Intrinsic Spin Relaxation Research Articles

Localization in inhomogeneously broadened systems using the Gibbs phenomenon

Spectra and images derived from the Fourier transformation of time-domain signals can often exhibit overshoots and/or “ringing” near sharp features. Such artifacts are due to the slow convergence of the Fourier series near such features, an effect referred to as the Gibbs phenomenon. While usually viewed as being purely mathematical in origin, the Gibbs phenomenon can often be found in a variety of physical situations, such as in imaging and spectroscopy. In this work, a physical description of the Gibbs phenomenon is presented where it is interpreted as an interference effect whereby slower destructive interference or “Fourier dephasing” occurs near sharp spectral features compared with the Fourier dephasing observed away from such features. Differences in Fourier dephasing can be exploited to localize magnetization near physical boundaries on timescales about an order of magnitude faster than can be achieved using conventional frequency or spatially selective pulses. This localization, which is reversible, also occurs on much faster timescales than can be attributed to irreversible sources, such as restricted diffusion or spatial variations of the intrinsic spin relaxation within the sample.

Low-symmetry topological materials for large charge-to-spin interconversion: The case of transition metal dichalcogenide monolayers

The spin polarization induced by the spin Hall effect (SHE) in thin films typically points out of the plane. This is rooted on the specific symmetries of traditionally studied systems, not in a fundamental constraint. Recently, experiments on few-layer ${\rm MoTe}_2$ and ${\rm WTe}_2$ showed that the reduced symmetry of these strong spin-orbit coupling materials enables a new form of {\it canted} spin Hall effect, characterized by concurrent in-plane and out-of-plane spin polarizations. Here, through quantum transport calculations on realistic device geometries, including disorder, we predict a very large gate-tunable SHE figure of merit $\lambda_s\theta_{xy}\sim 1\text{--}50$ nm in ${\rm MoTe}_2$ and ${\rm WTe}_2$ monolayers that significantly exceeds values of conventional SHE materials. This stems from a concurrent long spin diffusion length ($\lambda_s$) and charge-to-spin interconversion efficiency as large as $\theta_{xy} \approx 80$\%, originating from momentum-invariant (persistent) spin textures together with large spin Berry curvature along the Fermi contour, respectively. Generalization to other materials and specific guidelines for unambiguous experimental confirmation are proposed, paving the way towards exploiting such phenomena in spintronic devices. These findings vividly emphasize how crystal symmetry and electronic topology can govern the intrinsic SHE and spin relaxation, and how they may be exploited to broaden the range and efficiency of spintronic materials and functionalities.

Intrinsic and extrinsic spin-orbit coupling and spin relaxation in monolayer PtSe2

Monolayer PtSe$_2$ is a semiconducting transition metal dichalcogenide characterized by an indirect band gap, space inversion symmetry, and high carrier mobility. Strong intrinsic spin-orbit coupling and the possibility to induce extrinsic spin-orbit fields by gating make PtSe$_2$ attractive for fundamental spin transport studies as well as for potential spintronics applications. We perform a systematic theoretical study of the spin-orbit coupling and spin relaxation in this material. Specifically, we employ first principles methods to obtain the basic orbital and spin-orbital properties of PtSe$_2$, also in the presence of an external transverse electric field. We calculate the spin mixing parameters $b^2$ and the spin-orbit fields $\Omega$ for the Bloch states of electrons and holes. This information allows us to predict the spin lifetimes due to the Elliott-Yafet and D'yakonov-Perel mechanisms. We find that $b^2$ is rather large, on the order of $10^{-2}$ and $10^{-1}$, while $\Omega$ varies strongly with doping, being about $10^{3} - 10^{4}$\,ns$^{-1}$ for %typical Fermi levels in the interval $(10-100)$ meV, carrier density in the interval $10^{13}-10^{14}$\,cm$^{-2}$ at the electric field of 1 V/nm. We estimate the spin lifetimes to be on the picosecond level.

Optimized selection of slow-relaxing 13C transitions in methyl groups of proteins: application to relaxation dispersion.

Optimized selection of the slow-relaxing components of single-quantum 13C magnetization in 13CH3 methyl groups of proteins using acute (< 90°) angle 1H radio-frequency pulses, is described. The optimal selection scheme is more relaxation-tolerant and provides sensitivity gains in comparison to the experiment where the undesired (fast-relaxing) components of 13C magnetization are simply 'filtered-out' and only 90° 1H pulses are employed for magnetization transfer to and from 13C nuclei. When applied to methyl 13C single-quantum Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion experiments for studies of chemical exchange, the selection of the slow-relaxing 13C transitions results in a significant decrease in intrinsic (exchange-free) transverse spin relaxation rates of all exchanging species. For exchanging systems involving high-molecular-weight species, the lower transverse relaxation rates translate into an increase in the information content of the resulting relaxation dispersion profiles.

