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19–22 March 2007 “ GDR Physique Quantique Mésoscopique ”. Universal conductance fluctuations, and Domain-wall dephasing in ferromagnetic GaMnAs nanowires:. a large phase coherence length for a quantum spintronics in nanomagnets. R. Giraud , L. Vila, L. Thevenard, - PowerPoint PPT Presentation
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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
Laboratoire de PhotoniqueLaboratoire de Photoniqueet de Nanostructureset de Nanostructures
R. GiraudR. GiraudAussois, March 2007Aussois, March 2007
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 ?
Laboratoire de PhotoniqueLaboratoire de Photoniqueet de Nanostructureset de Nanostructures
R. GiraudR. GiraudAussois, March 2007Aussois, March 2007
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’
Laboratoire de PhotoniqueLaboratoire de Photoniqueet de Nanostructureset de Nanostructures
R. GiraudR. GiraudAussois, March 2007Aussois, March 2007
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
Laboratoire de PhotoniqueLaboratoire de Photoniqueet de Nanostructureset de Nanostructures
R. GiraudR. GiraudAussois, March 2007Aussois, March 2007
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
Laboratoire de PhotoniqueLaboratoire de Photoniqueet de Nanostructureset de Nanostructures
R. GiraudR. GiraudAussois, March 2007Aussois, March 2007
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
Laboratoire de PhotoniqueLaboratoire de Photoniqueet de Nanostructureset de Nanostructures
R. GiraudR. GiraudAussois, March 2007Aussois, March 2007
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)
Laboratoire de PhotoniqueLaboratoire de Photoniqueet de Nanostructureset de Nanostructures
R. GiraudR. GiraudAussois, March 2007Aussois, March 2007
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...
Laboratoire de PhotoniqueLaboratoire de Photoniqueet de Nanostructureset de Nanostructures
R. GiraudR. GiraudAussois, March 2007Aussois, March 2007
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
Laboratoire de PhotoniqueLaboratoire de Photoniqueet de Nanostructureset de Nanostructures
R. GiraudR. GiraudAussois, March 2007Aussois, March 2007
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
Laboratoire de PhotoniqueLaboratoire de Photoniqueet de Nanostructureset de Nanostructures
R. GiraudR. GiraudAussois, March 2007Aussois, March 2007
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
Laboratoire de PhotoniqueLaboratoire de Photoniqueet de Nanostructureset de Nanostructures
R. GiraudR. GiraudAussois, March 2007Aussois, March 2007
Nano Team
Perpendicular anisotropy : UCF temperature and bias behaviour
Temp. dependenceBias Current dependence
Equivalence of the Bias and Temperature dependence of UCF
Laboratoire de PhotoniqueLaboratoire de Photoniqueet de Nanostructureset de Nanostructures
R. GiraudR. GiraudAussois, March 2007Aussois, March 2007
Nano Team
Perpendicular anisotropy : check of the UCF nature
Redistribution of the microscopic structural disorder configurationNew reproducible magneto-fingerprint
Single-domainmagnetization
state
Laboratoire de PhotoniqueLaboratoire de Photoniqueet de Nanostructureset de Nanostructures
R. GiraudR. GiraudAussois, March 2007Aussois, March 2007
Nano Team
Universal Conductance Fluctuations in epitaxial ferromagnetic GaMnAs nanowires: A large effective phase coherence length Dephasing by a spin disorder (domain walls) Dominant mechanisms ?
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
Laboratoire de PhotoniqueLaboratoire de Photoniqueet de Nanostructureset de Nanostructures
R. GiraudR. GiraudAussois, March 2007Aussois, March 2007
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
Laboratoire de PhotoniqueLaboratoire de Photoniqueet de Nanostructureset de Nanostructures
R. GiraudR. GiraudAussois, March 2007Aussois, March 2007
Nano Team
L=220nm, W=50nm
Temperature dependence of the UCF amplitude & Decoherence
Laboratoire de PhotoniqueLaboratoire de Photoniqueet de Nanostructureset de Nanostructures
R. GiraudR. GiraudAussois, March 2007Aussois, March 2007
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 ?
Laboratoire de PhotoniqueLaboratoire de Photoniqueet de Nanostructureset de Nanostructures
R. GiraudR. GiraudAussois, March 2007Aussois, March 2007
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
Laboratoire de PhotoniqueLaboratoire de Photoniqueet de Nanostructureset de Nanostructures
R. GiraudR. GiraudAussois, March 2007Aussois, March 2007
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)
Laboratoire de PhotoniqueLaboratoire de Photoniqueet de Nanostructureset de Nanostructures
R. GiraudR. GiraudAussois, March 2007Aussois, March 2007
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 ?
Laboratoire de PhotoniqueLaboratoire de Photoniqueet de Nanostructureset de Nanostructures
R. GiraudR. GiraudAussois, March 2007Aussois, March 2007
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
Laboratoire de PhotoniqueLaboratoire de Photoniqueet de Nanostructureset de Nanostructures
R. GiraudR. GiraudAussois, March 2007Aussois, March 2007
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
Laboratoire de PhotoniqueLaboratoire de Photoniqueet de Nanostructureset de Nanostructures
R. GiraudR. GiraudAussois, March 2007Aussois, March 2007
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
Laboratoire de PhotoniqueLaboratoire de Photoniqueet de Nanostructureset de Nanostructures
R. GiraudR. GiraudAussois, March 2007Aussois, March 2007
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
Laboratoire de PhotoniqueLaboratoire de Photoniqueet de Nanostructureset de Nanostructures
R. GiraudR. GiraudAussois, March 2007Aussois, March 2007
Nano Team
Dephasing by spin disorder (domain walls) -3-
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
Laboratoire de PhotoniqueLaboratoire de Photoniqueet de Nanostructureset de Nanostructures
R. GiraudR. GiraudAussois, March 2007Aussois, March 2007
Nano Team
Dephasing by spin disorder (domain walls) -4-
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)
Laboratoire de PhotoniqueLaboratoire de Photoniqueet de Nanostructureset de Nanostructures
R. GiraudR. GiraudAussois, March 2007Aussois, March 2007
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)
Laboratoire de PhotoniqueLaboratoire de Photoniqueet de Nanostructureset de Nanostructures
R. GiraudR. GiraudAussois, March 2007Aussois, March 2007
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