Experimental separability of channeling giant magnetoresistance in $\mathrm{Co}∕\mathrm{Cu}∕\mathrm{Co}$

The magnitude of the electronic channeling contribution is a significant open issue in the understanding of giant magnetoresistance (GMR). We show that for the technologically important system $\mathrm{Co}∕\mathrm{Cu}∕\mathrm{Co}$, channeling GMR can be isolated and quantified experimentally through measurement in the limit of rapid surface diffuse scattering. First-principles based Boltzmann transport calculations are compared with experimental in situ magnetoconductance data, which support the possibility of a significant contribution from channeling. Cyclic control of atomic-scale surface roughness, applied during in situ measurement, will enable a quantitative estimate of the channeling contribution.

Figure 1

(Color online) ${\mathbf{k}}_{\Vert }$-resolved map of contributions to CIP-GMR, measured as $\Delta G\left({\mathbf{k}}_{\Vert }\right)=G_P\left({\mathbf{k}}_{\Vert }\right)-G_{\mathrm{AP}}\left({\mathbf{k}}_{\Vert }\right)$. Left to right: calculations for (100), (110), and (111) oriented $\mathrm{Co}\left(20\right)∕\mathrm{Cu}\left(30\right)∕\mathrm{Co}\left(20\mathrm{\AA }\right)$ trilayers. Top to bottom: perfectly specular top surface scattering $(p_{\text{top}}=1)$ to perfectly diffuse top surface scattering $(p_{\text{top}}=0)$. The white lines bracket the channeling states in Cu, for which no allowed majority state in Co exists. Note that contributions to $\Delta G\left({\mathbf{k}}_{\Vert }\right)$ are independent of surface scattering. Increasing contributions to $\Delta G\left({\mathbf{k}}_{\Vert }\right)$ represented by ascending brightness in color, from black to yellow.

Figure 2

(Color online) Top: Calculated total GMR, measured as $\Delta G_{\mathrm{tot}}\left(t_{\mathrm{Co}}\right)$, and channeling GMR, measured as $\Delta G_{\mathrm{chan}}\left(t_{\mathrm{Co}}\right)$, in a (111) $\mathrm{Co}\left(20\right)∕\mathrm{Cu}\left(30\mathrm{\AA }\right)∕\mathrm{Co}\left(t_{\mathrm{Co}}\right)$ trilayer, for specular- and diffuse-scattering top surfaces ($p_{\text{top}}=1$ and $p_{\text{top}}=0$ respectively). Middle: comparison across orientations: $\Delta G_{\mathrm{SDS}}\left(t_{\mathrm{Co}}\right)$ and channeling $\Delta G_{\mathrm{chan}}\left(t_{\mathrm{Co}}\right)$ for (100), (110), and (111) oriented trilayers, $p_{\text{top}}=0$. Bottom: comparison of behaviors $\Delta G_{\mathrm{SDS}}\left(t_{\mathrm{Co}}\right)$ for bulk and $\text{bulk}+\text{interface}$ SDS in (111) trilayers. See text for details.

Figure 3

Experimental $\Delta G\left(t_{\mathrm{Co}}\right)$ for a bottom-pinned $\mathrm{Co}\left(20\right)∕\mathrm{Cu}\left(30\right)∕\mathrm{Co}\left(t\right)$ spin valve, measured in situ. Points: experiment; lines: calculations of $\Delta G_{\mathrm{SDS}}$, offset by $\Delta G=+0.7\mathrm{m}{\Omega }^{-1}$, for different values of surface scattering. See text for details.