Spins in Solids 1
Magnetic Magnetic PolaronsPolarons ininConcentrated and Diluted Magnetic Concentrated and Diluted Magnetic
SemiconductorsSemiconductorsS. von Molnár
Martech, The Florida State University, Tallahassee FL 32306
Past support by DARPA and the Office of Naval Research, ONR N00014-99-1-1094 and
MDA -972-02-1007For: Spins in Solids,
June 23rd, 2006.
Gd3-xvxS4
Ref. 1
Spins in Solids 2
Example δM δρ(T)
Why ?
The Insulator-metal transition at TC in Eu0.95La0.05S
TC ∼ 25 K
Ref. 2
Spins in Solids 3
δM δρ(T)
The Insulator-metal transition at TC in Eu0.99La0.01Se
Example
Ref. 3
Spins in Solids 4
Extra Energy Term in Magnetic Semiconductors
α B*
S S s J 2 HµgErr
+=
αS r
: Value of S averaged over region occupied by electron, s
1 2
2 >> 1Results in :
• Giant band splitting ES (EuS) ~ 0.5 eV
• Magnetic polarons ⇒ Local FM order in PM host
Spins in Solids 5
Europium Chalcogenides : EuX (X= O, S, Se, Te)
Prototype System
EuX : Prime example of concentrated magnetic semiconductor
EuS, EuO : First ferromagnetic insulators (ideal Heisenberg ferromagnets)
magnetism transport, optics, ...σ⋅ rrSJ
dopingcarrier injection
optical excitation δn δM δθp, δTC δρ(T)
Example
δn δθp
Ref. 4
Spins in Solids 6
Optical Red Shift in EuX
SsJ2E sfrr
−= EuS : Jsf ≈ 4.3 10-2 eV
4f
d(t2g)
Ref. 5
Spins in Solids 7
Schottky Device
4f states
Capacitance vs. Voltage of a EuS-Sn junction having T above and below the Curie temperature.
Band-Splitting + Spin Polarization
MetalFermiLevel
ϕ
1.7V 2.4V
d
EuSIn or Sn
Ref. 6
Spins in Solids 8
Fowler-Nordheim Tunneling
MetalFermiLevel
MetalFermiLevel
ϕ
eVTunneling
Bottom of the empty conduction band in EuX I
V
H
Meservey-Tedrow Technique
Characterization: Spin Polarization
Metal contact
Insulator
Ferromagnet
AldI/dV
V
Ref. 7
Ref. 8
Spins in Solids 9
E
N(E)
∆
−∆EF
eV
F S
µH
H
Measurement of spin polarization using Zeemansplitting
eV/∆
Meservey and Tedrow (1994)Ref. 9
Spins in Solids 10
Results for CrO2
-0.6 -0.4 -0.2 0.0 0.2 0.4 0.60.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
G (V
) / G
N
V (mV)0.0 0.5 1.0 1.5 2.0 2.50
20
40
60
80
100
∆ (µ
eV)
H (T)
-0.5 0.0 0.50.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
H = 0.0 T = 0.5 T = 1.0 T = 1.5 T = 2.0 T = 2.5 T
G (V
) / G
N
V (mV)
Results: Zeeman splitting
T =400 mK
+2.5T-2.5T
Spins in Solids 11
Lateral all electrical all sc spintronics device
Detector
Injector
Semiconductor
1. Source of spin polarized electrons
2. Long spin diffusion length ( SD)
L< SD
3. Efficient spin injection and detection
Conductivity mismatch
Spins in Solids 12
Schmidt et.al., PRB, 2000
Solutions:
Use injector
with 100% spin
polarization
Non-diffusive
injection
Conductivity
matching
Spin Injection: the conductivity mismatch
RF1↑
I↑
I↓
I
RSC↓RF1↓
RSC↑ RF2↑
RF↓
σF > σSC
Ref. 10Ref. 10
Spins in Solids 13
3. What about the interface?
2. GaAs: ~100µmspin diffusion lengthJ. M . Kikkawa and D. D. Awscahlom, Nature 397, (1999)
Single EuS/GaAs heterojunction in both the injector and the detector modes
V
EuSGaAs
I
1.1. EuS: ~100% spin EuS: ~100% spin polarizationpolarization
L. Esaki, P. J. Stiles and S. von Molnár, Phys. Rev. Lett. 19, (1967)
e- ?
