The recently discovered two-dimensional (2D) magnetic insulator CrI3 is an intriguing case for basic research and spintronic applications since it is a ferromagnet in the bulk, but an antiferromagnet in bilayer form, with its magnetic ordering amenable to external manipulations. Using first-principles quantum transport approach, we predict that injecting unpolarized charge current parallel to the interface of bilayer-CrI3/monolayer-TaSe2 van der Waals heterostructure will induce spin-orbit torque (SOT) and thereby driven dynamics of magnetization on the first monolayer of CrI3 in direct contact with TaSe2. By combining calculated complex angular dependence of SOT with the Landau-Lifshitz-Gilbert equation for classical dynamics of magnetization, we demonstrate that current pulses can switch the direction of magnetization on the first monolayer to become parallel to that of the second monolayer, thereby converting CrI3 from antiferromagnet to ferromagnet while not requiring any external magnetic field. We explain the mechanism of this reversible current-driven nonequilibrium phase transition by showing that first monolayer of CrI3 carries current due to evanescent wavefunctions injected by metallic transition metal dichalcogenide TaSe2, while concurrently acquiring strong spin-orbit coupling (SOC) via such proximity effect, whereas the second monolayer of CrI3 remains insulating. The transition can be detected by passing vertical read current through the vdW heterostructure, encapsulated by bilayer of hexagonal boron nitride and sandwiched between graphite electrodes, where we find tunneling magnetoresistance of 240%. arXiv:1909.13876v2 [cond-mat.mes-hall]

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

The recent observation (Gorbachev et al 2014 Science 346 448) of nonlocal resistance R NL near the Dirac point (DP) of multiterminal graphene on aligned hexagonal-boron nitride (G/hBN) has been interpreted as the consequence of topological valley Hall currents carried by the Fermi sea states just beneath the bulk gap E g induced by inversion symmetry breaking. However, the corresponding valley Hall conductivity s xy v , quantized inside E g , is not directly measurable. Conversely, the Landauer-Büttiker formula, as a numerically exact approach to observable nonlocal transport quantities, yields R NL ≡ 0 for the same simplistic Hamiltonian of gapped graphene that generates s ¹ 0 xy v OPEN ACCESS RECEIVED

We review a unified approach for computing: (i) spin-transfer torque in magnetic trilayers like spin-valves and magnetic tunnel junction, where injected charge current flows perpendicularly to interfaces; and (ii) spin-orbit torque in magnetic bilayers of the type ferromagnet/spin-orbit-coupledmaterial, where injected charge current flows parallel to the interface. The experimentally explored and technologically relevant spin-orbit-coupled-materials include 5d heavy metals, topological insulators, Weyl semimetals and transition metal dichalcogenides. Our approach requires to construct the torque operator for a given Hamiltonian of the device and the steady-state nonequilibrium density matrix, where the latter is expressed in terms of the nonequilibrium Green's functions and split into three contributions. Tracing these contributions with the torque operator automatically yields field-like and damping-like components of spin-transfer torque or spin-orbit torque vector, which is particularly advantageous for spin-orbit torque where the direction of these components depends on the unknown-in-advance orientation of the current-driven nonequilibrium spin density in the presence of spin-orbit coupling. We provide illustrative examples by computing spin-transfer torque in a one-dimensional toy model of a magnetic tunnel junction and realistic Co/Cu/Co spin-valve, both of which are described by first-principles Hamiltonians obtained from noncollinear density functional theory calculations; as well as spin-orbit torque in a ferromagnetic layer described by a tight-binding Hamiltonian which includes spin-orbit proximity effect within ferromagnetic monolayers assumed to be generated by the adjacent monolayer transition metal dichalcogenide. In addition, we show how spin-orbit proximity effect, quantified by computing (via first-principles retarded Green's function) spectral functions and spin textures on monolayers of realistic ferromagnetic material like Co in contact with heavy metal or monolayer transition metal dichalcogenide, can be tailored to enhance the magnitude of spin-orbit torque. We also quantify errors made in the calculation of spin-transfer torque when using Hamiltonian from collinear density functional theory, with rigidly rotated magnetic moments to create noncollinear magnetization configurations, instead of proper (but computationally more expensive) self-consistent Hamiltonian obtained from noncollinear density functional theory. * bnikolic@udel.edu 1 For easy navigation, we provide a list of abbreviations used throughout the Chapter: 1D-Particle Current z y x Co Lead Co Lead Cu(a) (b) M free fixed M Co Pt θ θ M free MoS 2 Co M free θ (c) FIG. 2. Schematic view of: (a) FM/NM/FM trilayer for calculations of STT in spin-valves; (b) FM/HM bilayer for calculations of SOT in the presence of the spin Hall current along the z-axis generated by the HM layer; and (c) FM/monolayer-TMD for calculations of SOT in the absence of any spin Hall current. The semi-infinite FM layers in (a) are chosen as Co (0001), and t...

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 ...