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