Quantum-classical approach to nonequilibrium system of conduction electrons interacting with localized spins in spintronics
| Author(s) | Bajpai, Utkarsh | |
| Date Accessioned | 2022-01-25T15:59:22Z | |
| Date Available | 2022-01-25T15:59:22Z | |
| Publication Date | 2021 | |
| SWORD Update | 2021-09-30T19:14:09Z | |
| Abstract | Spintronics 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. | en_US |
| Advisor | Nikolić, Branislav K. | |
| Degree | Ph.D. | |
| Department | University of Delaware, Department of Physics and Astronomy | |
| DOI | https://doi.org/10.58088/44a3-ky33 | |
| Unique Identifier | 1293448323 | |
| URL | https://udspace.udel.edu/handle/19716/30101 | |
| Language | en | |
| Publisher | University of Delaware | en_US |
| URI | https://login.udel.idm.oclc.org/login?url=https://www.proquest.com/dissertations-theses/quantum-classical-approach-nonequilibrium-system/docview/2587759651/se-2?accountid=10457 | |
| Keywords | Current-independent spin torque | |
| Keywords | Holstein-Primakoff transformation | |
| Keywords | Nonequilibrium dynamics | |
| Keywords | Local magnetic moment | |
| Keywords | Localized spins | |
| Keywords | Quantum mechanics | |
| Title | Quantum-classical approach to nonequilibrium system of conduction electrons interacting with localized spins in spintronics | en_US |
| Type | Thesis | en_US |