Spin Relaxation in Quasi-1D GaAs Mesowires: Control via Electric Field and Aspect Ratio

Abstract

We report on the measurements of spin relaxation in GaAs quasi-onedimensional mesowires, relying on spin noise spectroscopy, thus adding to the existing body of spin relaxation studies in bulk, two-dimensional and zero dimensional systems. In addition to temperature and magnetic field dependence, we modify the spin relaxation time via applied electric field and aspect ratio of the mesowires, suggesting that scalable spintronics devices with controllable spin relaxation are achievable. Overall, we observed higher spin-relaxation time in mesowires compared to bulk with a spin noise exhibiting D’yakonov-Perel scattering and other scattering behavior. Spectral spin noise data are interpreted in part via Glazov-Sherman model [1], where both, diffusive and ballistic spin relaxation are accounted for. (*) corresponding author: aisakovic@colgate.edu; iregx137@gmail.com Introduction and Motivation The use of electron spins as qubits for quantum computing among other applications remains an area of active research, particularly in the field of spintronics – a field of physics that studies spin dynamics and spin-dependent phenomena via spin noise spectroscopy in information processing [2]. Spintronic devices exploit electronic currents that are spin polarized, having an excess of one spin states over the other. Approximately two decades ago, the field of semiconductor spintronics started being of major interest due to the advantages over charge only based devices such as the potential to surpass the limits of speed-up and power consumption [3]. Spinand light-polarization effects in bulk and nanostructured semiconductors, where photon and charge confinement occur, are therefore at the core of the implementation of innovative optoelectronic devices for spintronics. Relatively early on, the community has realized two scale-down obstacles: (a) the spin phenomena we study are not always by default quantum spin phenomena, and (b) spin noise is ubiquitous. With a few exceptions, the work on spin noise to date has focused on studying spin noise in materials, such as bulk with various doping conditions (3D) [4, 5], quantum wells (2D) [6-13], or quantum dots (quasi-0D) [14-16]. This is understandable, given that these materials are more accessible than (nano)devices, so this work reports on simple (2-contacts) device configuration, and on quasi-1D (mesowire) geometry, which has also rarely been studied compared to other dimensionalities. One of the main aims of spintronics is the optimization of performance through maximizing the spin-decoherence or spin relaxation time [17]. Spin-dephasing related to spin-orbit interaction is however the main mechanism limiting the electron spin lifetime in III-V semiconductors and the spin-transport in spintronics devices based on these semiconductors [18]. Spin-dephasing mechanisms in bulk semiconductors and their nanostructures have been studied for many years with various methods [19, 20], however there is not yet a definitive description of spin-dephasing mechanisms in spintronics devices. There is a particular need to understand the effect of sample geometry on spin noise and thus spin lifetime (i.e. bulk 3D vs quantum well 2D, vs meso or nanowire (quasi-)1D vs quantum dot 0D), as different geometries are relevant for different device configurations and therefore for different applications [19, 20]. Spin relaxation is closely related to spin noise – spin fluctuations – as noise gives information on spin dynamics under external perturbations [20] , and thus many studies on spin noise in various systems have been done under varying conditions such as temperature, electric bias, magnetic field, sample geometry, and doping [4, 5, 21, 22]. Spin noise measurements provide information about spin relaxation time (spin dephasing time), τs , its power spectrum and the electrons’ or holes’ Landé g factor. Spin noise measurements in semiconductors can be performed by several methods ranging from electron paramagnetic resonance (EPR) [23] and nuclear magnetic resonance (NMR) [24], magnetooptical measurements (time-resolved photoluminescence, Hanle effect, Kerr rotation microscopy, Faraday’s effect [22, 25] and magnetic force microscopy [26]. A particularly useful technique is spin noise spectroscopy (SNS), which consists of optical measurements of spin noise via Faraday rotation of a probe light, induced by the stochastic spin polarization of an electron/hole ensemble. One advantage of using SNS is that it dissipates (almost) no energy in the sample, thus leaving the spin dynamics undisturbed when taking spin measurements [27] (For example, a polarized laser probe with energy slightly off resonance relative to the energy bandgap of the material introduces spin–orbit coupling between carriers and the laser photons helicity via dipole selection rules. The carriers’ ensemble spins are mapped onto the transmitted light polarization via the Faraday’s