Elliott-Yafet Spin Relaxation Research Articles

Evidence of Ferromagnetism and Ultrafast Dynamics of Demagnetization in an Epitaxial FeCl2 Monolayer.

The development of two-dimensional (2D) magnetism is driven not only by the interest of low-dimensional physics but also by potential applications in high-density miniaturized spintronic devices. However, 2D materials possessing a ferromagnetic order with a relatively high Curie temperature (Tc) are rare. In this paper, the evidence of ferromagnetism in monolayer FeCl2 on Au(111) surfaces, as well as the interlayer antiferromagnetic coupling of bilayer FeCl2, is characterized by using spin-polarized scanning tunneling microscopy. A Curie temperature (Tc) of ∼147 K is revealed for monolayer FeCl2, based on our static magneto-optical Kerr effect measurements. Furthermore, temperature-dependent magnetization dynamics is investigated by the time-resolved magneto-optical Kerr effect. A transition from one- to two-step demagnetization occurs as the lattice temperature approaches Tc, which supports the Elliott-Yafet spin relaxation mechanism. The findings contribute to a deeper understanding of the underlying mechanisms governing ultrafast magnetization in 2D ferromagnetic materials.

Transient and steady state magneto-optical studies of the CsPbBr3 crystal

We have studied the magneto-optical properties of photoexcitations in $\mathrm{CsPb}{\mathrm{Br}}_{3}$ single crystal using the technique of picosecond time-resolved quantum beatings (QBs) in the circularly polarized photoinduced reflection as well as steady state magnetocircular dichroism (MCD) in $\mathrm{CsPb}{\mathrm{Br}}_{3}$ film. In the Voigt geometry at magnetic field strength $B$ > 0, we observed fast and slow QB oscillations that we attribute to the Larmor precession frequency of electrons and holes, respectively. From the linear frequency dependence on $B$, we extract the carrier anisotropic Land\'e $g$ factors for applied B along [010] and [001]; for electrons $|{g}_{[001]}^{\mathrm{e}}|=1.95\ifmmode\pm\else\textpm\fi{}0.04$ and $|{g}_{[010]}^{\mathrm{e}}|=1.82\ifmmode\pm\else\textpm\fi{}0.04$, whereas for holes $|{g}_{[001]}^{\mathrm{h}}|=0.69\ifmmode\pm\else\textpm\fi{}0.02$ and $|{g}_{[010]}^{\mathrm{h}}|=0.76\ifmmode\pm\else\textpm\fi{}0.02$. These values are in excellent agreement with a k\ifmmode\cdot\else\textperiodcentered\fi{}p model calculation applied to $\mathrm{CsPb}{\mathrm{Br}}_{3}$. Surprisingly, at $B=0$, we still observed QB oscillation of \ensuremath{\sim}500 MHz that we interpret as due to the Overhauser field that originates from the spin-aligned nuclei caused by the Knight field. From the measured MCD spectrum vs $B$, we obtained the $g$ factor of the bright excitons ${g}_{\mathrm{ex}}=2.18\ifmmode\pm\else\textpm\fi{}0.08$ showing that the $g$ value of holes in $\mathrm{CsPb}{\mathrm{Br}}_{3}$ is positive. We also measured the temperature and magnetic field dependencies of the electron and hole spin dephasing times which support the Elliot-Yafet spin-relaxation mechanism.

Finite-Size Effect in Phonon-Induced Elliott-Yafet Spin Relaxation in Al.

The Elliott-Yafet theory of spin relaxation in nonmagnetic metals predicts proportionality between spin and momentum relaxation times for scattering centers such as phonons. Here, we test this theory in Al nanowires over a very large thickness range (8.5-300nm), finding that the Elliott-Yafet proportionality "constant" for phonon scattering in fact exhibits a large, unanticipated finite-size effect. Supported by analytical and numerical modeling, we explain this via strong phonon-induced spin relaxation at surfaces and interfaces, driven in particular by enhanced spin-orbit coupling.

