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Disorder effects in 2D ferromagnetic semiconductor structures:

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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

Quantum well with Mn delta layer

2D

cap-layer GaAs, 60-80 нм

δ-layer Mn

spacer GaAs, 1-5 нм

cap-layer GaAs, 30-40 nm

QW InGaAs, 9-10 нм

-layer Mn

spacer GaAs, 3 nm

QW InGaAs, 9-10 nm

GaAs, 5 нм

GaAs, 15-18 nm

δ-Be

-layer С

Buffer GaAs, 25 нм

Buffer layer GaAs, 0.5 μm

Substrate

i-GaAs (100)

Substrate

GaAs, (100)

Awshalom et al., 2004

Zaicev, et al., 2009

Aronzon et al., 2006, 2009, 2010, 2011, 2012

Wegscheider et al., 2007, 2010

Dietl et al. 2010

Sapega et al. 2012

Y. Furdyna et al.

Buffalo

B.N. Zvonkov et al.

N. Novgorod

Parametes of the samples

2

Transport proofs for ferromagnetism

Anomalous Hall effect

Resistivity

Hall resistance dependes on spin-orbit interaction and carrier polarization

RHd= yx = R0B + RsM

? Metal - insulator transition under rise of Mn content ?

- 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.

Fluctuation potential

After Gergel’ and Suris paper and Shklovskii and Efros

Formation of charge carrier puddles in the quantum well (QW) from

competition of doping disorder and nonlinear screening.

z0

Location of holes in the

transverse direction

Hole wavefunction in transverse

direction

Typical potential fluctuation Vfluc

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

Partially ionized Mn dopants

Model of nanoscaleinhomogeneities

RMS potential fluctuation:

z0

[Kennett, Tripathi, PRB (2006)]

Screening length

corresponds

to carrier density p:

n’a- Density of ionized Mn

atoms

PRB, 2011

EA + J(1-cos θi j )

θi j

Vb a r r i e r

Di j

Extra energy cost

due to spin

orientation

i

j

Electrical resistance:

Role of ferromagnetic correlations

PRB, 2011

Resistivity anomaly

corresponds to rapid

change of magnetic

contribution.

Cosine term changes appreciably when

magnetic correlation length becomes of

the order of droplet separation.

Resistivity

Two phase system

Tc

PRB, 2011

Tс– local transition in magnetic islands

Observed temperature dependence of resistancefor (a) Sample 4, in units of the resistance at 70 K, and (b)Sample 1, in units of the resistance at 90 K (points), and

theoretical fits (solid lines). Sample 4 is near the percolationthreshold and Sample 1 is well-insulating. The fits were madeusing Eq. (13). Parameters such as the activation energy EAand the droplet separation D1 were chosen close to the valuesobtained from the droplet model. The magnetic parametersJ and TC were then varied to obtain the above fits. In bothcases, the best fit value of TC was significantly larger thanthe temperature, at which the resistance anomaly (hump orshoulder) was observed.

Power spectral density of electrical noise

Percolation transition

in magnetic subsystem?

There are no transitions

in transport properties.

9

PRB, 2012

Noise fit: Frequency dependence

The long-time dependenceof 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.

PRB, 2012

Curie temperature dependence on the depth of quantum well

Mn

110 meV

GaAs

GaAs

GaAs

U=180 meV

U=140 meV

U=100 meV

55 and 57 set

48 set Mn 0.5 Ml

J. Phys. Conf. Ser. 2013

Curie temperature dependence on the spacer thickness

cap-layer GaAs, 60-80 нм

δ-layer Mn

spacer GaAs, 1-5 нм

cap-layer GaAs, 30-40 nm

QW InGaAs, 9-10 нм

-layer Mn

spacer GaAs, 3 nm

QW InGaAs, 9-10 nm

GaAs, 5 нм

GaAs, 15-18 nm

δ-Be

-layer С

Buffer GaAs, 25 нм

Buffer layer GaAs, 0.5 μm

Substrate

i-GaAs (100)

Substrate

GaAs, (100)

Mech

CVD

MBE

13

J. Phys. Conf. Ser. 2013

Models

Mn

M=0

GaMnAs

GaAs

GaInAs

Two phase system

Tc

Itinerant FM ordering in GaMnAs layer.

(S.Caprara et al. PRB (2011)).

Averkiev et al. – resonance tunneling.

PRB (2012).

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

JETP Letters (2008)

EF

Tс– local transition in magnetic islands

L

Mn layer –GaMnAs

GaMnAs

GaAs

GaInAs

Conclusion

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.

THANKS FOR YOUR ATTENTION!

15

z0

Model of nanoscale inhomogeneities

Assume Gaussian white noise

distribution for ionized dopants:

Fluctuation charge in circle of

radius R:

Disorder screened by holes in QW:

PRB, 2011

Ferromagnetic correlations: models

I. Isotropic 2D Heisenberg ferromagnet

No long-range magnetic order

at finite temperature.

