach to engineering quantum materials
NERCSWAN
OUTLINE• DMS: intro to the phenomenology
– General picture– Theoretical approaches to DMSs
• Are we stuck with low Tc?– Intrinsic limits– Extrinsic limits– Strategies to increase Tc
• Impurity band and valence band in doped semicondcutors• Low doped insulating GaAs:Mn
– Activation energy: dc-transport and doping trends– Ac-conductivity and doping trends
• Impurity-band to disordered-valence-band crossover in highly-doped metallic GaAs:Mn– Dc-transport: lack of activation energy – Ac-conductivity– Red-shift of ac-conductivity mid-infrared peak in GaMnAs
• Other successful descriptions of system properties within the disordered-valence band treatment of metallic GaMnAs
– Tc trends vs substitutional Mn doping and carrier density; Magnetic anisotropy; Temperature dependence of transport in metallic samples, Magnetization dynamics; Domain wall dynamics and resistances; Anisotropic magnetoresistance; TAMR; Anomalous Hall effect
• Conclusions
Mn
Ga
AsMn
Ferromagnetic semiconductors
GaAs - GaAs - standard III-V semiconductorstandard III-V semiconductor
Group-II Group-II Mn - Mn - dilute dilute magneticmagnetic moments moments & holes& holes
(Ga,Mn)As - fe(Ga,Mn)As - ferrromagneticromagnetic semiconductorsemiconductor
More tricky than just hammering an iron nail in a silicon wafer
Mn
Ga
AsMn
Mn–hole spin-spin interaction
hybridization
Hybridization like-spin level repulsion Jpd SMn shole interaction
Mn-d
As-p
(Ga,Mn)As(Ga,Mn)As
5 d-electrons with L=0 S=5/2 local moment
intermediate acceptor (110 meV) hole
- Mn local moments too dilute (near-neighbours couple AF)
- Holes do not polarize in pure GaAs
- Hole mediated Mn-Mn FM coupling
Mn
Ga
AsMn
Ohno, Dietl et al. (1998,2000);Jungwirth, Sinova, Mašek, Kučera, MacDonald, Rev. Mod. Phys. (2006), http://unix12.fzu.cz/ms
Heff
= Jpd
<shole> || -x
MnAs
Ga
heff
= Jpd
<SMn> || x
Hole Fermi surfaces
Ferromagnetic Mn-Mn coupling mediated by holes
Technologically motivated and scientifically fueled
Incorporate magnetic properties with semiconductor
tunability (MRAM, etc)
Understanding complex phenomena:•Spherical cow of ferromagnetic systems (still very complicated)•Engineered control of collective phenomena•Benchmark for our understanding of strongly correlated systems
Generates new physics:•Tunneling AMR•Coulomb blockade AMR•Nanostructure magnetic anisotropy engineering
ENGINEERING OF QUANUTM MATERIALS
More knobs than usual in semiconductors: density, strain, chemistry/pressure, SO coupling engineering
Dilute moment nature of ferromagnetic semiconductors
GaAs Mn
Mn
10-100x smaller Ms
One
Current induced switchingreplacing external field Tsoi et al. PRL 98, Mayers Sci 99
Key problems with increasing MRAM capacity (bit density):
- Unintentional dipolar cross-links- External field addressing neighboring bits
10-100x weaker dipolar fields
10-100x smaller currents for switching
Sinova et al., PRB 04, Yamanouchi et al. Nature 04
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]
Recently discovered in metals as well!
