Elliott-Yafet Spin Relaxation Research Articles

Strong spin-orbit fields and Dyakonov-Perel spin dephasing in supported metallic films

Spin dephasing by the Dyakonov-Perel mechanism in metallic films deposited on insulating substrates is revealed, and quantitatively examined by means of density functional calculations combined with a kinetic equation. The surface-to-substrate asymmetry, probed by the metal wave functions in thin films, is found to produce strong spin-orbit fields and a fast Larmor precession, giving a dominant contribution to spin decay over the Elliott-Yafet spin relaxation up to a thickness of 70 nm. The spin dephasing is oscillatory in time with a rapid (sub-picosecond) initial decay. However, parts of the Fermi surface act as spin traps, causing a persistent tail signal lasting 1000 times longer than the initial decay time. It is also found that the decay depends on the direction of the initial spin polarization, resulting in a spin-dephasing anisotropy of 200% in the examined cases.

Sizeable Kane–Mele-like spin orbit coupling in graphene decorated with iridium clusters

The spin-orbit coupling strength of graphene can be enhanced by depositing iridium nanoclusters. Weak localization is intensely suppressed near zero fields after the cluster deposition, rather than changing to weak anti-localization. Fitting the magnetoresistance gives the spin relaxation time, which increases by two orders with the application of a back gate. The spin relaxation time is found to be proportional to the electronic elastic scattering time, demonstrating the Elliot–Yafet spin relaxation mechanism. A sizeable Kane–Mele-like coupling strength of over 5.5 meV is determined by extrapolating the temperature dependence to zero.

Re-examination of the Elliott–Yafet spin-relaxation mechanism

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 spin–diagonal electrostatic 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 Yafet’s original calculation, which neglects the spin-mixing in the single-particle states for the determination of the ensemble spin. The important novel quantity in our calculation is a torque operator that determines the spin dynamics due to incoherent scattering. The contribution (1) to this torque vanishes exactly. From this general result, we derive a modified expression for the EY spin relaxation time for Kramers degenerate bands.

Spin splitting in 2D monochalcogenide semiconductors.

We report ab initio calculations of the spin splitting of the uppermost valence band (UVB) and the lowermost conduction band (LCB) in bulk and atomically thin GaS, GaSe, GaTe, and InSe. These layered monochalcogenides appear in four major polytypes depending on the stacking order, except for the monoclinic GaTe. Bulk and few-layer ε-and γ -type, and odd-number β-type GaS, GaSe, and InSe crystals are noncentrosymmetric. The spin splittings of the UVB and the LCB near the Γ-point in the Brillouin zone are finite, but still smaller than those in a zinc-blende semiconductor such as GaAs. On the other hand, the spin splitting is zero in centrosymmetric bulk and even-number few-layer β-type GaS, GaSe, and InSe, owing to the constraint of spatial inversion symmetry. By contrast, GaTe exhibits zero spin splitting because it is centrosymmetric down to a single layer. In these monochalcogenide semiconductors, the separation of the non-degenerate conduction and valence bands from adjacent bands results in the suppression of Elliot-Yafet spin relaxation mechanism. Therefore, the electron- and hole-spin relaxation times in these systems with zero or minimal spin splittings are expected to exceed those in GaAs when the D’yakonov-Perel’ spin relaxation mechanism is also suppressed.

