Browsing by Author "Bajpai, Utkarsh"
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Item Quantum many-body states and Green's functions of nonequilibrium electron-magnon systems: Localized spin operators versus their mapping to Holstein-Primakoff bosons(Physical Review B, 2021-11-22) Bajpai, Utkarsh; Suresh, Abhin; Nikolić, Branislav K.It is well-known that operators of localized spins within a magnetic material satisfy neither fermionic nor bosonic commutation relations. Thus, to construct diagrammatic many-body perturbation theory requiring the Wick theorem, the spin operators are usually mapped to the bosonic ones with Holstein-Primakoff (HP) transformation being the most widely used in magnonics and spintronics literature. However, to make calculations tractable, the square root of operators in the HP transformation is expanded into a Taylor series truncated to some low order. This poses a question on the range of validity of the truncated HP transformation when describing nonequilibrium dynamics of localized spins interacting with each other or with conduction electron spins—a problem frequently encountered in numerous transport phenomena in magnonics and spintronics. Here we apply exact diagonalization techniques to a Hamiltonian of fermions (i.e., electrons) interacting with HP bosons versus a Hamiltonian of fermions interacting with the original localized spin operators to compare their many-body states and one-particle equilibrium and nonequilibrium Green's functions (GFs). We employ as a test bed a one-dimensional quantum Heisenberg ferromagnetic spin-S XXX chain of N≤7 sites, where S=1 or S=5/2, and the ferromagnet can be made metallic by allowing electrons to hop between the sites while interacting with the localized spins via sd exchange interaction. For these two different versions of the Hamiltonian of this model, we compare the structure of their ground states, time evolution of excited states, spectral functions computed from the retarded GF in equilibrium, and matrix elements of the lesser GF out of equilibrium. Interestingly, magnonic spectral function can be substantially modified by acquiring additional peaks due to quasibound states of electrons and magnons once the interaction between these subsystems is turned on. The Hamiltonian of fermions interacting with HP bosons gives an incorrect ground state and electronic spectral function unless a large number of terms are retained in the truncated HP transformation. Furthermore, tracking the nonequilibrium dynamics of localized spins over longer time intervals requires a progressively larger number of terms in truncated HP transformation, even if a small magnon density is excited initially, but the required number of terms is reduced when interaction with conduction electrons is turned on. Finally, we show that recently proposed [M. Vogl et al., Phys. Rev. Res. 2, 043243 (2020); J. König et al., SciPost Phys. 10, 007 (2021)] resummed HP transformation, where spin operators are expressed as polynomials in bosonic operators, resolves the trouble with truncated HP transformation while allowing us to derive an exact quantum many-body (manifestly Hermitian) Hamiltonian consisting of a finite and fixed number of boson-boson and electron-boson interacting terms.Item Quantum-classical approach to nonequilibrium system of conduction electrons interacting with localized spins in spintronics(University of Delaware, 2021) Bajpai, UtkarshSpintronics is the fundamental study of magnetization dynamics and transport of charge and spin angular momentum of electrons within a magnetic material which has also given rise to many applications, for e.g., the Giant-Magnetoresistance (GMR) effect in spintronics has led to the invention of nonvolatile magnetic random access memory (MRAM). In a similar direction, a new proposal for a highly efficient and fast memory device was made by Stuart Parkin from IBM Almaden Research Center at San Jose, CA, known as the racetrack memory. It consists of information stored in a magnetic nanowire as a series of bits (for e.g., 01011) that correspond to alternating direction of magnetic domains separated by “domain-walls” (DWs) whose real-space position can be manipulated by injecting electronic currents through the nanowire. The bit-states can then be read by a static read-head. The DW motion occurs due to spin torques exerted on its local magnetic moments (LMMs) by the conduction electrons that are pushed out of equilibrium either due to the externally injected currents which generates the traditional current-dependent spin transfer torque (STT), or, due to the time-dependence of LMMs that generates additional current-independent spin torque due to backaction of conduction electrons originating from a time-retardation effect where the conduction electron spin “lags” behind and takes finite time in responding to the dynamics of LMMs which causes a misalignment between the conduction electron spin and the orientation of LMMs, thereby generating a spin torque. Currently, conventional micromagnetic simulations based on the Landau-Lifshitz-Gilbert (LLG) equation are routinely employed to describe time-evolution of LMMs in the presence conduction electrons, but ad hoc spin torque terms have to be included by phenomenological techniques valid only for specific models that are restricted by approximations and do not capture the complicated self-consistent backaction of conduction electrons. ☐ To investigate such current-independent spin torque due to backaction of conduction electrons, in this thesis we develop a numerically exact quantum-classical hybrid scheme, dubbed “TDNEGF+LLG framework”, where conduction electrons are described quantum-mechanically by time-dependent nonequilibrium Green functions (TDNEGFs) self-consistently coupled to LMMs described by a modified