D’yakonov–Perel and Elliot–Yafet spin relaxation rates in InGaAs/InAlAs multiple quantum wells at room temperature

Room-temperature spin relaxation rates resulting from the D’yakonov–Perel (DP) and Elliot–Yafet (EY) mechanisms were determined by combining microscopic and macroscopic Kerr rotation measurements in narrow-gap (001) InGaAs/InAlAs quantum wells (QWs). Two samples with different DP relaxation rate were compared and we found that EY relaxation rate () was approximately double the value of the average DP relaxation rate even in the asymmetric QWs with large spin–orbit parameters. We also found that the anisotropy of spin relaxation time owing to the DP mechanism is weakened significantly in the system in which the EY mechanism dominates the spin relaxation.

Selective enhancement of Kane Mele-type spin-orbit interaction in graphene

In order to enhance the spin orbit interaction (SOI) in graphene for seeking the dissipationless quantum spin Hall devices, unique Kane-Mele-type SOI and high mobility samples are desired. However, the common external modification of graphene often introduces “extrinsic” Rashba-type SOI, which will destroy the possible topological state, bring a certain degree of impurity scattering and reduce the sample mobility. Here we show that by the EDTA-Dy molecule dressing, the carrier mobility is even improved, and the quantum Hall plateaus are observed more clearly. The Kane-Mele type SOI is mimicked after dressing, which is evidenced by the suppressed weak localization at equal carrier densities and simultaneous Elliot-Yafet spin relaxation. This is attributed to the spin-flexural phonon coupling induced by the enhanced graphene ripples, as revealed by the in-plane magnetotransport measurement.

Absence of spin Hall magnetoresistance in Pt/(CoNi)n multilayers

We systematically studied the magnetoresistance effect in a Pt/(CoNi)n multilayer system with perpendicular magnetic anisotropy and the fcc (111) texture. The angular dependence of magnetoresistance, including high-order cosine terms, was observed in a plane perpendicular to the electrical current; this was attributed to the geometrical-size effects caused by crystal symmetry, the ordered arrangement of grains, and the anisotropic interface magnetoresistance effect caused by the breaking of the symmetry at interfaces. Based on the accuracy of our experimental results, the magnitude of spin Hall magnetoresistance (SMR) in Pt/(CoNi)n was expected to be below $1\times10^{-4}$. However, on evaluating the spin Hall angle of $\geq$ 0.07 for Pt using spin-torque ferromagnetic resonance measurements, the theoretical magnitude of SMR in our samples was estimated to exceed $7\times10^{-4}$. This absence of SMR in the experimental results can be explained by the Elliott-Yafet spin relaxation of itinerant electrons in the ferromagnetic metal, which indicates that the boundary conditions of the spin current in the heavy metal/ferromagnetic insulator may not be applicable to all-metallic heterostructures.

Energy-Efficient Multiferroic Spin-Devices and Spin-Circuits

Spin-devices are switched by flipping spins without moving charge in space and this can lead to ultra-low-energy switching replacing traditional transistors in beyond Moore’s law era. In particular, the electric field-induced magnetization switching has emerged to be an energy-efficient paradigm. Here, we review the recent developments on ultra-low-energy, area-efficient, and fast spin-devices using multiferroic magnetoelectric composites. It is shown that both digital logic gates and analog computing with transistor-like high-gain region in the input-output characteristics of multiferroic composites are feasible. We also review the equivalent spin-circuit representation of spin-devices by considering spin potential and spin current similar to the charge-based counterparts using Kirchhoff’s voltage/current laws, which is necessary for the development of large-scale circuits. We review the spin-circuit representation of spin pumping, which happens anyway when there is a material adjacent to a rotating magnetization and therefore it is particularly necessary to be incorporated in device modeling. Such representation is also useful for understanding and proposing experiments. In spin-circuit representation, spin diffusion length is an important parameter and it is shown that a thickness-dependent spin diffusion length reflecting Elliott–Yafet spin relaxation mechanism in platinum is necessary to match the experimental results.

