# Molecular orbital concept on spin-flip transport in molecular junctions

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## Abstract

The spin-dependent electron transport correlated with spin-flip dynamics in a molecular junction was investigated in the wave-packet and Green’s function approaches. The molecular junction adopted in this work is described by a simple one-dimensional tight-binding chain including a localized spin. The spin exchange coupling *J* between the localized and conduction electron spins was taken into account through the *s-d* Hamiltonian. The wave-packet simulations showed that the transmission probabilities in both the spin-flip and no-flip processes show large peaks at the eigenvalues of the spin singlet (−3*J*/4) and triplet (*J*/4) states, and that, different transmission properties appear at the mid-gap of the two eigenvalues: the spin-flip process shows a moderate decrease, whereas the no-flip process an abrupt drop. Dividing the *s-d* Hamiltonian into two submatrices and referring to the molecular orbital concept for the coherent electron transport, we found that the moderate decrease in the spin-flip process at the mid-gap is the result of a coherent-and-cooperative contribution from the singlet and triplet states of the conduction and localized electron spins, and that, the abrupt drop in the no-flip process at the mid-gap is mainly caused by the coherent cancellation from the singlet and triplet states. The molecular orbital concept available for the electron transport including spin-flip scattering processes is described in Green’s function method, in analogy to the one derived for the spinless electron transport.

## Keywords

Spin-dependent electron transport Spin-flip Molecular junction Wave packet Green’s function Molecular orbital## Notes

### Acknowledgments

It is a great pleasure to dedicate this paper to Prof. A. Imamura, who was a supervisor of one of the authors (TT) in Hiroshima University from 1995 to 1998. The lectures on the molecular orbital theory given by A. Imamura have continued to inspire the interests of one of the authors (TT) in the field of the molecular science. This work was partially supported by the Grant-in-Aid for Young Scientists (B), MEXT of Japan. The author would like to thank S. Konabe for technical information on wave-packet dynamics.

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