We introduce a multiscale framework which combines time-dependent nonequilibrium Green function (TD-NEGF) algorithms, scaling linearly in the number of time steps and describing quantummechanically conduction electrons in the presence of time-dependent fields of arbitrary strength or frequency, with classical time evolution of localized magnetic moments described by the Landau-Lifshitz-Gilbert (LLG) equation. The TD-NEGF+LLG framework can be applied to a variety of problems where current-driven spin torque induces dynamics of magnetic moments as the key resource for next generation spintronics. Previous approaches to such nonequilibrium many-body system (like steady-state-NEGF+LLG framework) neglect noncommutativity of a quantum Hamiltonian of conduction electrons at different times and, therefore, the impact of time-dependent magnetic moments on electrons leading to pumping of spin and charge currents. The pumped currents can, in turn, self-consistently affect the dynamics of magnetic moments themselves. Using magnetic domain wall (DW) as an example, we predict that its motion will pump time-dependent spin and charge currents (on the top of unpolarized DC charge current injected through normal metal leads to drive the DW motion), where the latter can be viewed as a realization of quantum charge pumping due to time-dependence of the Hamiltonian and left-right symmetry breaking of the two-terminal device structure. The conversion of AC components of spin current, whose amplitude increases (decreases) as the DW approaches (distances from) the normal metal lead, into AC voltage via the inverse spin Hall effect offers a tool to precisely track the DW position along magnetic nanowire. We also quantify the DW transient inertial displacement due to its acceleration and deceleration by pulse current and the entailed spin and charge pumping. Finally, TD-NEGF+LLG as a nonperturbative (i.e., numerically exact) framework allows us to establish the limits of validity of the so-called spin-motive force (SMF) theory for pumped charge current by time-dependent magnetic textures-the perturbative analytical formula of SMF theory becomes inapplicable for large frequencies (but unrealistic in magnetic system) and, more importantly, for increasing noncollinearity when the angles between neighboring magnetic moments exceed 10 • . arXiv:1802.05682v3 [cond-mat.mes-hall] 9 Aug 2018 x y z Electron Flow J t t J sd

Shift current-a photocurrent induced by light irradiating noncentrosymmetric materials in the absence of any bias voltage or built-in electric field-is one of the mechanisms of the so-called bulk photovoltaic effect. It has been traditionally described as a nonlinear optical response of a periodic solid to continuous wave light using a perturbative formula, which is linear in the intensity of light and which involves Berry connection describing the shift in the center of mass position of the Wannier wave function associated with the transition between the valence and conduction bands of the solid. Since shift current is solely due to off-diagonal elements of the nonequilibrium density matrix that encode quantum correlations, its peculiar space-time dynamics in response to femtosecond light pulse employed locally can be expected. To study such response requires to analyze realistic twoterminal devices, instead of traditional periodic solids, for which we choose paradigmatic Rice-Mele model sandwiched between two metallic electrodes and apply to it time-dependent nonequilibrium Green function algorithms scaling linearly in the number of time steps and capable of treating nonperturbative effects in the amplitude of external time-dependent fields. This reveals novel features: superballistic transport, signified by time dependence of the displacement, ∼t ν with ν>1, of the photoexcited charge carriers from the spot where the femtosecond light pulse is applied toward the electrodes; and photocurrent quadratic in light intensity at subgap frequencies of light due to twophoton absorption processes that were missed in previous perturbative analyses. Furthermore, frequency dependence of the DC component of the photocurrent reveals shift current as a realization of nonadiabatic quantum charge pumping enabled by breaking of left-right symmetry of the device structure. This demonstrates that a much wider class of systems, than the usually considered polar noncentrosymmetric bulk materials, can be exploited to generate nonzero DC component of photocurrent in response to unpolarized light and optimize shift-current-based solar cells and optoelectronic devices.