Tunable and enhanced Rashba spin-orbit coupling in iridate-manganite heterostructures

Tailoring spin-orbit interactions and Coulomb repulsion are the key features to observe exotic physical phenomena such as magnetic anisotropy and topological spin texture at oxide interfaces. Our study proposes a novel platform for engineering the magnetism and spin-orbit coupling at LaMnO3/SrIrO3 (3d-5d oxide) interfaces by tuning the LaMnO3 growth conditions which controls the lattice displacement and spin-correlated interfacial coupling through charge transfer. We report on a tunable and enhanced interface-induced Rashba spin-orbit coupling and Elliot-Yafet spin relaxation mechanism in LaMnO3/SrIrO3 bilayer with change in the underlying magnetic order of LaMnO3. We also observed enhanced spin-orbit coupling strength in LaMnO3/SrIrO3 compared to previously reported SrIrO3 layers. The X-Ray spectroscopy measurement reveals the quantitative valence of Mn and their impact on charge transfer. Further, we performed angle-dependent magnetoresistance measurements, which show signatures of magnetic proximity effect in SrIrO3 while reflecting the magnetic order of LaMnO3. Our work thus demonstrates a new route to engineer the interface induced Rashba spin-orbit coupling and magnetic proximity effect in 3d-5d oxide interfaces which makes SrIrO3 an ideal candidate for spintronics applications.

Determining complex spin mixing conductance and spin diffusion length from spin pumping experiments in magnetic insulator/heavy metal bilayers

Magnetic insulators are promising materials for the development of energy-efficient spintronics. Unlike metallic counterparts, the magnetic insulators are characterized by the imaginary part of the interfacial spin mixing conductance as well in a bilayer with heavy metals, and it is responsible for the field-like toque in spin–orbit torque devices. Here, we study the underlying theoretical constructs and develop a general strategy to determine the complex spin mixing conductance from the experimental results of ferromagnetic resonance and spin pumping. The results show that the imaginary part of the spin mixing conductance can be one order more than the real part and it matches the critical trend of spin mixing conductance with thickness of the heavy metal. The interpretation of experimental results also indicates that at small thicknesses, the interface contribution becomes significant and a bulk diffusion model cannot explain the results. A thickness-dependent spin diffusion length is necessary too that is tantamount to the Elliott–Yafet spin relaxation mechanism in the heavy metals. Also, we effectively explain the experimental results while inserting a copper layer with varying thicknesses in between the magnetic insulator and the heavy metal using spin-circuit formalism.

Magnetic impurities as the origin of the variability in spin relaxation rates in Cu-based spin transport devices

The Elliott-Yafet spin relaxation mechanism posits linear proportionality between spin and momentum lifetimes in low spin-orbit coupling nonmagnetic metals, and is widely accepted in spintronics. Accurate experimental determination of the Elliott-Yafet proportionality constants (${\ensuremath{\beta}}_{i}$) between the spin and momentum relaxation times for individual scattering sources is challenging, however. This is apparent from the literature on nonlocal spin transport in Cu, for example, where reported phonon (${\ensuremath{\beta}}_{\mathrm{ph}}$) and defect (${\ensuremath{\beta}}_{\mathrm{def}\phantom{\rule{4pt}{0ex}}}$) Elliott-Yafet constants vary by an order of magnitude. In recent work we discovered that even part-per-million-level magnetic impurity concentrations can substantially influence spin relaxation in Cu, via a spin transport analog of the Kondo effect. To clarify whether this could explain the reported variability in ${\ensuremath{\beta}}_{i}$, here we report on a comprehensive study of spin transport in Cu-based lateral nonlocal spin valves, varying the ferromagnetic contact material, interface structure, Cu thickness, and post-fabrication annealing conditions, resulting in widely varied microstructures and magnetic impurity concentrations. Quantifying the effects of magnetic impurities on charge and spin transport we demonstrate the dramatic, even dominant, effect these can have on spin relaxation rates, and thus extracted ${\ensuremath{\beta}}_{i}$. Minimization of magnetic impurity effects is achieved via Al interlayer insertion or moderate annealing, restoring the expected temperature dependence for phonon-mediated spin relaxation, and enabling more reliable determination of ${\ensuremath{\beta}}_{i}$ for phonons (740 \ifmmode\pm\else\textpm\fi{} 200), and nonmagnetic defects (240 \ifmmode\pm\else\textpm\fi{} 50). The latter contribution is shown to be dominated by grain boundaries in these polycrystalline Cu films. Cross-sectional transmission electron microscopy measurement of grain sizes in actual nonlocal spin valve devices then establishes a useful empirical relationship between average grain size and spin diffusion length. These measurements highlight the importance of magnetic impurities in metallic spin transport, explain the wide variability in reported ${\ensuremath{\beta}}_{\mathrm{ph}}$ and ${\ensuremath{\beta}}_{\mathrm{def}}$ in Cu, and elucidate the relationship between metallic spin transport and microstructure.