EuS/GaAsEuS/GaAs HeterostructureHeterostructure
Ref. 11Ref. 11
Ref. 12Ref. 12
Spins in Solids 14
T<TC
EF
∆ES (EuS) ~ 0.5 eV
High - close to 100% spin polarization
EuS: Magnetic and transport properties
EuS: a ferromagnetic insulator with TC=16.5K
EuS:Conductivity tuning100% spin polarization
I.J. Guilaran et al.,PRB 68, 144424 (2003)Ref. 13
Spins in Solids 15
Zeeman splitting and the I-V characteristics
T >TCEuS - paramagnetic
EuSΦΒ
Both spin species haveequal probability oftunneling through the barrier.
∆ΦB=½ ∆ES
T<TC EuS - ferromagnetic
ΦB↓ = ΦB + ∆ΦB
ΦB↑ = ΦB - ∆ΦB
Spin up electrons have much higher probability of tunneling through the barrier – the spin filter effect.
EuS film measurements
Semiconductingparamagnetic region
Increased spin scattering
Ferromagnetic region
0 50 100 150 200 250 300
0
2
4
6
8
10
12
14
16
18
R(kΩ
)
T (K )
55K
ΦΒ
Spins in Solids 16
Schottky device: GaAs/EuS; Injection from EuS into GaAs
eVB )06.024.0( ±=∆Φ
0 5 1 0 1 5 2 0 2 5 3 0 3 50 .0
0 .2
0 .4
0 .6
0 .8
1 .0
Nor
mal
ized
∆Φ
B
T (K )
S=7/2 Brillouin function
00C00B E))(T(T)/Iln(I(T)∆Φ ×=
Brillouin fit to the insulating EuSTC : Field emission is probing thedepletion region of the EuS barrier
0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0
0
1 x 1 0 - 1 4
2 x 1 0 - 1 4
3 x 1 0 - 1 4
4 x 1 0 - 1 4
5 x 1 0 - 1 4
I 0*exp
(-ΦΒ/E
00)
T ( K )Thermionic field emission
Field emissionCurrent rises due to the barrier lowering
)))exp(V/E(T)/EΦ(exp(IT)I(V, 0000B0 −=Tribovic et al.(2005)
Transport across EuS/GaAs HJ dominated by depletion region of EuS
Ref. 14Ref. 14
Spins in Solids 17
I-M transition in EuO
Low concentration (Eu excess, accidental)
I ≠ F(HA)
Example
Penny et al. (1972)
See also Oliver et al. (1970)
Shapira et al. (1973)
Ref. 15Ref. 15
Ref. 16Ref. 16
Ref.17Ref.17
Spins in Solids 18
Example
M-I Transition
Insulating EuTe ⇒ Antiferromagnet
n = 8 1018 cm-3
Ref. 17
Spins in Solids 19
Example Gd3-xvxS4 v = vacancy
AF insulator x=1/3
F.M. metal x=0
Large negative MR
EC
EF
( ) kTEE0
FCe −ρ=ρ
EC-EF ∝ H ; EC-EF |H=0 ≈ 60 K
#2 n = 1.6 1020 cm-3
#3 n = 8.7 1019 cm-3
Ref. 18
Spins in Solids 20
The paramagnetic polaron [A.F. is much the same]
“Gedanken experiment”; T > TN (TC)
Magnetic PolaronsUbiquitous in all magnetic semiconductorse.g. CdMnTe, GaMnAs, …, (LaCa)MnO3 ...
Carrier motion impeded
External field or magnetic order (internal field) will align spins outside of red circle.
e- captured
aligns neighboring spinselectron
(hole)Donor
(acceptor)
“
”
Ref. 3
Spins in Solids 21
n1 > n2
n2 > n3
n3 ~ 1020 cm-3
n3 ≈ 0
Evidence for magnetic polarons
+ =A.F
F.M
• M0 gives minimum size of polaron
• Constant slope means incomplete saturation
Ms = 190 emu/gm
Ref. 1
Spins in Solids 22
Stability of polaron
If no impurity present
R
∆F
Polaron solution for R →∞
If coulomb trap exists
R
∆FPolaron stable at rP,
Increases with H → I-M
rP (H=0) rP (H>0)
For PM, FM (EuS): ∆T = T - θ ~ 3 K
For AF (EuTe): ∆T ~ T < TN
More recently (1999)Khomskii and collaborators
Ref. 19
(Ref. 20)
Spins in Solids 23
Magnetic polarons
A: / Pr ...
