Abstract
We extract local current distributions from interatomic currents calculated using a fully relativistic quantum mechanical scattering formalism by interpolation onto a three-dimensional grid. The method is illustrated with calculations for Pt$|$Ir and Pt$|$Au multilayers as well as for thin films of Pt and Au that include temperature-dependent lattice disorder. The current flow is studied in the "classical" and "Knudsen" limits determined by the sample thickness relative to the mean free path $\lambda$, introducing current streamlines to visualize the results. For periodic multilayers, our results in the classical limit reveal that transport inside a metal can be described using a single value of resistivity $\rho$ combined with a linear variation of $\rho$ at the interface while the Knudsen limit indicates a strong spatial dependence of $\rho$ inside a metal and an anomalous dip of the current density at the interface which is accentuated in a region where transient shunting persists.
Highlights
The standard way to measure a bulk resistivity ρ is the four-point-probe technique [1,2,3], which assumes isotropic current propagation
We introduce a discrete scheme to interpolate local currents [35] calculated using a fully relativistic density functional theory (DFT)-based scattering code [36] and apply it to evaluate the full spatial profile of currents in thin films of Pt and Au, which are of interest to the spintronics community as well as in Pt|Au and Pt|Ir multilayers
Different regimes of electron transport can be identified depending on the ratio of the electron mean-free path λ to the critical dimension d of the scattering geometry that is the Knudsen number (Kn)
Summary
The standard way to measure a bulk resistivity ρ is the four-point-probe technique [1,2,3], which assumes isotropic current propagation. If the mean-free-path λ is comparable to d, the whole concept of a local resistivity becomes moot and, as illustrated, specular (reflection) and diffusive reflection play a role in determining the current distribution in such films [4,15]. A very recent attempt to determine this current distribution combined different thin film resistivity models with four-point-probe measurements for a large number of samples where the individual layer thicknesses were varied systematically [24]. This indirect approach was made necessary by the absence of a direct method to observe how current flows in the different layers of multilayer samples. Stejskal et al concluded their study by emphasizing the need for more detailed structural characterization to be
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