Disorder effects in 2D ferromagnetic semiconductor structures:

GaAs/InGaAs/GaAs quantum well with remote Mn delta-layer

B. Aronzon, A. Davydov, K. Kugel, V. Tripathi, K. Dhochak, A. Lashkul and E. Lahderanta

1. Introduction. Structure description. Proofs of 2D and ferromagnetic ordering.2. Disorder effects. Resistivity.3. Disorder effects. Noise.4. The nature of ferromagnetic ordering. Models.5. Conclusion.

Semiconductor spintronics. 2 problems. Tc and 2D

2

Quantum well with Mn delta layer

2D

GaAs, 15-18 nm

-layer Mn

spacer GaAs, 3 nm

QW InGaAs, 9-10 nm

-layer С

Buffer layer GaAs, 0.5 μm

cap-layer GaAs, 30-40 nm

Substratei-GaAs (100)

Awshalom et al., 2004Zaicev, et al., 2009Aronzon et al., 2006, 2009, 2010, 2011, 2012Wegscheider et al., 2007, 2010Dietl et al. 2010Sapega et al. 2012

Buffer GaAs, 25 нм

cap-layer GaAs, 60-80 нм

δ-layer Mn

spacer GaAs, 1-5 нм

QW InGaAs, 9-10 нм

GaAs, 5 нмδ-Be

SubstrateGaAs, (100)

B.N. Zvonkov et al.N. Novgorod

Y. Furdyna et al.Buffalo

Parametes of the samplesParametes of the samples

3

-12 -8 -4 0 4 8 12

5000

10000

15000

20000

25000T=5KB _I_ xy

Rx

x, O

hm

B, T

0 4 8 1214600

14800

15000

15200

Rxx

, Ohm

B, T

T=5K

B in plane

Quantum Hall Effect

Mn 0.5ML

10 200

20

40n

s = 4.56*1011cm-2

Rxx

, KO

hm

B, T

GaAs(Mn)/In0.17

Ga0.83

As/GaAs

d=10nm,

0 10 20 300

10

20

30

40

InGaAs/GaAs QW

Rxy

, KO

hm

B, T

Rk = h/e2

2D

J. Appl. Phys. 107, 023905 (2010)

Transport proofs for ferromagnetism

Pure carbon doping (Sample 5) shows no resistance anomaly. Samples 1 and 4 show hysteresis in magnetisation curve. [ JETP Lett. (2008)] Anomalous Hall effect observed in all samples doped with Mn.

? Metal - insulator transition under rise of

Mn content ?

Resistivity Anomalous Hall effect

Hall resistance dependes on spin-orbit interaction and carrier polarization

RHd= yx = R0B + RsM

Formation of charge carrier puddles in the quantum well (QW) from competition of doping disorder and nonlinear screening.

z0

Partially ionized Mn dopants

Typical potential fluctuation Vfluc

Location of holes in thetransverse direction

Hole wavefunction in transversedirection

After Gergel’ and Suris paper and Shklovskii and Efros

Fluctuation potential

Schematic of the quantum well potential (shown inverted). Dashed (blue) line represents the quantum well potential in the absence of fluctuations and the solid (red) line shows the potential well with an attractive fluctuation potential. The dotted line indicates the Mn dopants at a distance from the left face of the quantum well.

Model of nanoscale inhomogeneitiesModel of nanoscale inhomogeneities

z0

2

20

2

1log16 z+

R+

en'ze=zV c

2a2

fluc

RMS potential fluctuation:

n’a - Density of ionized Mnatoms

Screening length correspondsto carrier density p:

p

n'=R a

c

/

[Kennett, Tripathi, PRB (2006)]

PRB, 2011

Electrical resistanceElectrical resistance: : Role of ferromagnetic correlationsRole of ferromagnetic correlations

Mijij

ijA

D=

TJ+TE=T

ξ/expθcos

/θcos1/exp0ρρ

Vb a r r i e r

i j

θi j

EA + J(1-cos θ

i j )

Extra energy cost due to spin orientation

Di j

Resistivity anomalycorresponds to rapid change of magnetic contribution.

