Full First-Principles Theory of Spin Relaxation in Group-IV Materials

Abstract

We present a generally applicable parameter-free first-principles method to determine electronic spin relaxation times and apply it to the technologically important group-IV materials silicon, diamond and graphite. We concentrate on the Elliott-Yafet mechanism, where spin relaxation is induced by momentum scattering off phonons and impurities. In silicon, we find a ∼ T −3 temperature dependence of the phonon-limited spin relaxation time T1 and a value of 4.3 ns at room temperature, in agreement with experiments. For the phonon-dominated regime in diamond and graphite, we predict a stronger ∼ T −5 and ∼ T −4.5 dependence that limits T1 (300 K) to 180 and 5.8 ns, respectively. A key aspect of this study is that the parameter-free nature of our approach provides a method to study the effect of any type of impurity or defect on spin-transport. Furthermore we find that the spin-mix amplitude in silicon does not follow the E −2 g band gap dependence usually assigned to III-V semiconductors but follows a much weaker and opposite E 0.67 g dependence. This dependence should be taken into account when constructing silicon spin transport models.The physical roadblocks looming in the charge-based semiconductor device technology require paradigmshifting approaches to create new logic devices capable of lower power consumption and higher performance. This has motivated a search for new alternative logic variables, among which the spin of electrons is a natural candidate, which needs to be efficiently and reliably injected, transported, and detected. Although extensive studies have been done in direct-gap materials, the understanding of spin-transport and spin-life time dependence in the technologically relevant group-IV materials is surprisingly incomplete. Silicon and the carbon polytypes diamond and graphite are particularly relevant because long spin relaxation times can be expected in materials with inversion symmetry and low atomic number Z. For those, the main spin-relaxation mechanism at high temperatures is the Elliott-Yafet (EY) mechanism mediated through spin-orbit coupling [1,2], which scales as Z 2 .Silicon, an attractive potential spintronics material due to its compatibility with current technologies, has a relatively large spin orbit-coupling (44 meV) [3]. Nevertheless, Lepine's electron spin resonance (ESR) measurements [4,5], recently confirmed for low temperatures by Appelbaum et al. [6,7], found for its spin relaxation time T 1 a value of 7 ns at room temperature, which puts it well within the usable range. The experimental situation is less clear for carbon, whose lower Z-number promises longer spin relaxation times. Diamond with a spin-orbit coupling of 13 meV [8] is especially expected to have a long electronic spin relaxation time, which however has never been measured. For graphite, the most recent experimental data from 1961 [9, 10] suggest a large range for T 1 between 1-300 ns. For both diamond and graphite, no reliable theoretical predictions have been reported. Finally, the E −2 g dependence of th...

Spin and energy relaxation in germanium studied by spin-polarized direct-gap photoluminescence

“…Spin relaxation times of holes have been shown to be below 1 ps, 17 whereas electron spin relaxation times are in the ns range below 200 K. 13,22,23 Yet very little is known about spin flip scattering by dopants and the role played by impurities in determining spin dynamics in different temperature regimes. 24,25 Inspired by the quasi direct-gap behavior of Ge and by the possibility to optically initialize spins, we report in this work a spin-polarized photoluminescence (PL) study focused on the recombination across the direct-gap of bulk Ge over a wide doping and temperature range. We directly measured the polarization state of the direct-gap emission by means of Stokes analysis, 26 shedding light on the optical orientation process and on the interplay between energy and spin relaxation channels.…”

Monte Carlo simulation of spin relaxation of conduction electrons in silicon

“…Different theoretical approaches have addressed the calculation of both the spin mixing probabilities and the matrix element expressions for all the phonon-induced spin-flip transitions in the conduction band. Among these, for example, the pseudopotential model reproducing spin-orbit splittings of the relevant electronic states [9,10], the group theory, the k•p perturbation method, the rigid-ion model [11], the parameter-free first-principles method and the density functional perturbation theory [12], the adiabatic band charge models, and the tight-binding models [13]. Starting from the detailed knowledge of a specific electron distribution, they calculate the relaxation rate τ i for each different scattering mechanism.…”

“…Despite these promising experimental results, theoretical research is still incomplete and a comprehensive investigation of the influence of transport conditions on the spin depolarization process in silicon structures, in a wide range of values of temperature and amplitude of external fields, is still missing. In particular, the theoretical description of spin properties of conduction electrons in silicon bulk requires very elaborate numerical and analytical methods, the results of which are sometimes not in full agreement [9][10][11][12][13][14].…”

Towards a Room-Temperature Spin Quantum Bus in Diamond via Electron Photoionization, Transport, and Capture

“…An attractive alternative is the coherent electrical transport of a spin from one spin register to the other. Diamond presents as an ideal spin transport material: its large electronic band gap, inversion symmetry, small spin-orbit interaction, and low nuclear spin density promise long spin-relaxation times [33]. Indeed, ab initio calculations predict a transport T 1 ∼ 180 ns at room temperature (10 times longer than in silicon) [33], which corresponds to an exceptional transport distance of ∼2 mm in high-purity diamond [34] with a modest electric field of ∼100 V=cm.…”

“…Diamond presents as an ideal spin transport material: its large electronic band gap, inversion symmetry, small spin-orbit interaction, and low nuclear spin density promise long spin-relaxation times [33]. Indeed, ab initio calculations predict a transport T 1 ∼ 180 ns at room temperature (10 times longer than in silicon) [33], which corresponds to an exceptional transport distance of ∼2 mm in high-purity diamond [34] with a modest electric field of ∼100 V=cm. Since only paramagnetic impurities (whose densities can be controlled) and magnetic field inhomogeniety offer additional dephasing mechanisms, transport is also expected to be coherent, with ultimately T 2 ∼ T 1 at room temperature [2,36].…”