II. Uniaxial 2D Heisenberg ferromagnet

M. Bander, D. Mills, PRB (1988)

for Ising

Voltage noise: magnetic fluctuations

Resistivity noise from magnetic fluctuations

Autocorrelation function

of magnetisation

Autocorrelation function contains information on dynamics, and can shed

light on the mechanism of ferromagnetism.

Magnetic correlations: dynamics

Resistivity noise is sensitive to

the dynamics of the ferromagnet:

Interested in two broad universality classes depending on

whether the dynamics has a hydrodynamic description:

Model A: No conserved order parameter

e.g. anisotropic Heisenberg

Model B: Conserved order parameter

e.g. Isotropic Heisenberg

Hohenberg, Halperin, RMP (1977)

2D

a/a, %

InхGa1-хAs

yMn

A

(GaAs)1-yMny

Sample

4831

.0

InхGa1-хAs

yMn

cap-layer GaAs, 30-40 nm

50

-layerMn

spacer GaAs, 3 nm

55

B

(GaAs)1-yMny

QW InGaAs, 9-10 nm

sample

4834

60

GaAs, 15-18 nm

-layer С

Buffer layer GaAs, 0.5 μm

z, nm

Substrate

i-GaAs (100)

z, nм

X-ray diagnostics of the samples

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

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

Mn content

40

Noise fit: Frequency dependence

Sample 4

T=4K

(Model B)

(Model A)

Model A:

Model B:

Model A: Random Telegraph

Model B: Diffusive spin dynamics

U(z)

(z)

0

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

L

M

Carrier-mediated FM via carriers in the quantum well.

2D conductivity channel

GaAs(Mn)

GaInAs

GaAs

GaInAs

GaAs

GaAs

E0

(z)

Mn

z

(z)

Mn

M

FM ordering inside Mn layer

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)

From Lucev et al. PRB 2009

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

Mn

GaInAs

GaAs

23

Модель

Mn

M=0

GaMnAs

GaAs

GaInAs

Двухфазная среда

Tc

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 слоявозникает 2D спин – поляризованное состояние.Волновая функцияпроникает 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

Tс– локальный ФМ в островках

L

Mn – содержащий слой GaMnAs

GaMnAs

GaAs

GaInAs

Voltage noise: frequency dependence

Sample 4

Characteristic frequency

Freq. dependence of the voltage noise for temperatures below

resistivity anomaly.

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

Conclusions

- 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).

намагниченность

Magn

Диэлектрический образец

Загадка 3

В чем причина необычного вида гистерезиса?

Exchange bias of hysteresis loop

Известен для двухвазных систем с ферро- и антиферромагнитными включениями,

например, в манганитах.

27

JETP Letters, 2008

MagnModel

Mn rich lake

Jf-af

Mn delta layer

M

spacer

Ferromagnetic region

Antiferromagnetic region

2DEG

Jf

QW, 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.

Due to quantization

spin of heavy holes aligns perpendicularly

Due to shape anisotropy

magnetic moment of Mn layer aligns along

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, 2008

PSS, 2008

29

Magnetization

Mag

Metallic sample

Low Mn content

Insulator sample

High Mn content

What is the

reason for

unusual

hysteresis

loop?

Exchange bias of hysteresis loop

Known for two phase systems with ferro - and anti-ferro inclusions,

for example, phase separation in manganites

31

JETP Letters, 2008

Model of nanoscale inhomogeneities 1

Formation of charge carrier puddles in the quantum well (QW) from

competition of doping disorder and nonlinear screening.

(Gergel' & Suris, JETP (1978))

Typical potential fluctuation

Partially ionized Mn dopants

Estimate of the droplet sizes

Virial theorem:

Droplet charge distributed over subbands:

Solve these nonlinear

equations to get droplet

size

Флуктуационный потенциал и температурная зависимость сопротивления

Вслед за работой Гергель, Сурис, ЖЭТФ (1978)

Загадка 1

Расчетная температура не совпадает с максимумом R(T).

Две температуры?

PRB 2011

АномальныйэффектХолла

AHE

Холловское сопротивлениеRHd= yx = R0B + RsM

Аномальный вклад пропорционален намагниченностии

зависит от S-O взаимодействия и спиновой поляризации носителей.

2D

расчет

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).

37

J. Phys. Cond. Matt. 2008, JAP2010

Fluctuation potential

After Gergel’ and Suris paper and Shklovskii and Efros

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

Voltage noise: charge fluctuations

Fluctuations in inter-droplet tunnelling

A. L. Rakhmanov et al., PRB (2001) [phase-separated manganites]

Random-telegraph type

(consistent with experiment)

Different from characteristic

time associated with resistivity.

Temperature dependence not in agreement with data.

Need to look at magnetic contribution to noise.

FM transition in the Mn layer affects the conductivity in QW

Mech

U(z)

5569

GaInAs

FM transition

occurs

GaAs

GaAs

Mn

V-band

z

L

Two-dimensionality

Sample 3 (metallic)

- 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)]

Photolumiscence InGaAs/GaAs:Mn

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

Outline

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

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