Cosine term changes appreciably whenmagnetic correlation length becomes ofthe order of droplet separation.

PRB, 2011

Observed temperature dependence of resistance for (a) Sample 4, in units of the resistance at 70 K, and (b) Sample 1, in units of the resistance at 90 K (points), andtheoretical fits (solid lines). Sample 4 is near the percolation threshold and Sample 1 is well-insulating. The fits were made using Eq. (13). Parameters such as the activation energy EA and the droplet separation D1 were chosen close to the values obtained from the droplet model. The magnetic parameters J and TC were then varied to obtain the above fits. In both cases, the best fit value of TC was significantly larger than the temperature, at which the resistance anomaly (hump or shoulder) was observed.

Resistivity

PRB, 2011

Two phase system

Tc

Tс – local transition in magnetic islands

9

Power spectral density of electrical noise

10 100

1E-16

1E-15

1E-14

1E-13

at 150Hz

Pow

er S

pect

ral D

ensi

ty (

Hz

-1)

T (K)

at 10Hz

0,1 1 10 100 1000

1E-14

1E-13

1E-12

Pow

er S

pect

al d

ensi

ty x

freq

uenc

y

frequency, Hz

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

0 1 2 3 4 5

23K

22.6K

21.4K

21.5K

20.9K

20.6K

20.3K

20.1K

18.94K

18.94K

0.15

0 10 20 30 40 50 60 70 80 90

1,5x104

2,0x104

Rxx

, Ohm

T, K

4417

Percolation transitionin magnetic subsystem?

There are no transitions in transport properties.

PRB, 2012

10

Noise fit: Frequency dependenceNoise fit: Frequency dependenceThe long-time dependence of the resistivity autocorrelation functionSρ(t) extracted from the noise data at T = 4.0 K together with fits. The red curve is a fit to Sρ(t)=A/t1.05 + Bln(t/t0), blue curve is a fit to Sρ(t) = A/t2/5 + Bln(t/t0). In 2D, Sρ(t ) ∼ t−1 behavior is expected for a disordered RKKY ferromagnet and Sρ (t ) ∼ t−2/5 for double-exchange ferromagnets. The logarithmic time dependence indicates 1/f noise contributions. The fit to the RKKY model is better than to the double exchange.

Frequency dependence of noise at T = 4 K (solid curve) together with fits to the low- and high-frequency regimes. At the low-frequency end, the dashed curve and the dotted curve are fits to Sρ ∼ A − Bf2 and Sρ ∼ A − B lnf − Cf,respectively. At the high-frequency end, the fit is to Sρ ∼Af−1.53. 1.53

ρf~fS

PRB, 2012

Noise fit: Temperature dependenceNoise fit: Temperature dependence

Sample 4f = 150Hz

TefS cT /

~ 2

Fit to TC= 52K

PRB, 2012

Curie temperature dependence on the depth of quantum well

-4 -2 0 2 4 60

0,2

0,4

0,6

z

q0z

u0=3

51015

max

80 100 120 140 160 180

0

10

20

30

40

Tc,

K

E, meV

Mn 0,25 MC Mn 0,3 MC

5570

5765

5569

5572

5764

5763

J. Phys. Conf. Ser. 2013

55 and 57 set

48 set Mn 0.5 Ml

0.10 0.15 0.2020

25

30

35

40

Tc,

K

E, eV

4836

4834

4843

4831

4832 -4846

110 meV

U=100 meV U=140 meV U=180 meV

GaAs GaAs GaAs

Mn

131 2 3 4 525

30

Tc,

K

d, nm

Buffer GaAs, 25 нм

cap-layer GaAs, 60-80 нм

δ-layer Mn

spacer GaAs, 1-5 нм

QW InGaAs, 9-10 нм

GaAs, 5 нм

δ-Be

SubstrateGaAs, (100)

