19–22 march 2007 “ gdr physique quantique mésoscopique ”

Laboratoire de PhotoniqueLaboratoire de Photoniqueet de Nanostructureset de Nanostructures

R. GiraudR. GiraudAussois, March 2007Aussois, March 2007

Nano Team

19–22 March 200719–22 March 2007

“ “ GDR Physique Quantique Mésoscopique ”GDR Physique Quantique Mésoscopique ”

Universal conductance fluctuations, and Domain-wall dephasing

in ferromagnetic GaMnAs nanowires:

Laboratoire de Photonique et de Nanostructures – CNRS/LPNRoute de Nozay, F – 91460 Marcoussis, France

R. Giraud, L. Vila, L. Thevenard, A. Lemaître, F. Pierre, J. Dufouleur,

D. Mailly, B. Barbara, G. Faini

a large phase coherence length for a quantum spintronics in nanomagnets



Nano Team

Outline

The MesoSpin project at LPN

Phase-coherent spin transport in nanostructures: Spin-orbit coupling vs. Exchange interaction

Phase-coherent spin transport in ferromagnets: Strong decoherence mechanisms Strategy for mesoscopic transport in nano-magnets

Universal Conductance Fluctuations in epitaxial ferromagnetic GaMnAs nanowires: A large effective phase coherence length Dephasing by a spin disorder (domain walls) Dominant mechanisms ?



Nano Team

i) Spin-SET , Spin Qu-bit

Phase-coherent manipulation of a localized or a delocalized spin

All-electrical control of the two spin-states of a single electron spin localized in a vertical quantum dot

The MesoSpin project contributes to make a new link between spintronics and mesoscopic physics

It is based on all-semiconducting III-V materials, and uses an epitaxial ferromagnet GaMnAs,

eventually integrated onto a conventional semiconducting heterostructure

ii) Coherent spin transport Phase-coherent control of a spin current

in a ferromagnet or a 2DEG

L = 1 µm

W = 150 nm

Ø ~ 100 nm

W ~ 30 nm

Ø ~ 100 nm

Electrical spectroscopy of TAMR in a spin Zener-Esaki diodeR. Giraud et al., APL 05’



Nano Team

Spin-Orbit coupling

Coherent manipulation of a spin-polarized current

Exchange interaction

vs.

L. Vila et al., PRL 07’

Gate-controlled spin precession in a 2DEG Spin precession through a domain wall(non adiabatic spin transport)

possibly tuned by an electric and/or a magnetic fieldThe Datta/Das spin FETS. Datta, B. Das, APL 90’

Dephasing of a coherent spin current by DW J. Nitta, et al., PRL 97’

From J. Nitta

«

the micron scale the nano scale

Bychkov-Rashba coupling in III-V materials

DW l spin flip<l spin-orbit (π-rotation) l exchange

(π-rotation)

= 2m*L

ħ2 =

2πγMS L2

D



Nano Team

Quantum corrections to the conductance as a probe of L

Saturation of L due to magnetic impurities in a metal

F. Pierre et al., PRB 68, 085413 (2003)

Mesoscopic transport & Magnetism (1)

V

I

+ time-reversed paths

Closed orbits...

P. Mohanty, et al., PRL 97’

H. Pothier, et al., PRL 97’

Exchange ‘field’ to freeze single-spin fluctuations…but only ultra-short L were reported to date,

probably due to a short inelastic mean free path Jaroszynski et al. 95’, Aprili et al. 97’, Lee 04’, Saitoh et al. 05’

L < 30 nm @ T = 30 mK

Classical magneto-conductance dominates over Quantum corrections



Nano Team

How to preserve phase coherence in a ferromagnet ? → reduce spin-flip scattering…

Conditions for quantum interferences in ferromagnets

Anisotropy ‘field’ to freeze low-energy spin waves fluctuations

Epitaxial ferromagnet to avoid low-energy spin fluctuations at grain boundaries

Reduced role of the spin-orbit interaction

Internal fields…

large Linel

Mesoscopic transport & Magnetism (2)

Exchange interaction to minimize energy exchanges within a spin bath

A ferromagnetic epilayer with a strong uniaxial magnetic anisotropy is a good candidate and should be equivalent to a non magnetic, low S-O coupling system, but with an internal Bexchange

At best: if spin-induced

decoherence is limited

perpendicular anisotropy Bint = Bext



Nano Team

Substitutional Mn = Acceptor

Bound magnetic polaron

Impurity band / Mobility edge

Delocalized hole-induced ferromagnetism

Mn : …3d54s2

Ga → Mn Mn2+ (S=5/2) + h

(J.-C. Girard, LPN)

