Analysis of spin-dependent tunnelling of electrons in solid state structures using the transfer-Hamiltonian method

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Abstract
The transfer-Hamiltonian (t-H) method is applied to study spin-dependent low-rate transfer of electrons between magnetically ordered metallic electrodes separated by a potential barrier. A weak coupling of the electrodes through the potential barrier is described with help of a t-H treated as a perturbation. Spin-dependent tunnelling probability amplitudes are expressed by a matrix with elements evaluated through an overlap between the spinor components of the electron wavefunctions from both sides of the potential barrier, resulting in spin-dependent tunnelling current and tunnelling conductance. In particular, the magnetic valve effect in tunnelling between two ferromagnets and elements of the theory of a spin-polarized scanning tunnelling microscope with a ferromagnetic tip are analysed. The t-H method is useful also in applications to tunnelling in magnetic nanostructures and multilayers.