MBE

1 2 3 4 522

24

26

28

30

32

5575Mn 0,3In 0,3

Tc,

K

d, nm

5574Mn 0,3In 0,3 5570

Mn 0,3In 0,3

GaAs, 15-18 nm

-layer Mnspacer GaAs, 3 nm

QW InGaAs, 9-10 nm

-layer С

Buffer layer GaAs, 0.5 μm

cap-layer GaAs, 30-40 nm

Substratei-GaAs (100)

CVD

Curie temperature dependence on the spacer thickness

Mech

J. Phys. Conf. Ser. 2013

Models

M=0

GaAs

Mn

GaMnAs GaInAs

GaAsGaMnAs GaInAs

Itinerant FM ordering in GaMnAs layer. (S.Caprara et al. PRB (2011)).

Averkiev et al. – resonance tunneling.PRB (2012).

EF

Mn layer – GaMnAs

Tс – local transition in magnetic islands

Two phase system

Tc

L

Meilikhov et al. – overlapping of the wave function tails with GaMnAs layer.

JETP Letters (2008)

15

THANKS FOR YOUR

ATTENTION!

Disorder and magnetic interactions affect strongly both transport and magnetic properties of the structures and could explain the temperature dependence of resistance and noise quantitatively.

Conclusion

Model of nanoscale inhomogeneitiesModel of nanoscale inhomogeneities

z0

Assume Gaussian white noisedistribution for ionized dopants:

r'rn'=nr'nrn a 2

Fluctuation charge in circle ofradius R:

2

a

R

n'=Rn

2

Disorder screened by holes in QW: ca Rn'=Rn=p //2

PRB, 2011

Ferromagnetic correlations: modelsFerromagnetic correlations: models

cc

ccM

TT,TTa

TT,TTa=

2/exp

≫/1/ξ

I. Isotropic 2D Heisenberg ferromagnet

II. Uniaxial 2D Heisenberg ferromagnet

jij

i SSJ=H No long-range magnetic orderat finite temperature.

KJ

TT

SKSSJ=H

c

ijzj

iji

/ln~

20

2

0γ

0

0

~/1/

2/exp

≫/

ξ

TT,TTa

TTT,TTa

TT,TTa

= cc

cc

M

M. Bander, D. Mills, PRB (1988) 1.25= for Ising

Voltage noise: mVoltage noise: magnetic fluctuationsagnetic fluctuations

,,DCe+CTJS ijMijD

ααααα

22ρ ω

ξ/ω0,/ρ/ω

Resistivity noise from magnetic fluctuations

q,eqdT

=r,C riqαβ

2αβαβ Im

2

Autocorrelation functionof magnetisation

Autocorrelation function contains information on dynamics, and can shedlight on the mechanism of ferromagnetism.

Magnetic correlations: dynamicsMagnetic correlations: dynamics

q,iq+

T=q,

M /1 2

0αβαβResistivity noise is sensitive to

the dynamics of the ferromagnet:

Interested in two broad universality classes depending on whether the dynamics has a hydrodynamic description:

2

0ω/const. Mq,

=q,

Model A: No conserved order parametere.g. anisotropic Heisenberg

Model B: Conserved order parametere.g. Isotropic Heisenberg 2

q,Dq=q,

0ω

Hohenberg, Halperin, RMP (1977)

0 10 20 30 40 50 60 70 80

0

2

4

A

(GaAs)1-yMny

a/a, %

InхGa1-хAs

yM

n

0.0

0.1

0.2

0.3

0 10 20 30 40 50 60 70 80

0

2

4

0.0

0.1

0.2

0.3

0.4

B (GaAs)1-yMny

InхGa1-хAs

z, nм

yM

n

Sample 4831

sample4834

Mn content

40

GaAs, 15-18 nm

50-layer Mn

spacer GaAs, 3 nm

QW InGaAs, 9-10 nm

-layer С

Buffer layer GaAs, 0.5 μm

cap-layer GaAs, 30-40 nm

Substratei-GaAs (100)

z, nm

.0

55

60

Profile of the deviation of the lattice constant from its value for GaAs along the sample depth (z)