One
Dipolar-field-free current induced switching nanostructures
Micromagnetics (magnetic anisotropy) without dipolar fields (shape anisotropy)
~100 nm
(b)
Domain wall
Strain controlled magnetocrystalline (SO-induced) anisotropy
Can be moved by ~100x smaller currents than in metals
Humpfner et al. 06,Wunderlich et al. 06
Huge & tunable magnetoresistance in (Ga,Mn)As side-gated nano-constriction FET
Wunderlich, Jungwirth, Kaestner, Shick, et al., preprint
Single-electron Single-electron transistortransistor
Coulomb blockade anisotropic magnetoresistance
Band structure (group velocities, scattering rates, chemical potentialchemical potential) depend on M
Spin-orbit coupling
If lead and dot differentIf lead and dot different (different carrier concentrations in our (Ga,Mn)As SET)
Q
0
DL'
D' )M()M()M(&
e
)M(Q)Q(VdQU
GMMGG0
20
C
C
e
)M(V&)]M(VV[CQ&
C2
)QQ(U
electric && magneticmagneticcontrol of Coulomb blockade oscillations
OUTLINE• DMS: intro to the phenomenology
– General picture– Theoretical approaches to DMSs
• Are we stuck with low Tc?– Intrinsic limits– Extrinsic limits– Strategies to increase Tc
• Impurity band and valence band in doped semicondcutors• Low doped insulating GaAs:Mn
– Activation energy: dc-transport and doping trends– Ac-conductivity and doping trends
• Impurity-band to disordered-valence-band crossover in highly-doped metallic GaAs:Mn– Dc-transport: lack of activation energy – Ac-conductivity– Red-shift of ac-conductivity mid-infrared peak in GaMnAs
• Other successful descriptions of system properties within the disordered-valence band treatment of metallic GaMnAs
– Tc trends vs substitutional Mn doping and carrier density; Magnetic anisotropy; Temperature dependence of transport in metallic samples, Magnetization dynamics; Domain wall dynamics and resistances; Anisotropic magnetoresistance; TAMR; Anomalous Hall effect
• Conclusions
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
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 while checking against experiments
“This is the art of condensed matter science, an intricate tangobetween theory and experiment whose conclusion can only beguessed at while the dance is in progress”
A.H.M et al., in “Electronic Structure and Magnetism in Complex Materials” (2002).
· Model Anderson Hamiltonian: (s - orbitals: conduction band; p - orbitals: valence band)
+ (Mn d - orbitals: strong on-site Hubbard int. local moment)
+ (s,p - d hybridization)
· 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; J
pd > 0
k.p Local Moment - Hamiltonian
IjIjvjI
pd SsRrJ
,
THE SIMPLE MODEL
ELECTRONS
Mn
ELECTRONS-Mn
Large S: treat classically
Two Approximations
2-Mean Field Approximation
MNJh ˆ
extH
rsJH
Field felt by band electrons
Field felt by local moments
1-Virtual Crystal Approximation
N MnIjI
Rr
Bastard, J. de Physique, 39 p. 87 (1978) Gaj, Phys. Stat. Solidi 89 p.655 (1978)
Theoretical Approaches to DMSs
• First Principles 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 TB models
•k.p Local Moment
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
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)
Jungwirth, Sinova, Masek, Kucera, MacDonald, Rev. of Mod. Phys. 78, 809 (2006)
Which theory is right?
KP EastwoodFast principles Jack
Impurity bandit vs Valence Joe
OUTLINE• DMS: intro to the phenomenology
– General picture– Theoretical approaches to DMSs
• Are we stuck with low Tc?– Intrinsic limits– Extrinsic limits– Strategies to increase Tc
• Impurity band and valence band in doped semicondcutors• Low doped insulating GaAs:Mn
– Activation energy: dc-transport and doping trends– Ac-conductivity and doping trends
• Impurity-band to disordered-valence-band crossover in highly-doped metallic GaAs:Mn– Dc-transport: lack of activation energy – Ac-conductivity– Red-shift of ac-conductivity mid-infrared peak in GaMnAs
• Other successful descriptions of system properties within the disordered-valence band treatment of metallic GaMnAs
– Tc trends vs substitutional Mn doping and carrier density; Magnetic anisotropy; Temperature dependence of transport in metallic samples, Magnetization dynamics; Domain wall dynamics and resistances; Anisotropic magnetoresistance; TAMR; Anomalous Hall effect
• Conclusions
Curie temperature limited to ~110K.