effect. The method is known in atom optics and has been adopted to study spin noise for spintronics material and devices [14, 28]. Several factors contribute to the large variability of spin noise measurements even in the same material, including: doping concentration, magnetic field, temperature, probe laser wavelength and intensity, and sample volume, and material dimensionality. A key challenge to determine the stochastic electron spin fluctuations at thermal equilibrium is to maintain nominally “un-perturbative” measurement conditions, consisting in avoiding optical absorption of the laser probe, maintaining low intensities and large spot sizes. Typically, SNS methods in doping conditions below the metal to insulator transition, provide a lower bound in spin dephasing time values compared to other methods, where spin dephasing dependence on laser intensity and magnetic field are very relevant. Many of the previous studies of spin noise have been performed in III-V GaAs based semiconductors systems due to its controllable purity and easy availability [20, 29, 30], although other materials have also been investigated, including ZnO [31], Mn ions diluted in CdTe [32] and electron-doped monolayers of MoS2 [33], to name but few. One aim of spin noise measurements is to elucidate the dominant dephasing mechanisms in different conditions (temperature, material, geometry, etc.). The major identified spin dephasing mechanisms in semiconductors are summarized in Table 1. These mechanisms are present with different contributions across different dimensionality as well. Table I A brief review of main spin relaxation processes in semiconductors Spin Relaxation Type Physical Situation Relaxation Characteristics Elliott-Yafet (EY) • Momentum scattering • Phonons, impurities • Small band gap τs ∝ T −1/2 D’yakonov-Perel (DP) • Spin-orbit splitting of conduction band w/ lack of inversion symmetry • n-doping τs ∝ T − 3 2 τs ∝ T −3 Bir-Aronov-Pikus (BAP) • Spin flipping • Overlap e and h wavefunctions p-doping needed τs ∝ T −1 Hyperfine relaxation • Due to hyperfine interaction • Overlap e and (nucleus) N wavefunctions • Ubiquitous at low temperatures (70K max) τs ∝ T −n n – experiment dependent We will draw conclusions on spin noise data in 1D-like fabricated GaAs nanostructures by reviewing the current understanding of spin noise from bulk 3D to 2D and 0D dimensionality, in regard to the interpretation of the noise mechanism. Spin relaxation time of bulk GaAs (n-doped or undoped) has been intensively studied by various methods and ultimately by SNS to determine its temperature, doping and magnetic field dependence, resulting now in a relatively well understood picture of the main dephasing mechanisms, that occur depending on doping and temperature up to room temperature. The dephasing mechanisms observed in bulk materials are associated with observed spin relaxation time dependence on doping and temperature. In Fig. 1(a) we summarize several published measurements of the spin dephasing time, τs, in bulk GaAs for different doping concentrations and temperatures. The spin noise measurements were done using different methods as described in the references, with doping variations studied over 3 orders of magnitude. Based on doping dependence, three regimes could be identified insulator-like, metal-like and the metal to insulator region (intermediate). In the metal-like phase, electrons are delocalized so the D’yakonov-Perel (DP) [34] mechanisms are dominating, providing spin dephasing time below the ns, while in the insulator phase, spin dephasing is due hyperfine interaction, permitting to achieve above 100 ns dephasing time. For bulk GaAs, temperature effects on the spin relaxation time for all doping conditions are weak up to 10K, where the electrons ensemble can be considered localized. For temperature above 10K up to 80K, for low doping and mixed phase doping below the metal-insulator phase, τs ∝ T −1.48 (i.e. DP mechanism). In the metallic phase more pronounced temperature dependence was observed with τs ∝ T, mostly due to scattering at the ionized impurities (EY mechanism). Closer to room temperature for dopant concentration from 2-3x10 cm, τ s ∝ T −3 [5, 35], following pure DP dephasing mechanism [4, 36]. The DP mechanism can be suppressed by dimensionality reduction form 3D→2D. In 2D structures, DP dephasing arises from two main contributions: intrinsic bulk inversion asymmetry (BIA) and structure induced asymmetry (SIA). The second can be controlled by the application of an electric field in specific growth direction, thus permitting at a critical field to compensate for the BIA dephasing term and thus suppress the DP mechanism [6]. For example, QWs (quantum wells) in GaAs attracted attention for spintronics due to their potential engineering of their growth direction along unconventional crystallographic axes to suppress DP effects due to the special symmetries of the SOI in these structures. Recent SNS measurements on one hand confirmed the suppression of DP-related