Disentangling interface and bulk contributions to the anisotropic magnetoresistance in Pt/Co/Pt sandwiches

We report on interfacial contributions to the anisotropic magnetoresistance (AMR) in Co layers sandwiched between Pt. Utilizing the Fuchs-Sondheimer formalism interface contributions can be separated from bulklike AMR. We demonstrate that for all-metal systems interfacial AMR is also present when varying the magnetization within the film plane. This interfacial in-plane AMR is two times smaller than the contribution that arises when the magnetization is varied within the plane perpendicular to the current direction. This finding is in contrast to the spin Hall MR found for ferromagnetic insulator/Pt bilayers revealing the existence of different MR effects at the interfaces of Pt with conducting and insulating ferromagnets.

Figure 1

Longitudinal MR behavior of Co/Pt layered structures. (a) Sketch of a Pt/Co/Pt sandwich and the experiment-related coordinate system. (b) Plot of $\rho$ as a function of orientation of magnetization $\mathbf{M}$ parametrized via the azimuthal and polar angle $\phi /\theta$. The $\mathbf{M}$ dependence of the resistivity $\rho$ can be described according to Eq. (1) utilizing the amplitudes $\mathrm{\Delta }{\rho }_{\mathrm{ip}}$ and $\mathrm{\Delta }{\rho }_{\mathrm{op}}$. The plot represents the system with $t_{\mathrm{Co}}=6\mathrm{nm}:{\rho }_{\mathrm{t}}=35.635\mu \mathrm{\Omega }\mathrm{cm},\mathrm{\Delta }{\rho }_{\mathrm{ip}}=0.284\mu \mathrm{\Omega }\mathrm{cm}$, and $\mathrm{\Delta }{\rho }_{\mathrm{op}}=0.195\mu \mathrm{\Omega }\mathrm{cm}$. The dotted curves give the experimental results for $\rho \left(\phi ,\theta ={90}^{\circ }\right)$ (black symbols), $\rho \left(\phi =\pm {90}^{\circ },\theta \right)$ (red symbols), and $\rho \left(\phi =0^{\circ },{180}^{\circ },\theta \right)$ (purple symbols). $\rho (\phi =+{90}^{\circ },\theta )$ and $\rho (\phi ={180}^{\circ },\theta )$ are displayed as $\rho (\phi =-{90}^{\circ },-\theta )$ and $\rho (\phi =0^{\circ },-\theta )$, respectively, for the sake of convenience. The experimental curves are obtained by rotating the magnetization by means of a field ${\mu }_0\left|\mathbf{H}\right|=6\mathrm{T}$ that is sufficient to always force $\mathbf{M}$ parallel to $\mathbf{H}$. Two of the three curves are sufficient to span the resistivity landscape. The generic resistivities are transverse resistivity ${\rho }_{\mathrm{t}}=\rho \left(\phi ={90}^{\circ },\theta ={90}^{\circ }\right)$, longitudinal resistivity ${\rho }_{\ell }=\rho \left(\phi =0^{\circ },\theta ={90}^{\circ }\right)$ ($\mathbf{M}$ along current direction j), and polar resistivity ${\rho }_{\mathrm{p}}=\rho \left(\theta =0^{\circ }\right)$ ($\mathbf{M}$ along film normal). (c) Magnetoresistance ratios $\mathrm{\Delta }{R}_{\mathrm{ip}}/R_{\mathrm{t}}$ and $\mathrm{\Delta }{R}_{\mathrm{op}}/R_{\mathrm{t}}$ versus Co thickness $t_{\mathrm{Co}}$. The solid lines are calculated via Eqs. (2, 3, 4) using the fit parameters that have been obtained following the procedure explained in the text.

Figure 2

Sandwich resistance $R_{\mathrm{t}}$ versus Co layer thickness $t_{\mathrm{Co}}$. The black line is a fit according to the layer model [Eqs. (2) and (3)]. The inset displays the resistivity of the sandwich ${\rho }_{\mathrm{t}}=R_{\mathrm{t}}\frac{(t_{\mathrm{Co}}+t_{\mathrm{Pt}})w}{l}$ versus $t_{\mathrm{Co}}$ calculated from the data and the $R_{\mathrm{t}}\left(t_{\mathrm{Co}}\right)$ fit (black line) as well as the resistivity of the Co layer ${\rho }_{\mathrm{t},\mathrm{Co}}$ versus $t_{\mathrm{Co}}$ calculated with Eq. (3) using the parameters obtained from fitting $R_{\mathrm{t}}\left(t_{\mathrm{Co}}\right)$ (red line).

Figure 3

Dependence of shunt-corrected MR on $t_{\mathrm{Co}}$. In (a) the difference resistivities $\mathrm{\Delta }{\rho }_{\mathrm{ip},\mathrm{Co}}$ and $\mathrm{\Delta }{\rho }_{\mathrm{op},\mathrm{Co}}$ are shown whereas (b) displays the MR ratios of the Co layers $\mathrm{\Delta }{\rho }_{\mathrm{ip},\mathrm{Co}}/{\rho }_{\mathrm{t},\mathrm{Co}}$ and $\mathrm{\Delta }{\rho }_{\mathrm{op},\mathrm{Co}}/{\rho }_{\mathrm{t},\mathrm{Co}}$. The dashed gray region highlights the bulk mean-free path of the Co layer ${\lambda }_{\mathrm{t},\mathrm{Co}\mathrm{bulk}}$ (including error margin). (a) The black dotted/solid line is a fit to $\mathrm{\Delta }{\rho }_{\mathrm{ip},\mathrm{Co}}\left(t_{\mathrm{Co}}\right)$ according to Eq. (6) in the absence/presence of interfacial contributions. The red solid line is a fit to $\mathrm{\Delta }{\rho }_{\mathrm{op},\mathrm{Co}}$ according to Eq. (5) taking interfacial contributions into account. The bulk contribution (GSE) is shown as the red dotted line. The inset highlights the results for $t_{\mathrm{Co}}>2\mathrm{nm}$. (b) The solid red and black lines are the model curves of the MR ratios of the Co layer taking the best fit results of (a). The denominator ${\rho }_{\mathrm{t},\mathrm{Co}}\left(t_{\mathrm{Co}}\right)$ is calculated by means of Eq. (3) and is displayed in the inset of Fig. 2.