A non-equilibrium quantum transport framework for spintronic devices with dynamical correlations

TL;DR

The paper addresses the challenge of modeling steady-state spintronic devices under finite bias in the presence of strong electronic correlations. It develops a DFT+NEGF+DMFT framework that downfolds the central region to a correlated subspace, solves a non-equilibrium impurity problem, and back-projects the dynamical self-energies to obtain transport observables. Applied to Cu/Co/vacuum/Cu and Fe/MgO/Fe MTJs, the approach reveals bias-driven non-Fermi-liquid behavior and substantial incoherent current in Co, while Fe remains near quasi-equilibrium with a modest incoherent contribution. This framework provides a rigorous, first-principles route to capture many-body scattering in spintronic transport and offers a path toward studying non-collinear and spin-orbit coupled devices, with implications for spin-transfer and spin-orbit torques.

Abstract

Two-terminal spintronic devices remain challenging to model under realistic operating conditions, where the interplay of complex electronic structures, correlation effects and bias-driven non-equilibrium dynamics may significantly impact charge and spin transport. Existing {\it ab initio} methods either capture bias-dependent transport but neglect dynamical correlations or include correlations but are restricted to equilibrium or linear-response regimes. To overcome these limitations, we present a framework for steady-state quantum transport, combining density functional theory (DFT), the non-equilibrium Greens' function (NEGF) method, and dynamical mean-field theory (DMFT). The framework is then applied to Cu/Co/vacuum/Cu and an Fe/MgO/Fe tunnel junction. In Co, correlations drive a transition from Fermi-liquid to non-Fermi-liquid behavior under finite bias, due to scattering of electrons with electron-hole pairs. In contrast, in the Fe/MgO/Fe junction, correlation effects are weaker: Fe remains close to equilibrium even at large biases. Nevertheless, inelastic scattering can still induce partly incoherent transport that modifies the device's response to the external bias. Overall, our framework provides a route to model spintronic devices beyond single-particle descriptions, while also suggesting new interpretations of experiments.

Figures (13)

• Figure 1: Schematic illustration of a typical two-terminal transport setup. (a) A two-terminal spintronic device is modelled as infinite along the transport direction and partitioned into a central (scattering) region contacted by semi-infinite metallic leads. (b) Each lead acts as an electronic reservoir. Under a finite bias voltage, $V$, the leads individually remain in equilibrium, with their electronic states occupied according to the Fermi-Dirac distribution functions, $f_{\mathrm{L(R)}}(E,\mu_\mathrm{L(R)})$, determined by the relative lead chemical potential $\mathrm{L(R)}$. The electrostatic potential $V(z)$ drops inside the central region.
• Figure 2: The device setup used in this work. (a) The Fe/MgO/Fe junction sandwiched between simple metallic electrodes, introduced in Sec. \ref{['section: Fe/MgO']}, shown as a prototypical example of a two-terminal device for DFT+NEGF calculations. Fe, Mg, and O atoms are represented by large red, cyan, and small red spheres, respectively, while the lead atoms are shown as yellow spheres. The Fe atoms define the correlated subspace. The formal lead/central region boundary is placed a few layers deeper inside the leads to ensure that interface effects are considered and that the correlated subspace does not interact directly with the leads, as required for Eq. (\ref{['eq:Sigmaaibath']}) to hold. The "extended region" is indicated by the green dashed box. Atoms outside this region are not coupled to $\mathcal{C}$ due to the finite spatial extent of the basis orbitals. (b) The projection maps the original device onto an effective one, with renormalized hopping between correlated atoms and effective coupling to the leads.
• Figure 3: Schematic representation of the DMFT loop
• Figure 4: The Cu/Co device investigated in this work. A Co layer is attached to a left Cu lead and separated from a right Cu lead by a 4 Å vacuum gap. Periodic boundary conditions are applied in the plane transverse to the stack.
• Figure 5: DFT and DMFT $3d$-Co PDOS and transmission coefficient at (a) $V=0$ V, (b) $V=0.3$ V, and (c) $V=0.8$ V. Spin-up (down) values are shown positive (negative).