classical LLG equation. TDNEGF+LLG framework microscopically includes the backaction of conduction electrons in a numerically exact fashion and the associated time-retardation effect is shown to manifest as a non-Markovian memory kernel that gives rise to a time-dependent and spatially-inhomogeneous Gilbert damping and magnetic inertia, both of which are missing in conventional micromagnetic simulations. In spintronics community, conduction electron spin and LMMs are putatively expected to be collinear in the so-called “adiabatic” limit (conduction electron spin–LMM interaction parameter Jsd goes to infinity) and thus any spin-torque is expected to be zero; on the contrary, we reveal that due to purely quantum-mechanical geometric effects, there exists an always-present noncollinearity between them which generates a “geometric” spin- torque analogous to geometric magnetism found in the field of nonadiabatic molecular dynamics. Furthermore, with an example of a two-terminal device hosting a spin wave (SW), we show that a chiral spin and charge pumping i.e., flow of current tied to direction of propagation of SW, can be observed. Previous interpretations of chiral spin and charge pumping have required a presence of spin-orbit (SO) interaction to cause a misalignment between the conduction electron spin and the orientation of LMMs. Nevertheless, within our framework, we demonstrate that SO interaction is not always necessary and the backaction of conduction electrons is enough to cause a misalignment of conduction electron spin and orientation of LMMs which leads to chiral charge and spin pumping. ☐ Nonetheless, even TDNEGF+LLG framework has a fundamental limitation. It treats the localized spin of LMMs classically when it must be described quantum mechanically by localized spin operators. However, due to lack of Wick theorem, localized spin operators are virtually always mapped to bosonic ones by the Holstein- Primako (HP) transformation whose square root is expanded and truncated as a power-series while retaining low-order terms for a tractable diagrammatic many-body perturbation theory. Therefore, we investigate the range of validity of truncated HP transformation by accurately tracking the nonequilibrium dynamics of LMMs in the absence or presence of interaction with conduction electrons in clusters composed of N ≤ 7 sites hosting spin-S localized spins. We compare the nonequilibrium dynamics of LMMs by exact-diagonalization of localized spin operators vs. their truncated HP transformation representation and find that including even as high as NT = 5 terms in the truncated HP transformation is insufficient to accurately simulate dynamics of LMMs up to even few femtoseconds (spintronics applications are typically at ∼ 1 ns). It also shows the degree of difficulty that must be overcome in order to obtain a fully quantum-mechanical description of conduction electrons interacting with LMMs.Item Robustness of quantized transport through edge states of finite length: Imaging current density in Floquet topological versus quantum spin and anomalous Hall insulators(Physical Review Research, 2020-09-17) Bajpai, Utkarsh; Ku, Mark J. H.; Nikolić, Branislav K.The theoretical analysis of topological insulators (TIs) has been traditionally focused on infinite homogeneous crystals with band gap in the bulk and nontrivial topology of their wave functions, or infinite wires whose boundaries host surface or edge metallic states. Such infinite-length edge states exhibit quantized conductance which is insensitive to edge disorder, as long as it does not break the underlying symmetry or introduce energy scale larger than the bulk gap. However, experimental devices contain finite-size topological region attached to normal metal (NM) leads, which poses a question about how precise is quantization of longitudinal conductance and how electrons transition from topologically trivial NM leads into the edge states. This particularly pressing issue for recently conjectured two-dimensional (2D) Floquet TI where electrons flow from time-independent NM leads into time-dependent edge states, the very recent experimental realization [J. W. McIver et al., Nat. Phys. 16, 38 (2020)] of Floquet TI using graphene irradiated by circularly polarized light did not exhibit either quantized longitudinal or Hall conductance. Here, we employ a charge-conserving solution for Floquet-nonequilibrium Green functions of irradiated graphene nanoribbon to compute longitudinal two-terminal conductance, as well as spatial profiles of local current density as electrons propagate from NM leads into the Floquet TI. For comparison, we also compute conductance of graphene-based realization of 2D quantum Hall, quantum anomalous Hall, and quantum spin Hall insulators. Although zero-temperature conductance within the gap of these three conventional time-independent 2D TIs of finite length exhibits small oscillations due to reflections at the NM-lead/2D-TI interface, it remains very close to perfectly quantized plateau at 2e2/h and completely insensitive to edge disorder. This is due to the fact that inside conventional TIs there is only edge local current density which circumvents any disorder. In contrast, in the case of Floquet TI both bulk and edge local current densities contribute equally to total current, which leads to longitudinal conductance below the expected quantized plateau that is further reduced by edge vacancies. We propose two experimental schemes to detect coexistence of bulk and edge current densities within Floquet TI: (i) drilling a nanopore in the interior of irradiated region of graphene will induce backscattering of bulk current density, thereby reducing longitudinal conductance by ∼28%; (ii) imaging of magnetic field produced by local current density using diamond nitrogen-vacancy centers.