Spin-phonon relaxation from a universal ab initio density-matrix approach

Designing new quantum materials with long-lived electron spin states urgently requires a general theoretical formalism and computational technique to reliably predict intrinsic spin relaxation times. We present a new, accurate and universal first-principles methodology based on Lindbladian dynamics of density matrices to calculate spin-phonon relaxation time of solids with arbitrary spin mixing and crystal symmetry. This method describes contributions of Elliott-Yafet and D’yakonov-Perel’ mechanisms to spin relaxation for systems with and without inversion symmetry on an equal footing. We show that intrinsic spin and momentum relaxation times both decrease with increasing temperature; however, for the D’yakonov-Perel’ mechanism, spin relaxation time varies inversely with extrinsic scattering time. We predict large anisotropy of spin lifetime in transition metal dichalcogenides. The excellent agreement with experiments for a broad range of materials underscores the predictive capability of our method for properties critical to quantum information science.

Spin-phonon relaxation times in centrosymmetric materials from first principles

We present a first-principles approach for computing the phonon-limited $T_1$ spin relaxation time due to the Elliot-Yafet mechanism. Our scheme combines fully-relativistic spin-flip electron-phonon interactions with an approach to compute the effective spin of band electrons in materials with inversion symmetry. We apply our method to silicon and diamond, for which we compute the temperature dependence of the spin relaxation times and analyze the contributions to spin relaxation from different phonons and valley processes. The computed spin relaxation times in silicon are in excellent agreement with experiment in the 50$-$300 K temperature range. In diamond, we predict intrinsic spin relaxation times of 540 $\mu$s at 77 K and 2.3 $\mu$s at 300 K. Our work enables precise predictions of spin-phonon relaxation times in a wide range of materials, providing microscopic insight into spin relaxation and guiding the development of spin-based quantum technologies.

Dynamical Aspects of Magnetic Switching in a Single Molecule-Based Spin Valve

The dynamics of the current-induced magnetic switching process is theoretically studied in a spin-valve device containing a single magnetic molecule of spin S 1. The analysis is performed by using the real-time diagrammatic technique in the sequential electron tunneling regime. In particular, we show that the magnetic moment of a molecule can be reversed also in the presence of intrinsic spin relaxation processes. Moreover, we discuss how the process of magnetic switching depends on a transport bias voltage as well as on some key parameters of the device.

Structural and magnetic properties of epitaxial thin films of the equiatomic quaternary CoFeMnSi Heusler alloy

We report the structural and magnetic properties of CoFeMnSi equiatomic quaternary Heusler alloy thin films. The epitaxial growth of the single-crystalline films with full $B2$ and partial $L{2}_{1}$ ordering on the Cr-buffered MgO(001) substrate was achieved using the in situ postannealing at temperature (${T}_{\mathrm{a}}$) of $500\ensuremath{-}600{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$. A saturation magnetization value of about $3.5\phantom{\rule{0.16em}{0ex}}{\ensuremath{\mu}}_{\mathrm{B}}/\mathrm{f}.\mathrm{u}.$ (where f.u. represents formula unit) was obtained at room temperature for the sample with ${T}_{\mathrm{a}}=600{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$, which is very close to the value of $3.7\phantom{\rule{0.16em}{0ex}}{\ensuremath{\mu}}_{\mathrm{B}}/\mathrm{f}.\mathrm{u}.$ reported previously for a bulk sample. Ferromagnetic resonance unveiled that negligible extrinsic relaxation due to magnetic softness as well as small intrinsic spin relaxation, i.e., the Gilbert damping constant of 0.005, which is smaller than that of permalloy. The spin magnetic moments for Co, Fe, and Mn atoms for the sample with ${T}_{\mathrm{a}}=600{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$ deduced from the x-ray magnetic circular dichroism were in agreement with those previously reported in the bulk sample, the effects of Fe-Mn swapping and Mn antisite disorder were discussed.

Advances in Two‐Dimensional Layered Materials

Advances in Two‐Dimensional Layered Materials

Spin-orbit coupling and spin relaxation in phosphorene: Intrinsic versus extrinsic effects

First-principles calculations of the essential spin-orbit and spin relaxation properties of phosphorene are performed. Intrinsic spin-orbit coupling induces spin mixing with the probability of $b^2 \approx 10^{-4}$, exhibiting a large anisotropy, following the anisotropic crystalline structure of phosphorene. For realistic values of the momentum relaxation times, the intrinsic (Elliott--Yafet) spin relaxation times are hundreds of picoseconds to nanoseconds. Applying a transverse electric field (simulating gating and substrates) generates extrinsic $C_{2v}$ symmetric spin-orbit fields in phosphorene, which activate the D'yakonov--Perel' mechanism for spin relaxation. It is shown that this extrinsic spin relaxation also has a strong anisotropy, and can dominate over the Elliott-Yafet one for strong enough electric fields. Phosphorene on substrates can thus exhibit an interesting interplay of both spin relaxation mechanisms, whose individual roles could be deciphered using our results.

