Electrical transport in nanoscale tunnel junctions

1
Electrical transport in nano-scale tunnel
junctions
Hiroyoshi Itoh Department of Applied Physics,
Nagoya University, Japan
Collaborators
J. Inoue, T. Kondo, S. Honda (Nagoya, Univ.) A.
Umerski, J. Mathon (UK)
Acknowledgements
Grant-in-aid for Science Research C,
JSPS FEMD-CREST (Y. Suzuki team), JST NAREGI
Grid Application Research in Nanoscience, MEXT
21st Century COE Program Frontiers of
Computational Science
2
Introduction
Nano-scale junctions

• Magnetic multilayers CIP-GMR, CPP-GMR, exchange
  coupling
• Fe/Cr, Co/Cu, etc

• Magnetic tunnel junctions TMR
• Fe/Al2O3/Fe, CoFe/Al2O3/Co, Fe/MgO/Fe, etc

• Perovskite manganite junctions TMR, GMR,
  exchange coupling
• (La-Sr)MnO3/SrTiO3/(La-Sr)MnO3,
  (La-Ba)MnO3/LaNiO3/(La-Ba)MnO3

• DMS heterostructures TMR
• (Ga-Mn)As/AlAs/(Ga-Mn)As

• Ferromagnet/ semimetal junction TMR, GMR

• Semiconductor/ semimetal junction

• Ferromagnet/ superconductor detection of spin
  polarization

• 2DEG with spin-orbit interaction spin
  accumulation, spin Hall effect

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Simplest model
1D parabolic band model
Conductance
Real system
Layered structure 3D, 2D Complex electronic
states spd-orbitals, interface states,
etc Disorder impurity, interfacial randomness,
etc Interaction Hunds coupling, spin-orbit
int., etc
This presentation
Effects of disorder NiFe/Al2O3/Cu/Co,
Fe/MgO/Fe Interface resonant states GaAs/GdAs
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Effect of disorder 1
k (wave vector parallel to layers)
H.Itoh et al. Physica B 237-238 (1997) 264, J.
Phys. Soc. Jpn. 68 (1999) 1632.
Metallic contact
Fermi surface
Fermi surface
ideal interface
In clean system, k conserved.
No current !
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Effect of disorder 1
k (wave vector parallel to layers)
H.Itoh et al. Physica B 237-238 (1997) 264, J.
Phys. Soc. Jpn. 68 (1999) 1632.
Metallic contact
disordered interface
In clean system, k conserved.
No current !
In disordered system, k not conserved.
Diffusive scattering vertex correction
Diffusive scattering (k ? k)
Disorder opens up new channels, and increases
conductance.
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Effect of disorder 2
Symmetry of Bloch wave function
Perfect lattice
Distorted lattice
s
py
No s-py hybridization for k(kx,0)
s-py hybridization
Disorder (lattice distortion, defect, impurity,
etc)
hybridization between Bloch states having
different symmetries
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Quantum oscillation of TMR
S. Yuasa, T. Nagahama, Y. Suzuki, Science 297
234 (2002)
P
AP
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Our calculation
H. Itoh, J. Inoue, A. Umerski, J. Mathon Phys.
Rev. B 68 (2003) 174421.

• Single orbital T.B.
• Disorder in insulator
• Linear response theory
• CPA vertex correction

kcp-period
disorder
kF-period
Present parameters
TMR ratio decreased by disorder
kcp period ? 3 layer kF period ? 5 layer

• period kcp-period ? kF-period
• asymptotic value ? 0

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Clean junction
k conserved
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Disordered junction
k not conserved
Diffusive scattering
?
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MTJ with MgO barrier
Experiments Nat. Mat., Dec. 2003
CoFe/MgO/CoFeB 220_at_R.T., Parkin et al.
(100)-oriented Fe/MgO/Fe 180_at_R.T., Yuasa et
al. single crystalline
Ballistic theories PRB, 2001
Butler et al., Mathon Umerski
Fe/MgO/Fe (001) MR gt 1,000
Conservations of k Bloch wave function
symmetry
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k(0,0)
Fe ?
Fe ?
MgO
Clean junction
Fe D1
MgO D1
Fe
MgO D1
D2
D2, D25
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Our calculation Fe/MgO/Fe
Fe spd-orbitals, bcc str.
MgO sp-orbitals, NaCl str.
s (Mg2)
majority
minority
MgO Lee Wong
gap7.8eV
Fe Papaconstantopoulos
Interface Harrison
p (O2-)