GaMnAs : an epitaxial ferromagnet

Tuning of the magnetic properties

Hydrogen-control of the hole density p

p TC

(L. Thevenard, A. Lemaître, LPN)

Domain Imagingby Kerr microscopy

(coll.: N. Vernier, J. Ferré, LPS)

135 µm x 176 µmGaMnAs/InGaAs: Demagnetized state @ 70 K

Strain-inducedmagnetic anisotropy

SQUID magnetometry(coll.: R.-M. Galéra, Institut Néel)



Nano Team

Tailored by the strains induced by the substrate on the epilayer

GaMnAs/GaAs : In-plane anisotropy GaMnAs/InGaAs : Out-of-plane anisotropy

GaMnAs MBE – growth engineering of the anisotropy

‘Large’ positive AMR

H > HA Single-domain magnetization stateH < HA Coherent rotation vs. Domain walls

Single-domain magnetization state

What a magnet !

Large Anomalous Hall Effect, No AMR

at any field...



Nano Team

Quantum Transport in GaMnAs nanowires

Nanowire: L=220nm, W=50nm

L

W

Quantum corrections to G

L. Vila, R. Giraud, L. Thevenard, A. Lemaître, F. Pierre, J. Dufouleur, D. Mailly, B. Barbara and G. FainiPhys. Rev. Lett. 98, 027204 (2007)

Classical conductance and Quantum corrections



Nano Team

L = 1 µm

W = 150 nm

Metallic behaviour!g ~ 26

p ~ 5.1020 cm-3

D ~ 1 cm2/s

ρ ~ 2 mΩ.cm

Perpendicular anisotropy : low temperature & bias behaviour

Measurements at eV < kBT

Ω

~

Ω

Much larger than measured with 3d-metal nanowires! large Lφ



Nano Team

Three traces at base temperature…

First run

Second run, 2 days later

(T raised to 4K..?)

24h after the green trace (with T=30mK)

Perpendicular anisotropy : Universal Conductance Fluctuations

Each trace is a 12h-measurement

Universal Conductance Fluctuations as a probe of L



Nano Team

Perpendicular anisotropy : UCF temperature and bias behaviour

Temp. dependenceBias Current dependence

Equivalence of the Bias and Temperature dependence of UCF



Nano Team

Perpendicular anisotropy : check of the UCF nature

Redistribution of the microscopic structural disorder configurationNew reproducible magneto-fingerprint

Single-domainmagnetization

state



Nano Team


Outline






Nano Team

Perp. anisotropy : Length dependence of the UCF amplitude

L

LN

heδGTot

23/23/2

L

LN1

hδG e

2

only if L < L(T)

L

L

Direct evidence of large L

L > L regime



Nano Team

L=220nm, W=50nm

Temperature dependence of the UCF amplitude & Decoherence



Nano Team

Large effective phase coherence lengths extracted from the ½classical analysis

L ~ 100 nm @ 100mK

L ~ LT ~ 1/T1/2

Universal scaling law

L=220nm, W=50nm

Temperature dependence of the UCF amplitude & Decoherence

Unusual decoherence mechanism ?

Deviations from standard ½ classical diffusive transport

(Breakdown of Fermi liquid theory + Multi-band hole transport)

Or ‘simply’…

(a similar result was obtained in Regensburg: K. Wagner et al., PRL 97, 056803 (2006))

D is an intrinsic limitation to larger values of Lφ

in ferromagnetic DMS

Decoherence ?



Nano Team

Universal Conductance Fluctuations as a probe of L

Effective phase coherence length extracted from UCF within the framework

of the semi-classical approximation…

Quasi-1D regime (LT > W) Quasi-2D regime (LT < W)

Grms (e2/h) = (L/L)3/2 Grms (e2/h) = LT/L*(L/L)1/2

→ Aperiodic conductance fluctuations

Analysis of the UCF amplitude Extraction of L

Similar values are obtained because of the same temperature dependence of L and LT

No dimensional crossover observed with temperature for nanowire widths W < 150 nm

V

I



Nano Team

Direct evidence of a large L : ‘Non local’ effects for L~L

L L

The wave function feels the microscopicconfiguration of the voltage probes

L > L

Only the nanowire contribution is probed

R. Giraud, L. Vila, A. Lemaître and G. Faini to appear in Appl. Surf. Science (2007)



Nano Team

Outline







Nano Team

Modification of the correlation fields

→ Another insight of the partial failure of the

semi-classical approximation...