(Invited) Spin-Based Silicon and CMOS-Compatible Devices

With CMOS feature size rapidly approaching ultimate scaling limits the electron spin attracts much attention as an alternative degree of freedom for low-power non-volatile applications [1]. Silicon, the main material of microelectronics, is perfectly suited for spin-driven applications, because it is mostly composed of nuclei without spin and is characterized by weak spin-orbit interaction [2]. Both factors favor a long electron spin lifetime in silicon. However, even a weak spin-orbit interaction causes the electron spin lifetime to decrease. The Elliot-Yafet spin relaxation due to phonons’ mediated scattering between the valleys along different crystallographic axes is the main spin relaxation mechanism in bulk silicon at room temperature [3,4]. This inter-valley scattering can be effectively eliminated by partially lifting the valley degeneracy either by stress or by confining an electron system. In strained silicon the spin lifetime can indeed be increased by a factor of two. In contrast, in silicon-on-insulator structures the spin lifetime is reduced; and methods to increase the spin lifetime are needed. Uniaxial stress dramatically reduces the spin relaxation and boosts the spin lifetime by an order of magnitude in thin silicon films [5]. The physical reason for the spin lifetime enhancement lies in the capability to lift completely the degeneracy between the two valleys in a confined electron systems by shear strain [6]. This degeneracy was a long-standing problem in silicon spintronics [7]; indeed, apart from causing a strong spin decoherence and relaxation, the degeneracy between the valleys introduces an unwanted competition between the quantum numbers of the valleys and electron spin, thus potentially threatening spin-based device operation. Therefore, lifting the valley degeneracy completely in a controllable way by means of standard stress techniques represents a major breakthrough in future silicon spin-driven applications. Despite impressive progress in spin injection in silicon at room temperature [2,8], the larger than predicted amplitude of the signal [2] is heavily debated prompting alternative explanations [9]. In addition, low efficiency of spin injection from ferromagnetic metal leads in silicon and the absence of a viable concept of electron spin manipulation in the channel by purely electrical means makes a practical realization of a device working on a principal similar to a MOSFET difficult. An experimental demonstration of the Datta-Das Spin FET [10] is pending for 25 years now. This motivates researchers to look into MOSFET and CMOS compatible spin-driven devices and applications. Commercially available CMOS compatible spin-transfer torque magnetic random access memory (MRAM) built on magnetic tunnel junctions (MTJs) possesses all properties characteristic to universal memory: fast operation, high density, and non-volatility. The reduction the critical current for magnetization switching is the main challenge. Perpendicular MTJs allow circumventing the problem at the expense of thermal stability [11]. The thermal stability is considerably increased in structures with a free layer composed of two vertically sandwiched layers [11]. An alternative path is to consider in-plane structures with composite free magnetic layers [12]. A substantial reduction of the critical current density is achieved, when the free layer is composed of two similar parts in the same plane next to each other [13]. The critical current reduction and/or switching is caused by the fact that the magnetization of the free layer remains in plane. MRAM can be used to build non-volatile logic-in-memory architectures with non-volatile storage elements on the top of logic circuits. Non-volatility and reduction of interconnects guarantee low-power consumption [14]. MRAM-CMOS hybrid ternary content-addressable memory and lock-up table circuits were demonstrated [14]. An alternative concept for non-volatile logic-in-memory circuits utilizes the same MRAM cells to store and process information simultaneously [15]. The work is supported by the European Research Council through the grant #247056 MOSILSPIN. 1. I.Zutic et al., Rev. Mod. Phys. 76 (2004) 323. 2. R.Jensen, Nature Materials 11 (2012) 400. 3. J.Ceng et al., Phys. Rev. Lett. 104 (2010) 016601. 4. P.Li and H.Dery, Phys. Rev. Lett. 107 (2011) 107203. 5. D.Osintsev et al., Solid-State Electron. 90 (2013) 34. 6. V.Sverdlov, Strain-induced effects in advanced MOSFETs, Springer 2011. 7. L.Zhang et al., Nature Commun. 4 (2013) 2396. 8. C.Li et al., Nature Commun. 2 (2011) 245. 9. Y.Song and H.Dery, Phys. Rev. Lett. 113 (2014) 047205. 10. S.Datta and B.Das, Appl. Phys. Lett. 56 (1990) 665. 11. S.Fukami et al., ASP-DAC 2014, p. 684. 12. A.Makarov et al., Phys. Stat. Solidi-RRL 5 (2011) 420. 13. A.Makarov et al., in: Future Trends in Microelectronics, J.Wiley&Sons, 2013, p.93. 14. T.Hanyu, ISCAS 2013, p.117. 15. H.Mahmoudi et al., in: Micro- and Nanoelectronics: Emerging Device Challenges and Solutions, CRC Press 2014, p.221.

Room-temperature spin thermoelectrics in metallic films

Considering metallic films at room temperature, we present the first theoretical study of the spin Nernst and thermal Edelstein effects which takes into account dynamical spin-orbit coupling, i.e., direct spin-orbit coupling with the vibrating lattice (phonons) and impurities. This gives rise to two novel processes, namely a dynamical Elliott-Yafet spin relaxation and a dynamical side-jump mechanism. Both are the high-temperature counterparts of the well-known $T = 0$ Elliott-Yafet and side-jump, central to the current understanding of the spin Hall, spin Nernst and Edelstein effects at low $T$. We consider the experimentally relevant regime $T > T_D$, with $T_D$ the Debye temperature, as the latter is lower than room temperature in transition metals such as Pt, Au and Ta typically employed in spin injection/extraction experiments. We show that the interplay between intrinsic (Bychkov-Rashba type) and extrinsic (dynamical) spin-orbit coupling yields a nonlinear $T$- dependence of the spin Nernst and spin Hall conductivities.