The conventional Landau-Lifshitz-Gilbert (LLG) equation is a widely used tool to describe dynamics of local magnetic moments, viewed as classical vectors of fixed length, with their change assumed to take place simultaneously with the cause. Here we demonstrate that recently developed [M. D. Petrović et al., Phys. Rev. Applied 10, 054038 (2018)] self-consistent coupling of the LLG equation to time-dependent quantum-mechanical description of electrons-where nonequilibrium spin density from time-dependent nonequilibrium Green function (TDNEGF) calculations is inserted within a torque term into the LLG equation while local magnetic moments evolved by the LLG equation introduce time-dependent potential in the quantum Hamiltonian of electronsmicroscopically generates time-retarded damping in the LLG equation described by a memory kernel which is also spatially dependent. For sufficiently slow dynamics of local magnetic moments on the memory time scale, the kernel can be expanded into power series to extract the Gilbert damping (proportional to first time derivative of magnetization) and magnetic inertia (proportional to second time derivative of magnetization) terms whose parameters, however, are time-dependent in contrast to time-independent parameters used in the conventional LLG equation. We use examples of single or multiple local magnetic moments precessing in an external magnetic field, as well as field-driven motion of a magnetic domain wall (DW), to quantify the difference in their time evolution computed from conventional LLG equation vs. TDNEGF+LLG quantum-classical hybrid approach. The faster DW motion predicted by TDNEGF+LLG approach reveals that important quantum effects, stemming essentially from a finite amount of time which it takes for conduction electron spin to react to the motion of classical local magnetic moments, are missing from conventional classical micromagnetics simulations. We also demonstrate large discrepancy between TDNEGF+LLG-computed numerically exact and, therefore, nonperturbative result for charge current pumped by a moving DW and the same quantity computed by perturbative spin motive force formula combined with the conventional LLG equation. arXiv:1810.11016v2 [cond-mat.mes-hall]

No abstract

The standard spin-transfer torque (STT)-where spin-polarized current drives dynamics of magnetization viewed as a classical vector-requires noncollinearity between electron spins carried by the current and magnetization of a ferromagnetic layer. However, recent experiments [A. Zholud et al., Phys. Rev. Lett. 119, 257201 (2017)] observing magnetization dynamics in spin valves at cryogenic temperatures, even when electron spin is collinear to magnetization, point at overlooked quantum effects in STT which can lead to highly nonclassical magnetization states. Using fully quantum many-body treatment, where an electron injected as spin-polarized wave packet interacts with local spins comprising the anisotropic quantum Heisenberg ferromagnetic chain, we define quantum STT as any time evolution of local spins due to initial many-body state not being an eigenstate of electron+local-spins system. For time evolution caused by injected spin-↓ electron scattering off local ↑-spins, entanglement between electron subsystem and local spins subsystem takes place leading to decoherence and, therefore, shrinking of the total magnetization but without rotation from its initial orientation which explains the experiments. Furthermore, the same processes-entanglement and thereby induced decoherence-are present also in standard noncollinear geometry, together with the usual magnetization rotation. This is because STT in quantum many-body picture is caused only by electron spin-↓ factor state, and the only difference between collinear and noncollinear geometries is in relative size of the contribution of the initial separable state containing such factor state to superpositions of separable many-body quantum states generated during time evolution.The standard spin-transfer torque (STT) [1], predicted in the seminal work of Slonczewski [2] and Berger [3], is a phenomenon where a flux of spin-polarized electrons injected into a ferromagnetic metal (FM) layer drives its magnetization dynamics. The origin of STT is transfer of spin angular momentum from electrons to local magnetic moments of the FM layer, so it is fundamentally a nonequilibrium quantum many-body physics effect. Nevertheless, local magnetic moments are typically treated as classical vectors of fixed length [1, 4] whose dynamics is governed by the Landau-Lifshitz-Gilbert (LLG) equation [5] extended by adding the STT term [6][7][8] T ∝ ŝ e × S(r).(1)Thus, the nonequilibrium spin density ŝ e caused by flowing electrons must be noncollinear to the direction of local spin S(r) [i.e., to the local magnetization proportional to local spin], to drive magnetization dynamics in such a classical picture. The dynamics can include oscillations or complete reversal, whose conversion into resistance variations has emerged as a key resource for next generation spintronic technologies, such as nonvolatile magnetic random access memories, microwave oscillators, microwave detectors, spin-wave emitters, memristors and artificial neural networks [9][10][11].For example, passing current through ...