Structural vs. Spin disorder

M

EF

+Strain-induced

inter-subbands mixing

Planar vs. Perpendicular

anisotropy



Nano Team

BZ < BA : Onset of coherent scattering by Domain Walls (no decoherence)

Planar anisotropy : Dephasing by spin disorder (domain walls)

First evidence of dephasing of free carriers by DWsL. Vila, R. Giraud, L. Thevenard, A. Lemaître, F. Pierre, J. Dufouleur, D. Mailly, B. Barbara and G. Faini

Phys. Rev. Lett. 98, 027204 (2007)

AMR saturation field HA

Pinned Domain WallsPlanar anisotropy

Uniform Single DomainPerpendicular anisotropy

faini

Tatara & Fukuyama PRL '97



Nano Team

Dephasing by a spin disorder (domain walls) -1-

Dephasing of free carriers by DWsL. Vila et al., Phys. Rev. Lett. 98, 027204

(2007)

Possible mechanisms for the additional dephasing in a ferromagnet

Internal exchange field due to the perpendicular magnetization component (modification of the Aharonov-Bohm flux) → much too small in a DMS ...

Dipolar stray field of a domain wall → even smaller

Modified AB phase

Negligible influence in ferromagnetic DMS !

Perpendicular applied field

BZ = HZ + HD + 4M

= 0 !for a thin film (b«a) …

Narrow nanowires stray fields …

… but the magnetization is small (MS<100mT)

DW

DW



Nano Team

Dephasing by spin disorder (domain walls) -2-

Dephasing of free carriers by DWsL. Vila et al., Phys. Rev. Lett. 98, 027204

(2007)Possible mechanisms for the additional dephasing in a ferromagnet

Berry phase in presence of a domain wall → but low density of DW (no multiplication at small fields)Yet, possible contribution in a non adiabatic spin transport regime ?

Spin precession inside a domain wall (non adiabatic regime; Lsf > DW) → should be sensitive to the internal DW structure

Spin dephasing

Spin manipulation of a coherent spin current based on exchange coupling

On-going measurements on a single pinned DW to identify the dominant mechanism



Nano Team


Possible mechanisms for the additional dephasing in a ferromagnet

Berry phase in presence of a domain wall → but low density of DW (no multiplication at small fields)Yet, possible contribution in a non adiabatic spin transport regime ?

Spin dephasing

Spin manipulation of a coherent spin current based on exchange coupling... but possibly also affected by a perturbative spin-orbit coupling (anisotropy)

Bi-axial anisotropy

Geometrical contribution interfering trajectories

on the Bloch sphere



Nano Team


Dephasing of free carriers by DWsL. Vila, R. Giraud, L. Thevenard, A. Lemaître, F. Pierre, J. Dufouleur, D. Mailly, B. Barbara and G. Faini

Phys. Rev. Lett. 98, 027204 (2007)

Advantage over non magnetic semiconductors for phase-coherent spin manipulation

Fast evolution of the phase on a short length scale fixed by the domain wall width (~ 20 nm) Combination of different accumulated phases : e.g., phase shift in an AB interferometer Controled phase manipulation under domain wall distortion (static E or B fields)

Some possible drawbacks/difficulties of spin manipulation in a ferromagnetic nanostructure

Control and Stability of the magnetic configuration (anisotropy, pinning)

Magnet manipulation : requires a small applied magnetic field

Well-defined, tunable length scales in a metallic regime

(e.g., DW , Lsf)



Nano Team

Summary & Conclusions

Large quantum interference effects have been unambiguously observed in epitaxial GaMnAs nanowires

Comparison between planar & perpendicular anisotropy: quantum interferences are dominated by structural disorder and an

Aharonov-Bohm phase at large magnetic fields (single-domain regime) an additional phase is observed at small fields in presence of a spin disorder

(dephasing by domain walls, due to either a Berry phase and/or non adiabatic spin transport -precession- through a magnetic domain wall)

This magnetic control of a phase coherent spin current gives a new way to manipulate the spin of free carriers, on a rather short lengthscale, using the exchange interaction and pinned domain walls.(alternative to the use of spin-orbit couplings)



Nano Team

Spin-Orbit coupling

Coherent manipulation of a spin-polarized current

Exchange interaction

vs.

L. Vila et al., PRL 07’

Gate-controlled spin precession in a 2DEG Spin precession through a domain wall(non adiabatic spin transport)

possibly tuned by an electric and/or a magnetic fieldThe Datta/Das spin FETS. Datta, B. Das, APL 90’

Dephasing of a coherent spin current by DW J. Nitta, et al., PRL 97’

From J. Nitta

«

the micron scale the nano scale

Bychkov-Rashba coupling in III-V materials

DW l spin flip«l spin-orbit (π-rotation) l exchange

(π-rotation)

= 2m*L

ħ2 =

2πγMS L2

D

19–22 march 2007 “ gdr physique quantique mésoscopique ”

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