/ ... La
Sr Ca
3 3
2 2
+ +
+ +
B Mn
Mn:
3
4
+
+
O2−
ABO3
−++−
++−
23O 4
xMn3x1Mn 2
xM3x1LaLaMnO3 x
AF insulator FM metal
de Gennes (1960)
Spin canting with increasing x
Magnetic Polarization !
Ref. 21
Ref. 22
Spins in Solids 24
Example
La0.67Ca0.33MnO3 Magnetoresistance
TC ≈ 270 K
CMR
Ref. 23
Spins in Solids 25
Lattice magnetic polaron
Coupling to lattice degrees of freedom essential
• Millis, et al. (1995) Ref. 24
• Röder, et al. (1996) Ref. 25
• Snyder, et al. (1996) Ref. 26
Two-fluid model
• Jaime et al. (1999) Ref. 27
Theory
• Gor’kov & Kresin (1998, 2000) Refs. 28,29
Noise Spectroscopy
•• Raquet et al. (2000) Ref. 30
•Merithew et al. (2000) Ref. 31
FMAF
FM
Insulator
FM
FM
Metal
Percolation
Spins in Solids 26
Spectroscopic Scanning Tunneling MicroscopyFäth et al. (1999)
La2/3Ca1/3MnO3
Generic spectroscopic images (0.61 µm x 0.61µm) of the local electronic structure taken just below TC.
From left to right and top to bottom.0, 0.3, 1, 3, 5, 9 Tesla
Ref. 32
Spins in Solids 27
Dilute Magnetic Semiconductors
♦ Take a well-known semiconductor and introduce a magnetic species substitutionally into the lattice
dilute magnetic systemdilute magnetic system
CdTe Cd1-xMnxTe
♦ Magnetic behavior is tunable by varying the concentration x
♦ Spin-spin interactions;ion-conduction band (valence band)ion-ion
Also: Hg1-xMnxTe Hg1-xFexTeZn1-xMnxTe Hg1-x-yCdxMnyTePb1-xMnxS etc.
Spins in Solids 28
Awschalom (1986) Ref. 33
Spins in Solids 29
Awschalom (1989) Ref. 34
Spins in Solids 30
M
E
A
BC
C) Magnetism occurs via spin flip exchange (Krenn, Zawadzki, Bauer, 1985)
⇓
e, h Mn2+NMn >> ne, nh
Mn polarization << 1
τ ~ 10-12 sec
Response (Static)
A) Sample transparent
B) Region of polaron formation(slightly below Eg ⇒ Bound exciton)
C) Above band gap ⇒ constant signalbut smaller than in B
Eg
Spins in Solids 31
InMnAs Characterization: Magnetism
Magnetization Measurements by SQUID:
1. Is the material single phase?
2. Determination of TC: M vs. (H,T), Arrott plots
InMnAs
Munekata et al. 1989
von Molnár et al. 1991
Ref. 35, 36
Spins in Solids 32
InMnAs
1.3% Mn, TC ≈ 10K
H. Ohno et al. (1992)
GaMnAs
5% Mn, TC ≈ 110K
H. Ohno et al. (1998)
(In, Mn)As, (Ga, Mn)As
Low temperature MBEfor more Mn incorporation
Hall sheet resistivity: )( 00 MRBRM
dRB
dRR sHall
SH +=+= ρ
sheet
H
RR
cM 1
≈ sheetS cR
dR
=because "SkewScattering"
Ref. 38
Ref. 37
Spins in Solids 33
Characterization: Magnetism
Magneto-Optical Characterization
Faraday rotation : Rapid Measurement of Magnetization and TC
Magneto-optical absorption : Exchange Constant
The splitting of the free exciton line vs. magnetization for GaMnAs
x = 0.00047x = 0.00027x = 0.00022
∆E = λ x <S>
and
x <S> ∝ M
Extrapolation : for x ~ 0.05 ∆E ~ 0.3 eV
Ref. 39
Spins in Solids 34
Large Polarons
p-type (In, Mn)As Ohno et al. (1992)
HBcRRH 00
0 ; µµχρ =+=
T1/3 ⇒ Weak localization (Imry, 1982)⇓ + Mag. Field dependence
Large Bound Magnetic PolaronLarge Bound Magnetic PolaronDiameter > 10 nm; contains large # of Mn, and holes!!