Spin-orbit coupling in elemental two-dimensional materials

The fundamental spin-orbit coupling and spin mixing in graphene and rippled honeycomb lattice materials silicene, germanene, stanene, blue phosphorene, arsenene, antimonene, and bismuthene is investigated from first principles. The intrinsic spin-orbit coupling in graphene is revisited using multi-band $k\cdot p$ theory, showing the presence of non-zero spin mixing in graphene despite the mirror symmetry. However, the spin mixing itself does not lead to the the Elliott-Yafet spin relaxation mechanism, unless the mirror symmetry is broken by external factors. For other aforementioned elemental materials we present the spin-orbit splittings at relevant symmetry points, as well as the spin admixture $b^2$ as a function of energy close to the band extrema or Fermi levels. We find that spin-orbit coupling scales as the square of the atomic number Z, as expected for valence electrons in atoms. For isolated bands, it is found that $b^2\sim Z^4$. The spin-mixing parameter also exhibits giant anisotropy which, to a large extent, can be controlled by tuning the Fermi level. Our results for $b^2$ can be directly transferred to spin relaxation time due to the Elliott-Yafet mechanism, and therefore provide an estimate of the upper limit for spin lifetimes in materials with space inversion center.

Quasiclassical theory of the spin–orbit magnetoresistance of three-dimensional Rashba metals

The magnetoresistance of a three-dimensional Rashba metal placed on top of a ferromagnetic insulator is theoretically investigated. In addition to the intrinsic Rashba spin–orbit interaction, we consider extrinsic spin–orbit coupling via side-jump and skew scattering, as well as Elliott–Yafet spin relaxation. The latter is anisotropic due to the mass anisotropy which reflects the noncentrosymmetric crystal structure. A quasiclassical approach is employed to derive coupled spin-diffusion equations, which are supplemented by boundary conditions that account for the spin-transfer torque at the interface of the bilayer. The magnetoresistance is fully determined by the current-induced spin polarization, i.e., it cannot in general be ascribed to a single (bulk) spin Hall angle. Our theory reproduces several features of the experiments, at least qualitatively, and contains established phenomenological results in the relevant limiting cases. In particular, the anisotropy of the Elliott–Yafet spin relaxation mechanism plays a major role for the interpretation of the observed magnetoresistance.

Determination of the spin Hall effect and the spin diffusion length of Pt from self-consistent fitting of damping enhancement and inverse spin-orbit torque measurements

Understanding the evolution of spin-orbit torque (SOT) with increasing heavy-metal thickness in ferromagnet/normal metal (FM/NM) bilayers is critical for the development of magnetic memory based on SOT. However, several experiments have revealed an apparent discrepancy between damping enhancement and damping-like SOT regarding their dependence on NM thickness. Here, using linewidth and phase-resolved amplitude analysis of vector network analyzer ferromagnetic resonance (VNA-FMR) measurements, we simultaneously extract damping enhancement and both field-like and damping-like inverse SOT in Ni$_{80}$Fe$_{20}$/Pt bilayers as a function of Pt thickness. By enforcing an interpretation of the data which satisfies Onsager reciprocity, we find that both the damping enhancement and damping-like inverse SOT can be described by a single spin diffusion length ($\approx$ 4 nm), and that we can separate the spin pumping and spin memory loss (SML) contributions to the total damping. This analysis indicates that less than 40% of the angular momentum pumped by FMR through the Ni$_{80}$Fe$_{20}$/Pt interface is transported as spin current into the Pt. On account of the SML and corresponding reduction in total spin current available for spin-charge transduction in the Pt, we determine the Pt spin Hall conductivity ($\sigma_\mathrm{SH} = (2.36 \pm 0.04)\times10^6 \Omega^{-1} \mathrm{m}^{-1}$) and bulk spin Hall angle ($\theta_\mathrm{SH}=0.387 \pm0.008$) to be larger than commonly-cited values. These results suggest that Pt can be an extremely useful source of SOT if the FM/NM interface can be engineered to minimize SML. Lastly, we find that self-consistent fitting of the damping and SOT data is best achieved by a model with Elliott-Yafet spin relaxation and extrinsic inverse spin Hall effect, such that both the spin diffusion length and spin Hall conductivity are proportional to the Pt charge conductivity.