Only metallic for ~3% to 6% Mn
High degree of compensation
Unusual magnetization (temperature dep.)
Significant magnetization deficit
But are these intrinsic properties of GaMnAs ??
“110K could be a fundamental limit on TC”
As
GaMn
Mn Mn
Problems for GaMnAs (late 2002)
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)?
EXAMPLE OF THE PHYSICS TANGO
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
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
Extrinsic effects: Interstitial Mn - a magnetism killer
Extrinsic 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 vary 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 Semicondcutors?
Tc linear in MnGa local (uncompensated) moment concentration; falls rapidly with decreasing hole density in heavily compensated samples.
Define Mneff = Mnsub-MnInt
NO INTRINSIC LIMIT NO EXTRINSIC LIMIT
There is no observable limit to the amount of substitutional Mn we can put in
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
0 1 2 3 4 5 6 70
20
40
60
80
100
120
140
160
180
TC(K
)
Mneff
(%)
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
- 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
LDA+U/CPA
(Al,Ga)As
Ga(As,P)
Ga(As,P)
10% Mn
10% Mn
5% Mn
theory
theory
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)?
III = I + II 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
No solubility limit for group-II Mn
substituting for group-II Zn !!!!
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
OUTLINE• DMS: intro to the phenomenology
– General picture– Theoretical approaches to DMSs
• Are we stuck with low Tc?– Intrinsic limits– Extrinsic limits– Strategies to increase Tc
• Impurity band and valence band in doped semiconductors• Low doped insulating GaAs:Mn
– Activation energy: dc-transport and doping trends– Ac-conductivity and doping trends
• Impurity-band to disordered-valence-band crossover in highly-doped metallic GaAs:Mn– Dc-transport: lack of activation energy – Ac-conductivity– Red-shift of ac-conductivity mid-infrared peak in GaMnAs
• Other successful descriptions of system properties within the disordered-valence band treatment of metallic GaMnAs
– Tc trends vs substitutional Mn doping and carrier density; Magnetic anisotropy; Temperature dependence of transport in metallic samples, Magnetization dynamics; Domain wall dynamics and resistances; Anisotropic magnetoresistance; TAMR; Anomalous Hall effect
• Conclusions
Example: Si:P --- shallow impurity where most of the binding energy is hydrogenic-like.
MI transition occurs when impurity bound states begin to overlap
For GaAs shallow impurities (C,Be,Zn,..) this occurs at 1018 cm-3
For intermediate impurities (Ea~110 meV) this occurs at higherimpurity concentration NMn~1020 cm-3
In Ga1-xMnxAs x=1% corresponds to a substitutional doping concentration of NMn~2.2 x 1020 cm-3
General picture of MI transition in doped semiconductors
General picture of MI transition in doped semiconductors: cross over from IB to VB
Mn-d-like localmoments
As-p-like holes
Mn
Ga
AsMn
EF
DO
S
Energy
spin
spin
with 5 d-electron local moment
on the Mn impurity
valence band As-p-like holes
As-p-like holes localized on Mn acceptors
<< 1% Mn
onset of ferromagnetism near MIT
Jungwirth et al. RMP ‘06
~1% Mn >2% Mn
MI transition in GaMnAs: cross over from IB to VB (no sharp boundary)
OUTLINE• DMS: intro to the phenomenology
– General picture– Theoretical approaches to DMSs
• Are we stuck with low Tc?– Intrinsic limits– Extrinsic limits– Strategies to increase Tc
• Impurity band and valence band in doped semicondcutors• Low doped insulating GaAs:Mn
– Activation energy: dc-transport and doping trends– Ac-conductivity and doping trends
• Impurity-band to disordered-valence-band crossover in highly-doped metallic GaAs:Mn– Dc-transport: lack of activation energy – Ac-conductivity– Red-shift of ac-conductivity mid-infrared peak in GaMnAs
• Other successful descriptions of system properties within the disordered-valence band treatment of metallic GaMnAs
– Tc trends vs substitutional Mn doping and carrier density; Magnetic anisotropy; Temperature dependence of transport in metallic samples, Magnetization dynamics; Domain wall dynamics and resistances; Anisotropic magnetoresistance; TAMR; Anomalous Hall effect
