Theoretical Aspects of SpinDependent Tunneling

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Theoretical Aspects of Spin-Dependent Tunneling

• Jürgen Henk

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Introduction

• Aim Electron spin electronics spintronics
• Devices Spin valves, magnetic tunnel
  transistors, MRAMs, planar tunnel junctions,
  magnetic STM

Theoretical description First-principles
calculations (DFT), magnetism (LSDA), transport
(diffusive, ballistic)
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Outline

• Planar tunnel junctions
• Theoretical approaches
• Computational
• Examples
• Spin valve Co/Cu/Co
• Hot spots Ni/Vac/Ni
• Bias voltage Co/Vac/Co
• Interface structure Fe/MgO/Fe
• Outlook

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Planar tunnel junctions

• Device

Ferromagnetic leads L R
Insulating spacer S
Parallel alignment (P)
Antiparallel alignment (AP)
Ballistic transport thin spacer Measured
tunneling current I, conductance G Tunneling
magneto-resistance (TMR)
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Planar tunnel junctions II

• Tunneling magneto-resistance depends on
• Electronic magnetic properties of leads
  spacer
• Thickness of the spacer
• Structure of the interfaces
• Geometry
• Electronic structure
• Magnetic structure
• Orientation of the lead magnetizations
• Bias voltage

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Jullieres model

• Density of states N in the leads L R
• Polarization
• Optimistic TMR
• Conductance G(P) gt G(AP)

Parallel alignment (P)
Antiparallel alignment (AP)
Spacer properties completely ignored
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Jullieres model II
Slonczewskis extension

• Spacer step barrier
• Transmission polarization

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Landauer-Büttiker Approach

• Electronic structures
• Leads homogenous Green function
• Spacer transition operator
• Conductance

Scattering channels Bloch states
Scattering at the spacer
Sum over all scattering channels paths ? TMR
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Landauer-Büttiker Approach II

• Formulation in multiple-scattering theory
  (layer-KKR MacLaren Butler)
• Principal building blocks layer
• Typical LEED algorithms
• Transmission
• Conductance
• Most time consuming Brillouin-zone integration

Spacer scattering matrix
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Computational

• First-principles calculations
• Scalar-relativistic spin-polarized KKR (LSDA,
  DFT)
• Self-consistent electronic structure
• Band structure, spectral densities, magnetic
  moments, charge transfer,
• Potentials
• Tunneling calculations
• Relativistic spin-polarized layer-KKR
• Landauer-Büttiker approach
• MacLaren-Butler algorithm
• Sophisticated Brillouin-zone sampling (adaptive
  mesh refinement)

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Spin valve Co/Cu/Co
TMR vs spacer thickness

• fcc-Co(001)/Cu/fcc-Co(001)
• Conducting spacer
• G(P) gt G(AP)
• Sizable TMR
• Almost independent on the spacer thickness
• Oscillations quantum-well states in the Cu spacer

Conductance vs spacer thickness
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Hot spots Ni/Vac/Ni

• Ni(001)/vacuum/Ni(001)
• Insulating spacer Focusing of the transmission
• Effective energy

Exponential decay
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Hot spots Ni/Vac/Ni II
Hot spots in the transmission Interface
resonances

• Transmission

Academic feature suppressed by disorder,
choice of the lead materials,
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Bias-voltage dependence Co/Vac/Co

• Typical finding for oxide barriers decrease of
  the TMR with bias voltage
• Origin defect scattering, magnons, ?
• Idea Replace the oxide by vacuum -gt no defects
• Replace the planar tunnel junction by a STM
  set-up
• Is the TMR still decreasing?

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Bias-voltage dependence Co/Vac/Co II
Co(0001)/vacuum/Co-STM tip Experimental results
with a magnetic STM
Small tip-sample distance (5 Å)
Large tip-sample distance (7 Å)
TMR constant
Dip at 0.2 eV
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Bias-voltage dependence Co/Vac/Co III

• Theory for a Co(0001)/vacuum/Co(0001) planar
  junction

• Problem bias voltage
• Simple solution
• Change the inner potentials of the leads (bias)
• Adapt a smooth interface barrier from LEED
• Barrier height automatically adjusted

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Bias-voltage dependence Co/Vac/Co IV

• TMR vs bias voltage

Spin-resolved bulk bands
Surface state
TMR constant
Spin-resolved spectral density of Co(0001)
Conductance vs bias voltage
Dip? Not found in theory but possibly related to
the majority surface state. Tip-induced feature?
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Interface structure Fe/MgO/Fe

• Fe(001)/MgO/Fe(001)
• Bulk electronic structure

MgO
Band gap too small (DFT) 4.24 eV vs 7.6 eV
(Expt.)
Fe
Majority
Minority
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Interface structure Fe/MgO/Fe II

• Geometry

Bulk Fe bcc
Bulk MgO fcc, NaCl
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Interface structure Fe/MgO/Fe III

• Interface geometry
• Standard model ideal cut paste structure
• New Formation of an FeO layer

FeO layer
X-ray diffraction Holger Meyerheim et al, PRL 87
(2001) 076102 Confirmed by total-energy
calculations (Arthur Ernst)
Empty spheres
Effect of the interface structure on the TMR?
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Interface structureFe/MgO/Fe IV

• Magnetic profiles
• 2 MgO layers
• Strongly dependent on calculational details on
  the interface structure

Layer-resolved magnetic moments
Standard model
FeO layer
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Interface structure Fe/MgO/Fe V

• Transmission for AP alignment 4 MgO layers

Standard model
FeO layer
Fe/(MgO)4/Fe
Fe/FeO/(MgO)4/FeO/Fe
Additional scattering at the FeO layer change of
the transmission
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Interface structure Fe/MgO/Fe VI

• Conductance TMR

Preasymptotic regime Increasing TMR
Exponential decay
Bulk potentials only
Standard model
FeO layer
Preliminary results work in progress
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Outlook work in progress

• Fe/MgO/Fe
• Inclusion of electron correlation (oxide layer)
  via self-interaction correction
• Co/Au/Vac/Co
• Effect of quantum-well states in the Au film
• Further projects
• Magnetic STM
• Bias voltage, tip shape, full potential, spin
  motion,

Drivers, supporters, observers,
Jamal Berakdar, Mohammed Bouhassoune, Patrick
Bruno, Markus Däne, Hai Feng Ding, Arthur Ernst,
Wolfram Hergert, Piotr Karas, Jürgen Kirschner,
Martin Lüders, Udo Schmidt, Dzidka Szotek, Walter
Temmerman, Wulf Wulfhekel,