Theoretical Details of Tunnel Magnetoresistance via inelastic hopping at regime $g\mu B\ll k_B T \ll eV$

TL;DR

This paper provides a rigorous theoretical derivation of tunnel magnetoresistance via phonon-assisted hopping through impurity chains under small magnetic fields and large bias, clarifying the physical mechanisms involved.

Contribution

It offers a detailed theoretical framework for tunnel magnetoresistance via inelastic hopping, supporting the Pauli blockade switch concept with a derivation based on Green functions and slave-boson formalism.

Findings

Derivation of master equations for spin-dependent density matrices.

Validation of the Pauli blockade switch mechanism.

Insight into the interplay of magnetic field and spin interactions.

Abstract

Detailed theoretical derivation is given for the tunnel magnetoresistance via phonon-assisted hopping through an impurity chain under small magnetic field and a large bias window. This derivation provides a rigorous basis for the physical picture of Pauli blockade switch proposed in our previous paper (arXiv:1404.0633). This picture captures the competition of external magnetic field and internal spin interactions in the tunnel barrier, and relies critically on the strong on-site Coulomb correlation at the impurities. The master equations are obtained by deriving the equations of motion for the Green functions at the impurity sites in a slave-boson representation, and utilizing the so-called Langreth theorem to finally express the spin-dependent density matrix in terms of the equilibrium distributions of the contact electrons and of the phonon reservoir.