• spd tight-binding model
• linear response theory
• numerical simulation
• (cluster 24aFex24aFe)
• average over 50 samples

Distortion of MgO lattice ? random potential
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Disordered junction (random potential in MgO)
P-alignment
conventional definition
1,600
MR ratio (pessimistic definition)
800
?-spin channel disorder ? conduction through D1
band
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Semiconductor/semimetal junction Interface
resonant states
Semimetal Bi, Sb, graphite, RE pnictide
Carrier hole electron
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Surface or interface states (Shockley states)

• Semiconductor surface
• Nobel metal (111) surface
• d-wave superconductor (110) surface Andreev
  bound states

Surface symmetric termination of periodic
potential
If interface states are formed near Fermi level,
transport properties of junction can be
affected.
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Our calculation GaAs/GdAs
J. Inoue, H. Itoh, S. Honda et al., J. Phys.
Cond. Mat. 16 (2004) S5563.
GdAs
semimetal
As
Gd
Ga
GaAs
semiconductor
int. Ga
int. Gd
bulk Gd
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Our calculation GaAs/GdAs
J. Inoue, H. Itoh, S. Honda et al., J. Phys.
Cond. Mat. 16 (2004) S5563.
GdAs
Obtained interface states do not hybridize with
propagating states of bulk GdAs due to k
conservation in clean junction.
semimetal
As
Effects of disorder
Gd
Ga
Formation of interface states
GaAs
semiconductor
Hybridization between interface states and
propagating states
int. Ga
int. Gd
bulk Gd
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Summary
Effect of disorder on transport in nano-scale
junction
Ideal clean system is (sometimes) singular point.
Conservation laws significantly restrict
conduction path. Disorder relaxes the restriction
and opens up new conduction channels.

• Diffusive scattering (k ? k)
• Hybridization between Bloch states having
  different symmetries

NiFe/Al2O3/Cu/Co junction Oscillation of MR
ratio around zero with a kF period
Fe/MgO/Fe junction Reduction of MR ratio by
distortion of MgO lattice
Interface resonant states
GaAs/GdAs clean junction Resonant states
formed at GaAs interface
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Quantum oscillation of TMR
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Problems in ballistic theroy
1. Origin of oscillation around zero
Spin diffusion in Cu ?
No! lsf ? 100 nm bulk Cu
Impurity scattering in Cu ?
No! RJ gtgt RCu
2. Period not determined by kF
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Conductance FM/ I/ NM spacer/ FM junction
kF-period
kcp-period
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Transmission probability
FM
I
NM
FM
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Conductance AP alignment
kF-period
kcp-period
diffusive (vertex correction)
specular
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DOS model
Julliere (1975), Maekawa Gäfvert (1982)
Spin polarization
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FM
FM
I
NM
impurity
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Quantum well at spacer
Co
Al-O
Cu spacer
Co
EF
minority
kF
kcp
majority
QW for minority state
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FM/ I/ FM spacer/ NM junction
Experiments FeCo/Al2O3/Fe/Cr
GP increased by disorder TMR increased ? bulk
value
Enhancement of TMR Maximum of TMR at Lspacer8 No
clear oscillation
Enhancement of TMR for thin FM spacer
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Projected Fermi surface
FM/ I/ FM spacer/ NM
FM/ I/ NM spacer/ FM
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Fe/MgO/Fe junction
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Clean junction (without randomness)
MR over 1,000
Large MR ratio conservations of k and band
symmetry
Butler, Mathon Umerski (2001)
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MgO
Fe ? D1

MgO
Fe ? D2
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Transmission probability T(k) clean junction,
dMgO8 ML
Parallel ?
Parallel ?
Antiparallel
k(0,0)
MgO
Fe ?
Fe ?
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Semimetal junction
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???????????????
Bi, Sb, As, C (graphite), R-V (RGd,Er and
VN,P,As)
Small overlap of valence and conduction bands
Semiconductor (SC)
Semimetal (SM)
L.Bolotov et al. (1998)
ErP
Semiconductor
Band overlap, gap controllable
Semimetal
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Ballistic limit (no disorder)
???????Fermi????k????
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k//0 (G-point) dominant contribution
DE0.1t
Small Fermi surface of SM