OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Modeling Electron and Spin Transport Through Quantum Well States
Xiaoguang Zhang
Oak Ridge National Laboratory
Yan Wang and Xiu Feng Han
Institute of Physics, CAS, China
Contact: [email protected]
Presented by Jun-Qiang Lu, ORNL
OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Outline
• Phase accumulation model for quantum well states double barrier magnetic tunnel junctions Coulomb blockade effect magnetic nanodots
• Circuit model for spin transport Tuning magnetoresistance for molecular junctions Measuring spin-flip scattering Effect of quantum well states
• Conclusion
OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Phase Accumulation Model for Thin Layer
• Free-electron dispersion
• Bohr-Sommerfeld quantization rule
» Phase shift on reflection from left boundary
» Phase shift on reflection from right boundary
» Additional phase due to roughness
» Layer thickness
€
E = EL +h2 k
2
2m*
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2kzt − Φ1 − Φ2 − Φ = 2nπ
€
Φ1
€
Φ
€
Φ2
€
t
OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Quantum Well States in Fe Spacer Layer of Fe/MgO/Fe/MgO/Fe Tunnel Junction
• (top) PAM model in good agreement with first-principles calculation
• (right) Experimentally observed resonances can be matched with the calculated QW states
PRL 97, 087210 (2006)
OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Coulomb Blockade Effect
• Experimental resonances all higher than calculated QW energies - difference due to Coulomb charging energy of discontinuous Fe spacer layer
• Using a plate capacitor model, Fe layer island size can be estimated from the Coulomb charging energy Deduced island size as a function of film
thickness agrees with measurement Resonance width proportional to the
Coulomb charging energy, suggesting smearing effect due to size distribution
PRL 97, 087210 (2006)
OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Phase Accumulation Model for Nanodots
• Disc shape with diameter d and thickness t
• QW energy divided into two terms
• Ez from 1D confinement PAM same as in the layer case
• E// from the zeros of the Bessel function Jn(x), for x=n
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E = E z + E //
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E // =μn
2h2
m2d
OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Quantum Well States in Nanodots
• (top) DOS of QW states for t=3 nm, d=6 nm (red) or d=9 nm (blue)
• A spin splitting is assumed. Inset shows spin polarization - note strong oscillation and negative polarization at some energies
• (bottom) Averaged DOS of discs with diameters over a continuous distribution between 6 and 9 nm.
• Coulomb charging energy (<0.2 eV) visible but causes minimal smearing effect
OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Circuit Model for Spin Transport
• A simple, two channel circuit model to represent an electrode-conducting molecular-electrode junction
• Each spin channel in the molecule has resistance 2RM
• Circuit model includes both (spin-dependent) contact tunneling resistances R() and the resistance of the molecule RM
• A spin-flip channel with a resistance RS connects the two spin channels
RM
RS
Spin up
Spin down
R+ RM
R+ RM
Spin polarization
P
OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Tuning Magnetoresistance
• Magnetoresistance ratio is
• Zero spin-flip scattering
“conductivity mismatch” if RM large
• For fixed RM and RS, maximum m is achieved if
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m =R↑R↓RS
(R↑ + RM )(R↓ + RM ) RS + RM + 12 (R↑ + R↓ )[ ]
P 2
1− P 2
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m =R↑R↓
(R↑ + RM )(R↓ + RM )
P 2
1− P 2
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R↑R↓ = RM (2RS + 3RM )
OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Spin-Flip Scattering in CoFe/Al2O3/Cu/Al2O3/CoFe junctions
• For double barrier magnetic tunnel junctions, magnetoresistance ratio
• GS=1/RS
• GP, GAP are tunneling conductances of single barrier magnetic junctions
• GS extracted from magnetoresistance measurements show linear temperature dependence and scaling with copper layer thickness
• Spin-flip scattering length at 4.2K estimated to be 1m
PRL 97, 106605 (2006)
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m =Gp − GAP
2GAP + GP + GAP γGS
OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Quantum well resonance in CoFe/Al2O3/Cu/Al2O3/CoFe junctions
• Spin-flip scattering proportional to spin accumulation in the copper layer
• For a single nonspin-polarized QW state near the Fermi energy, spin accumulation is
• E0=QW state energy• spin-splitting of chemical
potential• =smearing• Fitted spin-flit conductance agree
with experiment• MR diminishes at same bias of
QW resonancePRL 97, 106605 (2006)
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N ∝ arctanΔμ /2 − E0
η+ arctan
Δμ /2 + E0
η
OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY
Conclusions
• Spin-polarized QW states in nanoparticles may be a source of large magnetoresistance, but size distribution and Coulomb charging energy may smear the effect significantly
• Nonspin-polarized QW states can be a significant source of spin-flip scattering
• With fixed resistance in a molecule and fixed spin-flip scattering, maximum magnetoresistance can be achieved by adjusting the contact resistances which are spin-dependent