X-ray diagnostics of the samplesX-ray diagnostics of the samples2D

J. Appl. Phys. 107, 023905 (2010)

Noise fit: Frequency dependenceNoise fit: Frequency dependence

1.53ρ

f~fSModel A:

Model B:

~ f −2

~ f −1

CffBA~fS lnρ

2ρ BfA~fS (Model A)

(Model B)Sample 4T=4K

Model A: Random TelegraphModel B: Diffusive spin dynamics

GaInAs GaAsGaAs(Mn)

2D conductivity channel

z

E0

Mn

L

0

Carrier-mediated FM via carriers in the quantum well.

U(z)

(z)

(z)

GaAs GaAs

GaInAs

E.Z. Meilkhov and R.M. Farzetdinova, JETP Letters (2008)

M

23

Mn

(z)

MnGaAs

GaInAsThere is 2D spin – polarized collective state in the GaMnAs aria. The corresponding wave function is expanded inside quantum well and acts on carriers causing their spin-polarization.

FM ordering occurs in GaMnAs layer due to itinerant mechanism. Carriers in the quantum well do not invoolved. V.V. Tugushev et al.PRB (2009)

FM ordering inside Mn layer M

From Lucev et al. PRB 2009

Модель

M=0

GaAs

Mn

GaMnAs GaInAs

GaAsGaMnAs GaInAs

ФМ упорядочение в GaMnAs слое обусловлено обменом спинов Mn через носители в этом же слое. Носители из квантовой ямы в обмене почти не участвуют (S.Caprara et al.PRB (2011)). Вблизи дельта слоя возникает 2D спин – поляризованное состояние. Волновая функция проникает из дельта слоя в квантовую яму, вызывая спиновую поляризацию дырок.

Аверкиев и др. – резонансное туннелирование,Мейлихов и др. – перекрытие хвостов

волновой функции из КЯ в слой GaMnAs

EF

Mn – содержащий слой GaMnAs

Tс – локальный ФМ в островках

Двухфазная среда

Tc

L

Voltage noise: frequency dependenceVoltage noise: frequency dependence

Freq. dependence of the voltage noise for temperatures below resistivity anomaly.

f S f ~ f −0.53

f S f ~ f ?

Sample 4

Freq. dependence is not 1/f. Random telegraph? Griffiths?

Characteristic frequency

ConclusionsConclusions At low carrier density, competition of disorder and nonlinear screening causes formation of charge puddles in 2DHG.

Resistance anomaly arises when magnetic correlation length becomes comparable with a relevant length scale. Anomaly not evidence for a phase transition.

In 2D (unlike 3D) resistance anomaly may occur far below Curie temperature.

Noise is non-1/f over a large window of frequencies. Data in reasonable agreement with both Model A (Random Telegraph) and Model B (Diffusive spin dynamics).

27

намагниченность

-2 -1 0 1 2-1.0x10-4

-5.0x10-5

0.0

5.0x10-5

1.0x10-4

Mn in QW sampleT = 3 K

M (

em

u)

B (T)

0 20 40 60 80 1000.0

1.0x10-5

2.0x10-5

3.0x10-5

4.0x10-5

Mn in QW sample B = 1 TM

(e

mu

)T (K)

ZFC FC

Ferromagnet

Exchange bias of hysteresis loop

Известен для двухвазных систем с ферро- и антиферромагнитными включениями,например, в манганитах.

В чем причина необычного вида гистерезиса?

JETP Letters, 2008

Magn

Загадка 3

Диэлектрический образец

28

-8 -6 -4 -2 0 2 4 6 8

-8

0

8 10K

M

(e

mu

)

B (T)

НамагниченностьМалое содержание Mn

Magn

JETP Letters, 2007

29

Model

Mn rich lake

Ferromagnetic regionQW, high carrier

concentration

Magnetic moment of the lake is pinned by Jf-af

The percolation transition in magnetic system affect scattering and results in decrease of resistance – reason of the noise.