Ref. 37
Spins in Solids 35
Oiwa et al. (1998), Iye et al. (1999)
Magnetic field dependence due to Jpd σp • SMn
Ref. 40
Spins in Solids 36
Dilute Magnetic Oxides
Wide band gap semiconductors (~3eV) ZnO, TiO2, SnO2 doped with transition metal (TM) impurities
If FM, Tc> room temperature even at low dopant concentrationIf FM, moment per ion decreases as impurity concentration increasesGiant moments reported at low impurity concentrationLack of reproducibility between groupsDisorder dependence: more disorder, higher moment
Magnetic Polaron Percolation?Secondary Phases/Contamination?
Spins in Solids 37
Bound Magnetic Polarons
Electron trapped in defect site forms polaron with orbit rH=ε(m/m*)a0Magnetic impurities within orbit are coupledHigh dielectric constant ε implies large polaron radius and large momentNearest neighbour pairs couple AFM due to superexchange
• This could explain lower moment observed as TM concentration increases (more nn pairs)
Coey et al., Nature Mat.4, 173 (2005) Ref. 41
Spins in Solids 38
• Cobalt clusters form at reduced growth pressure.
• Linear log(R) vs T-1/2
characteristic of hopping transport in multiphase systems.
• X-ray analysis shows epitaxial structure of rutile.
TiO2:Co
Ref. 38Ref. 38
Spins in Solids 39
New Developments: (Cd,Mn)Te 2DES
Size stable (ferro) magnetic clusters
J. Jaroszynski et al. (cond-mat/0509189, 2006) Ref. 42
Spins in Solids 40
New Developments: La1-xSrxCoO3
Small Angle Neutron Scattering (SANS)
• I-M transition at x~.18
• Small q constant radius magnetic cluster
• Large q critical scattering: correlations @ Tc
• Two phase GMR and ln ρ~T-1/2
• For x=0 defect induced “Magnetic Exciton”
Wu et al. (2005) Ref. 43
Giblin et al. (2005) Ref. 44
Spins in Solids 41
Magnetic Polaron Percolation
Overlapping polarons align forming FM clusters
Effective polaron radius depends on temperature (for details Kaminski, Das Sarma PRL 88 247202) Ref. 45
Below Tc material is FM
Magnetic properties depend both on impurity concentration and defect concentration
May explain observed lack of reproducibility and dependence on film quality
Spins in Solids 42
Secondary Phases/Contamination
Reports of secondary magnetic phases forming in oxides (eg. Kundaliya et al. (2004). Nature Mat 3 709, Colis et al. (2005). Chem Phys Lett
415, 337-341 Refs. 46,47
Reports of segregation of magnetic TM impurities (eg. Kim et al. (2002). Appl. Phys Lett 81 2421, Kennedy et al. (2004). Appl Phys Lett 842832) Refs. 48,49
Reports of contamination from stainless steel tweezers (e.g. Abraham et al. (2005). Appl Phys Lett 87 252502. ) Ref. 50Reports of contamination from furnace during annealingMust be cautious in drawing conclusions
Very Recent Findings
GaN:Gd
a) For Gd concentration ~1016cm-3 – 1019 cm-3 => FM, Tc > room temperature
b) Low Gd concentration, magnetic moment/Gd ~ 4000 µB
EVEN WHEN INSULATING Dahr et al. (2005a) Ref. 51Polarization of GaN marix and percolation to achieve FM
Dahr et al. (2005b) Ref. 52c) Band Structure calculation propose polarization of donor electrons
Dalpain and Wei (2005) Ref. 53
Spins in Solids 43
Conclusions
Magnetic Magnetic polaronspolarons
are ubiquitousto concentrated and diluted magnetic
semiconductors
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