Abstract
Tunnelling between two semi-infinite ferromagnetic electrodes separated by vacuum is studied theoretically on an ab-initio level by using the fully relativistic spin-polarized screened Korringa-Kohn-Rostoker and the spin-polarized non-relativistic tight-binding linear muffin-tin orbital method. The Kubo-Greenwood equation is employed to calculate the non-local conductivity and layer-resolved sheet resistances; the transmission matrix formulation in turn is used to evaluate the conductance. We show that the dependence of sheet resistance on the imaginary part of the Fermi energy allows us to distinguish between the tunnelling and conductive regimes of electron transport. Our numerical studies of the system bcc Fe(100)/vacuum/bcc Fe(100) show quite dramatic variations in the electrostatic potential in the vacuum region and a gradual development of the tunnelling barrier with increasing thickness of the vacuum barrier. Varying the Madelung potential in the interior of the vacuum barrier allowed us to simulate spacers made of semiconducting or insulating material and to discuss the conditions for the presence of a magnetoresistance in such multilayers. As far as the thickness of the vacuum barrier is concerned the results obtained with the transmission matrix approach for fee Co(001)/vacuum/fee Co(001) show a similar tendency to those obtained within the Kubo-Greenwood equation for bcc Fe(100)/vacuum/bcc Fe(100); asymptotically, that is with increasing thickness of the vacuum barrier, the magnetoresistance tends to zero.