We analyze spin-dependent carrier dynamics due to incoherent electron-phonon scattering, which is commonly referred to as Elliott-Yafet (EY) spin-relaxation mechanism. For this mechanism one usually distinguishes two contributions: (1) from the elect
rostatic interaction together with spin-mixing in the wave functions, which is often called the Elliott contribution, and (2) the phonon-modulated spin-orbit interaction, which is often called the Yafet or Overhauser contribution. By computing the reduced electronic density matrix, we improve Yafets original calculation, which is not valid for pronounced spin mixing as it equates the pseudo-spin polarization with the spin polarization. The important novel quantity in our calculation is a torque operator that determines the spin dynamics. The contribution (1) to this torque vanishes exactly. From this general result, we derive a modified expression for the Elliott-Yafet spin relaxation time.
We study the heat-induced magnetization dynamics in a toy model of a ferrimagnetic alloy, which includes localized spins antiferromagnetically coupled to an itinerant carrier system with a Stoner gap. We determine the one-particle spin-density matrix
including exchange scattering between localized and itinerant bands as well as scattering with phonons. While a transient ferromagnetic-like state can always be achieved by a sufficiently strong excitation, this transient ferromagnetic-like state only leads to magnetization switching for model parameters that also yield a compensation point in the equilibrium M(T) curve.
We present a microscopic calculation of magnetization damping for a magnetic toy model. The magnetic system consists of itinerant carriers coupled antiferromagnetically to a dispersionless band of localized spins, and the magnetization damping is due
to coupling of the itinerant carriers to a phonon bath in the presence of spin-orbit coupling. Using a mean-field approximation for the kinetic exchange model and assuming the spin-orbit coupling to be of the Rashba form, we derive Boltzmann scattering integrals for the distributions and spin coherences in the case of an antiferromagnetic exchange splitting, including a careful analysis of the connection between lifetime broadening and the magnetic gap. For the Elliott-Yafet type itinerant spin dynamics we extract dephasing and magnetization times T_1 and T_2 from initial conditions corresponding to a tilt of the magnetization vector, and draw a comparison to phenomenological equations such as the Landau-Lifshitz or the Gilbert damping. We also analyze magnetization precession and damping for this system including an anisotropy field and find a carrier mediated dephasing of the localized spin via the mean-field coupling.
The slowdown of optical pulses due to quantum-coherence effects is investigated theoretically for an active material consisting of InGaAs-based double quantum-dot molecules. These are designed to exhibit a long lived coherence between two electronic
levels, which is an essential part of a quantum coherence scheme that makes use of electromagnetically-induced transparency effects to achieve group velocity slowdown. We apply a many-particle approach based on realistic semiconductor parameters that allows us to calculate the quantum-dot material dynamics including microscopic carrier scattering and polarisation dephasing dynamics. The group-velocity reduction is characterized in the frequency domain by a quasi-equilibrium slow-down factor and in the time domain by the probe-pulse slowdown obtained from a calculation of the spatio-temporal material dynamics coupled to the propagating optical field. The group-velocity slowdown in the quantum-dot molecule is shown to be substantially higher than what is achievable from similar transitions in typical InGaAs-based single quantum dots. The dependences of slowdown and shape of the propagating probe pulses on lattice temperature and drive intensities are investigated.
For the 3d ferromagnets iron, cobalt and nickel we compute the spin-dependent inelastic electronic lifetimes due to carrier-carrier Coulomb interaction including spin-orbit coupling. We find that the spin-dependent density-of-states at the Fermi ener
gy does not, in general, determine the spin dependence of the lifetimes because of the effective spin-flip transitions allowed by the spin mixing. The majority and minority electron lifetimes computed including spin-orbit coupling for these three 3-d ferromagnets do not differ by more than a factor of 2, and agree with experimental results.
We present an ab initio calculation of the k and spin-resolved electronic lifetimes in the half-metallic Heusler compounds Co(2)MnSi and Co(2)FeSi. We determine the spin-flip and spin-conserving contributions to the lifetimes and study in detail the
behavior of the lifetimes around states that are strongly spin-mixed by spin-orbit coupling. We find that, for non-degenerate bands, the spin mixing alone does not determine the energy dependence of the (spin-flip) lifetimes. Qualitatively, the lifetimes reflect the lineup of electron and hole bands. We predict that different excitation conditions lead to drastically different spin-flip dynamics of excited electrons and may even give rise to an enhancement of the non-equilibrium spin polarization.
Interconnected networks have been shown to be much more vulnerable to random and targeted failures than isolated ones, raising several interesting questions regarding the identification and mitigation of their risk. The paradigm to address these ques
tions is the percolation model, where the resilience of the system is quantified by the dependence of the size of the largest cluster on the number of failures. Numerically, the major challenge is the identification of this cluster and the calculation of its size. Here, we propose an efficient algorithm to tackle this problem. We show that the algorithm scales as O(N log N), where N is the number of nodes in the network, a significant improvement compared to O(N^2) for a greedy algorithm, what permits studying much larger networks. Our new strategy can be applied to any network topology and distribution of interdependencies, as well as any sequence of failures.
112 -
Christian M. Schneider
, Tobias A. Kesselring
, Jose S. Andrade Jr. andn Hans J. Herrmann
2012
The self-similarity of complex networks is typically investigated through computational algorithms the primary task of which is to cover the structure with a minimal number of boxes. Here we introduce a box-covering algorithm that not only outperform
s previous ones, but also finds optimal solutions. For the two benchmark cases tested, namely, the E. Coli and the WWW networks, our results show that the improvement can be rather substantial, reaching up to 15% in the case of the WWW network.
Spin and charge-current dynamics after ultrafast spin-polarized excitation in a normal metal are studied theoretically using a wave-diffusion theory. It is shown analytically how this macroscopic approach correctly describes the ballistic and diffusi
ve properties of spin and charge transport, but also applies to the intermediate regime between these two limits. Using the wave-diffusion equations we numerically analyze spin and charge dynamics after ultrafast excitation of spin polarized carriers in thin gold films. Assuming slightly spin-dependent momentum relaxation times, we find that a unified treatment of diffusive and ballistic transport yields robust signatures in the spin and charge dynamics, which are in qualitative agreement with recent experimental results [Phys. Rev. Lett 107, 076601 (2011)]. The influence of boundary effects on the temporal signatures of spin transport is also studied.
This paper presents a study of electron spin dynamics in bulk GaAs at low temperatures for elevated optical excitation conditions. Our time-resolved Faraday rotation measurements yield sub-nanosecond electron spin dephasing-times over a wide range of
n-doping concentrations in quantitative agreement with a microscopic treatment of electron spin dynamics. The calculation shows the occurrence and breakdown of motional narrowing for spin dephasing under elevated excitation conditions. We also find a peak of the spin dephasing time around a doping density for which, under lower excitation conditions, a metal-insulator transition occurs. However, the experimental results for high excitation can be explained without a metal-insulator transition. We therefore attribute the peak in spin-dephasing times to the influence of screening and scattering on the spin-dynamics of the excited electrons.