• Conclusions
Low doped insulating GaAs:MnActivation energy from dc-transport
J. S. Blakemore, W. J. Brown, M. L. Stass, and D. A. Woodbury, J. Appl. Phys. 44, 3352 (1973).
Low doped insulating GaAs:MnActivation energy from dc-transport
Sample Mn(4D) has Mn density 1.6 x1017 cm−3(, M5: 1.1 x1018cm−3, M10:1.9 x1019 cm−3, Mn5A: 9.3 x1019 cm−3.
J. S. Blakemore, W. J. Brown, M. L. Stass, and D. A. Woodbury, J. Appl. Phys. 44, 3352 (1973).
M. Poggio, R. C. Myers, N. P. Stern, A. C. Gossard, and D. D. Awschalom, Phys. Rev. B 72,
235313 (2005). MBE grown samples.
Low doped insulating GaAs:MnActivation energy from dc-transport
Infrared photoabsorption crossection measurements in bulk GaAs:Mn. Mn(4): 1.7 x1017 cm−3, Mn(5): 9.3 x1018 cm−3.
W. J. Brown and J. S. Blakemore, J. Appl. Phys. 43, 2242 (1972).
Expected absorption cross section for a non-shallow impurity (peak at 2Ea)
Consistent with the Ea obtained from the dc-transport, a peak at ~ 200 meV is observed in the weakly doped Mn(4) GaAs:Mn samples. At higher doped sample Mn(5) the peak is slightly red shifted (~ 180 meV) and broadened
OUTLINE• DMS: intro to the phenomenology
– General picture– Theoretical approaches to DMSs
• Are we stuck with low Tc?– Intrinsic limits– Extrinsic limits– Strategies to increase Tc
• Impurity band and valence band in doped semicondcutors• Low doped insulating GaAs:Mn
– Activation energy: dc-transport and doping trends– Ac-conductivity and doping trends
• Impurity-band to disordered-valence-band crossover in highly-doped metallic GaAs:Mn– Dc-transport: lack of activation energy – Ac-conductivity– Red-shift of ac-conductivity mid-infrared peak in GaMnAs
• Other successful descriptions of system properties within the disordered-valence band treatment of metallic GaMnAs
– Tc trends vs substitutional Mn doping and carrier density; Magnetic anisotropy; Temperature dependence of transport in metallic samples, Magnetization dynamics; Domain wall dynamics and resistances; Anisotropic magnetoresistance; TAMR; Anomalous Hall effect
• Conclusions
Impurity band to disordered-valence-band cross over in high-doped GaAs:Mn: dc-transport
Jungwirth, Sinova, MacDonald, Gallagher, Novak, Edmonds, Rushforth, Campion, Foxon, Eaves, Olejnik, Masek, Yang, Wunderlich, Gould, Molenkamp, Dietl, Ohno, arXiv:0707.0665
•For Mn doping around 1%, the conductivity curves can no longer be separated into an impurity-band dominated contribution at low temperatures and an activated valence-band dominated contribution at higher temperatures•Above 2%, no activation energy is observed even as high as 500 K where activation across the gap takes over
Impurity band to disordered-valence-band cross over in high-doped GaAs:Mn: dc-transport
Jungwirth, Sinova, MacDonald, Gallagher, Novak, Edmonds, Rushforth, Campion, Foxon, Eaves, Olejnik, Masek, Yang, Wunderlich, Gould, Molenkamp, Dietl, Ohno, arXiv:0707.0665
same growth conditions but <1% insulating
Comparable mobilities of shallow and intermediate acceptor systems
K. S. Burch, et al, Phys. Rev. Lett. 97, 087208 (2006), E. J. Singley, et al, Phys. Rev. Lett. 89, 097203 (2002). E. J. Singley, et al, Phys. Rev. B 68, 165204 (2003).