Spin properties of black phosphorus and phosphorene, and their prospects for spincalorics

Semiconducting black phosphorus attracts a lot of attention due to its extraordinary electronic properties. Its application to spincalorics requires the knowledge about the spin and thermal properties. Here, we describe first principles calculations of the spin–orbit coupling and spin scattering in phosphorene and bulk black phosphorus. We find that the intrinsic spin–orbit coupling is of the order of 20 meV for the valence and conduction band, both for phosphorene and bulk black phosphorus, and induces spin mixing with the probability –10−4. A strong anisotropy of b2 is observed. The calculated Elliott–Yafet spin relaxation times reach nanoseconds for realistic values of the momentum relaxation times. The extrinsic spin–orbit coupling, enabling the D’yakonov–Perel’ spin relaxation mechanism, is studied for phosphorene by application of a transverse electric field. We observe a strong anisotropy of the extrinsic effects for the valence band and much weaker for the conduction band. It is shown, that for small enough electric fields the spin relaxation is dominated by the Elliott–Yafet mechanism, while the D’yakonov–Perel’ matters for higher electric fields. Our theoretical results stay in a good agreement with the experimental findings, and indicates that long spin lifetimes in black phosphorus and phosphorene makes them prospective materials for spincalorics and spintronics.

Estimating the spin diffusion length and the spin Hall angle from spin pumping induced inverse spin Hall voltages

There exists considerable confusion in estimating the spin diffusion length of materials with high spin-orbit coupling from spin pumping experiments. For designing functional devices, it is important to determine the spin diffusion length with sufficient accuracy from experimental results. An inaccurate estimation of spin diffusion length also affects the estimation of other parameters (e.g., spin mixing conductance, spin Hall angle) concomitantly. The spin diffusion length for platinum (Pt) has been reported in literature in a wide range of 0.5 - 14 nm, and particularly it is a constant value independent of Pt's thickness. Here, the key reasonings behind such wide range of reported values of spin diffusion length have been identified comprehensively. Particularly, it is shown here that a thickness-dependent conductivity and spin diffusion length is necessary to simultaneously match the experimental results of effective spin mixing conductance and inverse spin Hall voltage due to spin pumping. Such thickness-dependent spin diffusion length is tantamount to Elliott-Yafet spin relaxation mechanism, which bodes well for transitional metals. This conclusion is not altered even when there is significant interfacial spin memory loss. Furthermore, the variations in the estimated parameters are also studied, which is important for technological applications.

Gate-Driven Pure Spin Current in Graphene

Spintronics, which utilizes spin as information carrier, is a promising solution for nonvolatile memory and low-power computing in the post-Moore era. An important challenge is to realize long distance spin transport, together with efficient manipulation of spin current for novel logic-processing applications. Here, we describe a gate-variable spin current demultiplexer (GSDM) based on graphene, serving as a fundamental building block of reconfigurable spin current logic circuits. The concept relies on electrical gating of carrier density dependent conductivity and spin diffusion length in graphene. As a demo, GSDM is realized for both single-layer and bilayer graphene. The distribution and propagation of spin current in the two branches of GSDM depend on spin relaxation characteristics of graphene. Compared with Elliot-Yafet spin relaxation mechanism, D'yakonov-Perel mechanism results in more appreciable gate-tuning performance. These unique features of GSDM would give rise to abundant spin logic applications, such as on-chip spin current modulators and reconfigurable spin logic circuits.