Antiferromagnetic region

Jf

Jf-af

M

Mn delta layer

spacer

2DEG

Due to shape anisotropymagnetic moment of Mn layer aligns along

Due to quantizationspin of heavy holes aligns perpendicularly

Is the exchange possible?Yes, due to high Fermi energy and disorder. dqw=10 nm, rloc= 20-30 nm, K in plane is about Kz

JETP Letters, 2008PSS, 2008

Magn

Nature for AFM regions

Tugushev et al. PRB (2009)

Magn

Fig from Lutcev et al. PRB (2009)

31

Magnetization

-2 -1 0 1 2-8.0x10-5

-4.0x10-5

0.0

4.0x10-5

8.0x10-5

M (

em

u)

B (T)

Mn in qw4831T = 3 K

0 20 40 60 80 100

0.0

1.0x10-5

2.0x10-5

3.0x10-5

4.0x10-5

Spin glass

Mn in qw4831 B = 1 T

M (

em

u)

T (K)

ZFC FC

-2 -1 0 1 2-1.0x10-4

-5.0x10-5

0.0

5.0x10-5

1.0x10-4

Mn in qw4834T = 3 K

M (

em

u)

B (T)

Metallic sampleLow Mn content

0 20 40 60 80 1000.0

1.0x10-5

2.0x10-5

3.0x10-5

4.0x10-5

Mn in qw4834 B = 1 TM

(e

mu

)

T (K)

ZFC FC

Ferromagnet

Insulator sampleHigh Mn content

Exchange bias of hysteresis loop

Known for two phase systems with ferro - and anti-ferro inclusions,for example, phase separation in manganites

What is thereason forunusualhysteresisloop?

JETP Letters, 2008

Mag

Model of nanoscale inhomogeneities Model of nanoscale inhomogeneities 11Formation of charge carrier puddles in the quantum well (QW) from competition of doping disorder and nonlinear screening.

Partially ionized Mn dopants

Typical potential fluctuation

(Gergel' & Suris, JETP (1978))

Estimate of the droplet sizesEstimate of the droplet sizes

Virial theorem:

pnflucnmax, R,zV=

k0n

22

2

1

2m

Droplet charge distributed over subbands:

22

2m

222

211

1

122

22

1

2

21

pmax,pmax,pa

max,max,max,max,

Rk+

Rk=Rn'

EEkk=EE

Solve these nonlinearequations to get dropletsize

T= 77 K

T= 5 K

Results of the calculationsResults of the calculations

Флуктуационный потенциал и температурная зависимость сопротивления

Вслед за работой Гергель, Сурис, ЖЭТФ (1978)

PRB 2011

Загадка 1Расчетная температура не совпадает с максимумом R(T).Две температуры?

AHE temperature dependence

-2 0 2

-200

-100

0

100

200

T=4.6 K; p=3.1*1011

cm-2,

=350 cm2/Vs

T=33 K;

p=3.3*1011

cm-2,

=850 cm2/Vs

T=100 K; p=1.4*1012

cm-2,

=1000 cm2/Vs

T=77K; p=1*1012

cm-2,

=1200 cm2/Vs

T=50 K; p=5*1011

cm-2,

=1100 cm2/Vs

RA

HE

, Ohm

B, T

0 20 40 60 80 100-300

-200

-100

0

100

200

300

p=4*1011 cm-2

p=650 cm2/V*s

at T=30 K;