T=292 K T=7 K
Associating peak to an IB is implausible because of:
(i) the absence of the activated dc-transport counterpart in the high-doped metallic samples,
(ii) the blue-shift of this mid-infrared feature with respect to the impurity band transition peak in the NMn 1019 cm −3 sample,
(iii) the appearance of the peak at frequency above 2Ea,(iv) the absence of a marked broadening of the peak with
increased doping.
Impurity band to disordered-valence-band cross over in high-doped GaAs:Mn: ac-absorption experiments
Impurity band to disordered-valence-band cross over in high-doped GaAs:Mn: ac-absorption experiments
W. Songprakob, R. Zallen, D. V. Tsu, and W. K. Liu, J. Appl. Phys. 91, 171 (2002).
J. Sinova, et al. Phys. Rev. B 66, 041202 (2002).
GaAs
x=5%
C-doped (shallow acceptor) experimentsat a doping well within the metal side
Virtual crystal approximation (no localizationeffects).
hole density: p=0.2, 0.3, ....., 0.8 nm-3
Hirakawa, et al Phys. Rev. B 65, 193312 (2002)
Impurity band to disordered-valence-band cross over in high-doped GaAs:Mn: red-shift of the IR peak in GaMnAs
At low doping near the MI transitionNon-momentum conserved transitions to localized states at the valence edge take away spectral weight from the low frequency
As metallicity/doping increases the localized states near the band edge narrow and the peak red-shifts as the inter-band part adds weight to the low-frequency part
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)
No-localization approximation
Exact diagonalization results in reasonable agreement with as-grown samples
x=4.0%, compensation from anti-sites
x=4.5%,
Lower compensation
x 2
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
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
OUTLINE• DMS: intro to the phenomenology
– General picture– Theoretical approaches to DMSs
• Are we stuck with low Tc?– Intrinsic limits– Extrinsic limits– Strategies to increase Tc
• Impurity band and valence band in doped semicondcutors• Low doped insulating GaAs:Mn
– Activation energy: dc-transport and doping trends– Ac-conductivity and doping trends
• Impurity-band to disordered-valence-band crossover in highly-doped metallic GaAs:Mn– Dc-transport: lack of activation energy – Ac-conductivity– Red-shift of ac-conductivity mid-infrared peak in GaMnAs
• Other successful descriptions of system properties within the disordered-valence band treatment of metallic GaMnAs
– Tc trends vs substitutional Mn doping and carrier density; Magnetic anisotropy; Temperature dependence of transport in metallic samples, Magnetization dynamics; Domain wall dynamics and resistances; Anisotropic magnetoresistance; TAMR; Anomalous Hall effect
• Conclusions
Effective Moment density, Mneff = Mnsub-MnInt due to AF Mnsub-MnInt pairs.
Tc increases with Mneff when compensation is less than ~40%.
No saturation of Tc at high Mn concentrations
Closed symbols are annealed samples
0 1 2 3 4 5 6 70
20
40
60
80
100
120
140
160
180
TC(K
)
Mneff
(%)
High compensatio
n
Linear increase of Tc with effective Mn
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:
Lopez-Sanchez and Bery 2003Hwang and Das Sarma 2005
Resistivity temperature dependence of metallic GaMnAs
theory theory
experiment
Ferromagnetic resonance: Gilbert damping
Aa,k()
I
M
Anisotropic Magnetoresistance
exp.
