O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 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: Presented by Jun-Qiang Lu, ORNL

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 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

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 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

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 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, (2006)

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 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, (2006)

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY Phase Accumulation Model for Nanodots Disc shape with diameter d and thickness t QW energy divided into two terms E z from 1D confinement PAM same as in the layer case E // from the zeros of the Bessel function J n (x), for x=  n

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 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

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 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 2R M Circuit model includes both (spin-dependent) contact tunneling resistances R  (  ) and the resistance of the molecule R M A spin-flip channel with a resistance R S connects the two spin channels RMRM RSRS Spin up Spin down R  + R M R  + R M Spin polarization P

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY Tuning Magnetoresistance Magnetoresistance ratio is Zero spin-flip scattering “conductivity mismatch” if R M large For fixed R M and R S, maximum m is achieved if

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY Spin-Flip Scattering in CoFe/Al 2 O 3 /Cu/Al 2 O 3 /CoFe junctions For double barrier magnetic tunnel junctions, magnetoresistance ratio G S =1/R S G P, G AP are tunneling conductances of single barrier magnetic junctions G S extracted from magnetoresistance measurements show linear temperature dependence and scaling with copper layer thickness Spin-flip scattering length at 4.2K estimated to be 1  m PRL 97, (2006)

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY Quantum well resonance in CoFe/Al 2 O 3 /Cu/Al 2 O 3 /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 E 0 =QW state energy  spin-splitting of chemical potential  =smearing Fitted spin-flit conductance agree with experiment MR diminishes at same bias of QW resonance PRL 97, (2006)

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 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