Generalized Elliott-Yafet spin-relaxation time for arbitrary spin mixing

We extend our recent result for the spin-relaxation time due to acoustic electron-phonon scattering in degenerate bands with spin mixing [New J. Phys. 18, 023012 (2015)] to include interactions with optical phonons, and present a numerical evaluation of the spin-relaxation time for intraband hole-phonon scattering in the heavy-hole (HH) bands of bulk GaAs. Comparing our computed spin-relaxation times to the conventional Elliott-Yafet result quantitatively demonstrates that the latter underestimates the spin-relaxation time because it does not correctly describe how electron-phonon interactions change the (vector) spin expectation value of the single-particle states. We show that the conventional Elliott-Yafet spin relaxation time is a special case of our result for weak spin mixing.

Gate-tunable black phosphorus spin valve with nanosecond spin lifetimes

Two-dimensional materials offer new opportunities for both fundamental science and technological applications, by exploiting the electron spin. While graphene is very promising for spin communication due to its extraordinary electron mobility, the lack of a band gap restricts its prospects for semiconducting spin devices such as spin diodes and bipolar spin transistors. The recent emergence of 2D semiconductors could help overcome this basic challenge. In this letter we report the first important step towards making 2D semiconductor spin devices. We have fabricated a spin valve based on ultra-thin (5 nm) semiconducting black phosphorus (bP), and established fundamental spin properties of this spin channel material which supports all electrical spin injection, transport, precession and detection up to room temperature (RT). Inserting a few layers of boron nitride between the ferromagnetic electrodes and bP alleviates the notorious conductivity mismatch problem and allows efficient electrical spin injection into an n-type bP. In the non-local spin valve geometry we measure Hanle spin precession and observe spin relaxation times as high as 4 ns, with spin relaxation lengths exceeding 6 um. Our experimental results are in a very good agreement with first-principles calculations and demonstrate that Elliott-Yafet spin relaxation mechanism is dominant. We also demonstrate that spin transport in ultra-thin bP depends strongly on the charge carrier concentration, and can be manipulated by the electric field effect.

Weak localization of bismuth cluster-decorated graphene and its spin\u2013orbit interaction

Weak-localization (WL) measurements were performed in a Bi cluster-decorated graphene sheet. The charge concentration was kept constant, and the amplitude of the conductance correction was suppressed after the Bi-cluster deposition. Detailed WL data were obtained while the gate and temperature were changed. Using E. McCann’s formula, the spin-relaxation time was extracted, which was found to increase with the elastic scattering time. This is attributed to the Elliott–Yafet spin relaxation and Kane–Mele type spin–orbit coupling (SOC). The SOC strength was enhanced to 2.64 meV as a result of the first deposition. The coverage effect is discussed according to the measurement after the second deposition.

Spin-charge coupled dynamics driven by a time-dependent magnetization

The spin-charge coupled dynamics in a thin, magnetized metallic system are investigated. The effective driving force acting on the charge carriers is generated by a dynamical magnetic texture, which can be induced, e.g., by a magnetic material in contact with a normal-metal system. We consider a general inversion-asymmetric substrate/normal-metal/magnet structure, which, by specifying the precise nature of each layer, can mimick various experimentally employed setups. Inversion symmetry breaking gives rise to an effective Rashba spin-orbit interaction. We derive general spin-charge kinetic equations which show that such spin-orbit interaction, together with anisotropic Elliott-Yafet spin relaxation, yields significant corrections to the magnetization-induced dynamics. In particular, we present a consistent treatment of the spin density and spin current contributions to the equations of motion, inter alia identifying a novel term in the effective force which appears due to a spin current polarized parallel to the magnetization. This "inverse spin filter" contribution depends markedly on the parameter which describes the anisotropy in spin relaxation. To further highlight the physical meaning of the different contributions, the spin pumping configuration of typical experimental setups is analyzed in detail. In the two-dimensional limit the build-up of a DC voltage is dominated by the spin galvanic (inverse Edelstein) effect. A measuring scheme that could isolate this contribution is discussed.