Orientation-Dependent Transparency of Metallic Interfaces

The spin dependence of the transmission and reflection of electrons at magnetic interfaces provides the key to understanding phenomena such as oscillatory exchange coupling, giant and tunneling magnetoresistance, spin transfer torque, spin pumping, and spin injection [1]. For well-studied material combinations such as Co|Cu and Fe|Cr, modest spin dependence of the interface transmission of the order of 10%–20% is sufficient to account for experimental observations. Although the theory of transport in small structures is formulated in terms of transmission and reflection matrices, measuring interface transparencies directly has proven quite difficult and the confrontation of theory and experiment is at best indirect and model-dependent. To identify interfaces suitable for experimental study, we undertook a systematic materials-specific study of the orientation dependence of the interface transmission between pairs of isostructural metals whose lattice constants match within a percent or so in the hope that it will prove possible to grow such interfaces epitaxially [2]

One of the metal pairs we studied was Al|Ag. Both metals have the fcc crystal structure, and their lattice constants are matched within 1%. Aluminum is a textbook example of a system well described by the (nearly) free-electron model. Silver, also usually assumed to be a free-electron-like material, is a noble metal with high conductivity. In spite of the simplicity of both metals’ electronic structures, the transmission through Al|Ag interfaces was found to differ quite significantly from the predictions of the free-electron model. In particular, between (111) and (001) orientations, we find a factor of 2 difference in interface transmission for clean Al|Ag interfaces. For free electrons, the anisotropy should vanish. Our result is insensitive to interface disorder. We could identify a new factor responsible for this difference which is not related to the standard velocity- or symmetry-mismatch mechanisms.

[1] A. Brataas, G.E.W. Bauer and P.J. Kelly, Non-collinear magnetoelectronics, Phys. Reports 427, 157-255 (2006).

[2] P.X. Xu, K. Xia, M. Zwieryzycki, M. Talanana, and P.J. Kelly, Orientation-Dependent Transparency of Metallic Interfaces, Phys. Rev. Lett. 96, 176602 (2005).

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Figure 1. Top row: Fermi surface projections for (a) Ag, (b) Al, and (c) transmission probabilities in the 2D Brillouin zone for the (111) orientation. Middle row: Same for the (001) orientation. The colour bars on the left indicate the number of scattering states in the leads for a given two-dimensional wave vector k||. The transmission probabilities indicated by the colour bars on the right can exceed 1 for k||s for which there is more than one scattering state in both Ag and Al. Bottom row: Fermi surfaces of (g) Ag and (h) Al, (i) the interface-adapted BZ for (001) and (111) orientations.