T. Jungwirth, M. Abolfath, J. Sinova, J. Kucera, A.H. MacDonald, Appl. Phys. Lett. 2002
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
ANOMALOUS HALL EFFECT IN GaMnAs
Experiments
Clean limit theory
Minimal disorder theory
ConclusionNo 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
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
BEFORE 2000
CONCLUSION: directors cut
BUT it takes MANY to do the physics tango!!
Texas A&M U., U. Texas, Nottingham, U. Wuerzburg,
Cambirdge Hitachi, ….
It IS true that it takes two to tango
2000-2004
2006NEW DMSs ,More heterostructures
NEXT
Mn-d-like localmoments
As-p-like holes
Mn
Ga
AsMn
EF
DO
S
Energy
spin
spin
GaAs:Mn – extrinsic p-type semiconductor
with 5 d-electron local moment
on the Mn impurity
valence band As-p-like holes
As-p-like holes localized on Mn acceptors
<< 1% Mn
onset of ferromagnetism near MIT
Jungwirth et al. RMP ‘06
~1% Mn >2% Mn
STILL LARGELY UNEXPLORED SYSTEMATICALLY: MIT
Impurity band to disordered-valence-band cross over in high-doped GaAs:Mn: red-shift of the IR peak in GaMnAs
At low doping near the MI transitionNon-momentum conserved transitions to localized states at the valence edge take away spectral weight from the low frequency
As metallicity/doping increases the localized states near the band edge narrow and the peak red-shifts as the inter-band part adds weight to the low-frequency part
Integrated read-out, storage, and transistor
Low current driven magnetization reversal
Parkin, US Patent (2004)
Magnetic race track memory
Yamanouchi et al., Nature (2004)
2 orders of magnitude lower criticalcurrents in dilute moment (Ga,Mn)As than in conventional metal FMsSinova, Jungwirth et al., PRB (2004)
Wunderlich, et al., PRL (2006)
Ideal to study spintronics fundamentals
Family of extraordinary MR effects, R(M),in ohmic, tunneling, Coulomb-blockade regimes
Low Ms (1-10% Mn moment doping): 100-10 x weaker mag. dipolar interactions can allow for100-10 x denser integration without unintentional dipolar cross-links
Strong SO-coupling:magnetocrystalline anisotropy ~ 10 mT & doping and strain dependent can replacedemagnetizing shape anisotropy fields & local control of magnetic configurations
... and more yet to be fully exploited
Impurity band to disordered-valence-band cross over in high-doped GaAs:Mn: ac-absorption experiments
Hot electron photoluminescence studies: comparison of Zn doped and Mn doped
Left panel: HPL spectra of GaAs doped with ~ 1017 cm−3 of Zn and ~ 1019 cm−3 of Zn. (replotted in logarithmic scale).
HPL spectra of GaAs doped with ~ 1017 cm−3 of Mn, and of ≈ 1% and ≈ 4% GaAs:Mn materials.
Eex is the HPL excitation energy. Arrows indicate the spectral feature corresponding to impurity band transitions in the low-doped materials.
A. Twardowski and C. Hermann, Phys. Rev. B 32, 8253 (1985).
V. F. Sapega, M. Moreno, M. Ramsteiner, L. D¨aweritz, and K. H. Ploog, Phys. Rev. Lett. 94, 137401 (2005).
Allan MacDonald U of Texas
Tomas JungwirthInst. of Phys. ASCR
U. of Nottingham
Joerg WunderlichCambridge-Hitachi
Bryan GallagherU. Of Nottingham
Tomesz DietlInstitute of Physics, Polish Academy of
Sciences
Other collaborators: Jan Masek, Karel Vyborny, Bernd Kästner, Carten Timm, Charles Gould, Tom Fox,
Richard Campion, Laurence Eaves, Eric Yang, Andy Rushforth, Viet Novak
Hideo OhnoTohoku Univ.
Laurens MolenkampWuerzburg
Jairo SinovaTexas A&M Univ.
Ewelina HankiewiczFordham Univesrsity