3 T

0.3T

1 T

RA

HE, O

hm

T, K

AHE change sign with T

Two contributions intrinsic and side-jump

AHE

0 20 40 60 80 100-200

-100

0

100

10

20

Bsa

tur, T

RA

HE, O

hm

T, K

5569

37

-4 -2 0 2 4

-40

-20

0

20

40

Rxy

a, O

hm

0.5 ML

B, T

17 K

-4 -2 0 2 4

-400

-200

0

200

1.2 ML

Rxy

a, O

hm

B, T

55 K

2/ xxaxy

axy

2/ xxnxy

nxy

heaxy /07.0 2 hea

xy /17.0 2he /1.0 22Dрасчет

222

22

1

c

cnxy m

рe 2// nxy

axy

nxy

axy

S.Y. Liu, X.L. Lei, Phys. Rev. B 72, 195329 (2005).V.K. Dugaev, P. Bruno, M. Taillefumier, B. Canals, C. Lacroix, Phys. Rev. 71, 224423 (2005).

AHE

J. Phys. Cond. Matt. 2008, JAP2010

Аномальный эффект ХоллаХолловское сопротивление RHd= yx = R0B + RsMАномальный вклад пропорционален намагниченности и зависит от S-O взаимодействия и спиновой поляризации носителей.

axy

Fluctuation potential

After Gergel’ and Suris paper and Shklovskii and Efros

Schematic of the quantum well potential (shown inverted). Dashed (blue) line represents the quantum well potential in the absence of fluctuations and the solid (red) line shows the potential well with an attractive fluctuation potential. The dotted line indicates the Mn dopants at a distance from the left face of the quantum well.

Geometry of the Geometry of the dropletsdroplets

Voltage noise: charge fluctuationsVoltage noise: charge fluctuations

Fluctuations in inter-droplet tunnellingA. L. Rakhmanov et al., PRB (2001) [phase-separated manganites]

2

2

2

2ω

1

/1

ij2

ijCE

D+

DTe

ijClocijD

ij

TJT+Ee

D

cos1///1

02

Different from characteristictime associated with resistivity.

Random-telegraph type(consistent with experiment)

Temperature dependence not in agreement with data.Need to look at magnetic contribution to noise.

GaInAs

GaAs

V-band

FM transition in the Mn layer affects the conductivity in QW

z

Mn

GaAs

L

U(z)

Mech

GaInAs

GaAsGaAs

V-band

z

Mn

L

U(z)

FM transitionoccurs

0 20 40 60 80 100

4.0x1011

8.0x1011

1.2x1012

1.6x1012

2.0x1012

Tcl

Tc

T, K

p, cm-2

FM transition in the Mn layer affects the conductivity in QW

0 20 40 60

9.0x1011

1.2x1012

2000

2500

3000

p, c

m-2

T, K

p, cm^-2

,

cm

2 /V

*s

mob, cm^2/V*s

QW 4831

Mech

5569

Two-dimensionalityTwo-dimensionality

Negative magnetoresistance consistent with 2D weak localisation corrections.

Observation of Shubnikov-de Haas oscillations for fields perpendicular to plane of hole gas.

Quantum Hall effect in all samples, including Sample 1. [B. A. Aronzon et al., J. Appl. Phys. (2010)]

Sample 3 (metallic)

Photolumiscence InGaAs/GaAs:Mn

0 4 80.0

0.5

1.0

1,33 1,34

dS = 3 nm

B = 5 T

EL

inte

nsity

h (eV)

Psa

t

reference LED

dS (nm)

dS= 3 nm

EL PL

B (T)

PC

(a)

0 5 10

0.0

0.2

0.4 (b)

reference LED

Pc(B) dependences for EL and PL

of sample 2 and of the reference sample 5 without δ-Mn layer. Inset shows polarized EL spectra; (b) Pc(9 T) values vs. ds in LEDs

with x = 0.1.

Zaitsev, Kulakovskii et al. Jetp letters 90,730 (2009)

Psat (9 T) values vs. ds

45

1. Introduction. Structure description. Proofs of 2D and ferromagnetic ordering.2. Disorder effects. Resistivity.3. Disorder effects. Noise.4. The nature of ferromagnetic ordering. Models.5. Conclusion.

Semiconductor spintronics. 2 problems. Tc and 2D

Outline