Electron spin relaxation due to D'yakonov-Perel' and Elliot-Yafet mechanisms in monolayerMoS2: Role of intravalley and intervalley processes

We investigate the in-plane spin relaxation of electrons due to the D'yakonov-Perel' and Elliot-Yafet mechanisms including the intra- and inter-valley processes in monolayer MoS$_2$. We construct the effective Hamiltonian for the conduction band using the L\"{o}wdin partition method from the anisotropic two-band Hamiltonian with the intrinsic spin-orbit coupling of the conduction band included. The spin-orbit coupling of the conduction band induces the intra- and inter-valley D'yakonov-Perel' spin relaxation. In addition, the Elliot-Yafet spin relaxation also takes place due to the interband spin mixing. We find that the D'yakonov-Perel' mechanism dominates the in-plane spin relaxation. In the framework of this mechanism, the intravalley process is shown to play a more important role at low temperature whereas the intervalley one becomes more important at high temperature. At the temperature in between, the leading process of the in-plane spin relaxation changes from the intervalley to intravalley one as the electron density increases. Moreover, we find that the intravalley process is dominated by the electron-electron Coulomb scattering even with high impurity density since the dominant term in the spin-orbit coupling is isotropic, which does not lead to the spin relaxation together with the electron-impurity scattering. This is very different from the previous studies in semiconductors and graphene.

Electrical Spin Injection and Detection in Mn5Ge3/Ge/Mn5Ge3 Nanowire Transistors

In this Letter, we report the electrical spin injection and detection in Ge nanowire transistors with single-crystalline ferromagnetic Mn5Ge3 as source/drain contacts formed by thermal reactions. Degenerate indium dopants were successfully incorporated into as-grown Ge nanowires as p-type doping to alleviate the conductivity mismatch between Ge and Mn5Ge3. The magnetoresistance (MR) of the Mn5Ge3/Ge/Mn5Ge3 nanowire transistor was found to be largely affected by the applied bias. Specifically, negative and hysteretic MR curves were observed under a large current bias in the temperature range from T = 2 K up to T = 50 K, which clearly indicated the electrical spin injection from ferromagnetic Mn5Ge3 contacts into Ge nanowires. In addition to the bias effect, the MR amplitude was found to exponentially decay with the Ge nanowire channel length; this fact was explained by the dominated Elliot-Yafet spin-relaxation mechanism. The fitting of MR further revealed a spin diffusion length of lsf = 480 ± 13 nm and a spin lifetime exceeding 244 ps at T = 10 K in p-type Ge nanowires, and they showed a weak temperature dependence between 2 and 50 K. Ge nanowires showed a significant enhancement in the measured spin diffusion length and spin lifetime compared with those reported for bulk p-type Ge. Our study of the spin transport in the Mn5Ge3/Ge/Mn5Ge3 nanowire transistor points to a possible realization of spin-based transistors; it may also open up new opportunities to create novel Ge nanowire-based spintronic devices. Furthermore, the simple fabrication process promises a compatible integration into standard Si technology in the future.

Temperature dependence of spin lifetime of conduction electrons in bulk germanium

Optically generated spin polarized electrons in bulk n-type Ge samples have been detected by using a radio-frequency modulation technique. Using the Hanle effect in an external magnetic field, the spin lifetime was measured as a function of temperature in the range 90 K to 180 K. The lifetime decreases with increasing temperature from ∼5 ns at 100 K to ∼2 ns at 180 K. We show that the temperature dependence is consistent with the Elliott-Yafet spin relaxation mechanism [R. J. Elliot, Phys. Rev. 96, 266 (1954)].

Comparison of spin lifetimes in n-Ge characterized between three-terminal and four-terminal nonlocal Hanle measurements

We compared the temperature dependence of spin lifetime in n-Ge characterized from three-terminal (3T) and four-terminal (4T) Hanle measurements using single-crystalline Fe/MgO/n-Ge tunnel junctions. The bias conditions of the two schemes were chosen to be about the same in order to compare the spin lifetimes (τ3T and τ4T). The temperature dependences of τ3T and τ4T behave in a very similar way at the low temperature region (T ≤ 10 K), and both τ3T and τ4T decrease as the temperature increases, which is consistent with the dominating Elliot–Yafet spin relaxation mechanism in bulk Ge. However, when the temperature is higher than 10 K, τ4T is longer than τ3T, which may be explained by the fact that 3T Hanle measurements are more easily affected by additional scattering effects caused by the accompanied charge current and electric field in the 3T geometry.

Testing the Elliott-Yafet spin-relaxation mechanism in KC8: A model system of biased graphene

Temperature dependent electron spin resonance (ESR) measurements are reported on stage 1 potassium doped graphite, a model system of biased graphene. The ESR linewidth is nearly isotropic and although the g-factor has a sizeable anisotropy, its majority is shown to arise due to macroscopic magnetization. Albeit the homogeneous ESR linewidth shows an unusual, non-linear temperature dependence, it appears to be proportional to the resistivity which is a quadratic function of the temperature. These observations suggests the validity of the Elliott-Yafet relaxation mechanism in KC8 and allows to place KC8 on the empirical Beuneu-Monod plot among ordinary elemental metals.

ChemInform Abstract: Spin Transport and Relaxation in Graphene

AbstractReview: 120 refs.

Electrical spin injection and transport in germanium

We report the first experimental demonstration of electrical spin injection, transport, and detection in bulk germanium (Ge). The nonlocal magnetoresistance (MR) in n-type Ge is observable up to 225 K. Our results indicate that the spin relaxation rate in the n-type Ge is closely related to the momentum scattering rate, which is consistent with the predicted Elliot-Yafet spin relaxation mechanism for Ge. The bias dependence of the nonlocal MR and the spin lifetime in n-type Ge is also investigated.

Surface Spin Flip Probability of Mesoscopic Ag Wires

Spin relaxation in mesoscopic Ag wires in the diffusive transport regime is studied via nonlocal spin valve and Hanle effect measurements performed on Permalloy/Ag lateral spin valves. The ratio between momentum and spin relaxation times is not constant at low temperatures. This can be explained with the Elliott-Yafet spin relaxation mechanism by considering the momentum surface relaxation time as being temperature dependent. We present a model to separately determine spin flip probabilities for phonon, impurity and surface scattering and find that the spin flip probability is highest for surface scattering.

Interplay of intrinsic and extrinsic mechanisms to the spin Hall effect in a two-dimensional electron gas

In order to describe correctly the interplay of extrinsic and intrinsic spin–orbit mechanisms to the spin Hall effect, it is necessary to consider different sources of spin relaxation. We take into account the spin relaxation time τ DP due to the Dyakonov–Perel mechanism as well as the Elliott–Yafet spin-relaxation time τ s due to the spin–orbit scattering from impurities. The total spin Hall conductivity depends crucially on the ratio τ s / τ DP .

New mechanism of the spin-galvanic effect

A mechanism of the spin-galvanic effect associated with spin-dependent scattering is proposed. The electrical current in a system of spin-polarized two-dimensional carriers is induced due to interference of spin-preserving scattering processes and spin relaxation processes. The spin-galvanic effect is studied for heterostructures with the Elliott-Yafet and Dyakonov-Perel spin relaxation mechanisms. The proposed contribution to the spin-galvanic current may be dominant in A3B5 asymmetric quantum wells.

2D ANOMALOUS MAGNETORESISTANCE IN THE PRESENCE OF SPIN–ORBIT SCATTERING

The model of weak localization in 2D semiconductor structures in the whole range of classically weak magnetic fields in the presence of the Elliot–Yafet spin relaxation has been developed. It was shown that the spin–orbit interaction influences the value of magnetoresistance in small magnetic fields (within diffusion approximation) and when diffusion approximation is no longer valid.

Spin relaxation inn-doped GaAs due to impurity and electron-electron Elliot-Yafet scattering

We calculate the spin relaxation time of conduction electrons in n-doped bulk gallium arsenide. We consider the Elliot-Yafet spin-relaxation mechanism, driven by Coulombic-impurity and electron-electron scattering. We find that these two scattering mechanisms result in relaxation times of equal order of magnitude, but with disimilar dependences on doping density and temperature. Our theoretical results are compared with experimentally measured spin relaxation times in gallium arsenide.

Light-induced magnetization in Hg1−xCdxTe

We report the first observation of light-induced magnetization in a diamagnetic II–VI semiconductor. By improving the sensitivity of the pick-up coil arrangement, while still using standard RF-SQUID techniques, the photomagnetization (PM) of excited spin-polarized conduction electrons was detected with a signal-to-noise ratio of 3 using circularly polarized CO laser radiation (500 mW/cm 2). The samples were epitaxially grown p-type Hg 1− x Cd x Te layers on (100) CdTe with compositions f x = 0.25 to x = 0.29. The onset of PM occurs at the energy gaps, and the light-induced magnetic flux per illuminated sample area was 15–20 pT at maximum. PM is linear with laser intensity and vanishes for linear polarization of light. The spin-relaxation time which determines the maximum PM was deduced from the half-width of the depolarization curve applying a transverse magnetic field (Hanle effect). If the corresponding g ∗-factor ( g ∗ = -43 , for x = 0.28) was taken from band structure calculations, the relaxation of PM is obviously determined by Auger lifetime recombination processes for carrier energies smaller than the LO-phonon energy, and by Elliott-Yafet spin relaxation for energies above this threshold. The measurements were performed at a fixed temperature T = 2 K.