Spin dynamics of an individual Cr atom in a semiconductor quantum dot under optical excitation

We studied the spin dynamics of a Cr atom incorporated in a II-VI semiconductor quantum dot using photon correlation techniques. We used recently developed singly Cr-doped CdTe/ZnTe quantum dots to access the spin of an individual magnetic atom. Auto-correlation of the photons emitted by the quantum dot under continuous wave optical excitation reveals fluctuations of the localized spin with a timescale in the 10 ns range. Cross-correlation gives quantitative transfer time between Cr spin states. A calculation of the time dependence of the spin levels population in Cr-doped quantum dots shows that the observed spin dynamics is dominated by the exciton-Cr interaction. These measurements also provide a lower bound in the 20 ns range for the intrinsic Cr spin relaxation time.

Room-temperature electron spin relaxation of nitroxides immobilized in trehalose: Effect of substituents adjacent to NO-group

Trehalose has been recently promoted as efficient immobilizer of biomolecules for room-temperature EPR studies, including distance measurements between attached nitroxide spin labels. Generally, the structure of nitroxide influences the electron spin relaxation times, being crucial parameters for room-temperature pulse EPR measurements. Therefore, in this work we investigated a series of nitroxides with different substituents adjacent to NO-moiety including spirocyclohexane, spirocyclopentane, tetraethyl and tetramethyl groups. Electron spin relaxation times (T1, Tm) of these radicals immobilized in trehalose were measured at room temperature at X- and Q-bands (9/34GHz). In addition, a comparison was made with the corresponding relaxation times in nitroxide-labeled DNA immobilized in trehalose. In all cases phase memory times Tm were close to 700ns and did not essentially depend on structure of substituents. Comparison of temperature dependences of Tm at T=80–300K shows that the benefit of spirocyclohexane substituents well-known at medium temperatures (∼100–180K) becomes negligible at 300K. Therefore, unless there are specific interactions between spin labels and biomolecules, the room-temperature value of Tm in trehalose is weakly dependent on the structure of substituents adjacent to NO-moiety of nitroxide. The issues of specific interactions and stability of nitroxide labels in biological media might be more important for room temperature pulsed dipolar EPR than differences in intrinsic spin relaxation of radicals.

Electron spin dynamics in GaN

Gallium nitride is a promising material system for spintronics, offering long spin relaxation times and prospects for room‐temperature ferromagnetism. We review the electron spin dynamics in bulk GaN. Time‐resolved magneto‐optical studies of both the wurtzite and the cubic phase of GaN show the dominance of Dyakonov–Perel (DP) relaxation for free conduction band electrons. Spin relaxation in the wurtzite phase is characterized by an intrinsic spin relaxation anisotropy and the limitation of spin lifetimes by a strong Rashba term. Spin lifetimes are strongly enhanced in cubic GaN, where only a weak Dresselhaus term contributes to DP relaxation. Ion‐implanted wurtzite GaN shows a strong increase of electron spin lifetimes for increasing implantation dose, caused by increasing localization of carriers. The spin dynamics of conduction band electrons in Gd‐implanted GaN as a candidate for a room‐temperature ferromagnetic semiconductor is also only governed by localization effects and does not show signs of an efficient exchange coupling between the electrons and the magnetic Gd ions.

Intrinsic electron spin relaxation due to the D'yakonov–Perel' mechanism in monolayer MoS2

Intrinsic electron spin relaxation due to the D'yakonov-Perel' mechanism is studied in monolayer Molybdenum Disulphide. An intervalley in-plane spin relaxation channel is revealed due to the opposite effective magnetic fields perpendicular to the monolayer Molybdenum Disulphide plane in the two valleys together with the intervalley electron-phonon scattering. The intervalley electron-phonon scattering is always in the weak scattering limit, which leads to a rapid decrease of the in-plane spin relaxation time with increasing temperature. A decrease of the in-plane spin relaxation time with the increase of the electron density is also shown.

Effect of anisotropic spin absorption on the Hanle effect in lateral spin valves

We have succeeded in fully describing dynamic properties of spin current including the different spin absorption mechanisms for longitudinal and transverse spins in lateral spin valves, which enable one to elucidate intrinsic spin transport and relaxation mechanisms in the nonmagnet. The deduced spin lifetimes are found independent of the contact type. From the transit-time distribution of spin current extracted from the Fourier transform in Hanle measurement data, the velocity of the spin current in Ag with Py/Ag Ohmic contact turns out much faster than that expected from the widely used model.

Spin Injection into a Superconductor with Strong Spin-Orbit Coupling

We demonstrate spin injection into superconducting Nb by employing a spin absorption technique in lateral spin valve structures. Spin currents flowing in a nonmagnetic Cu channel are preferably absorbed into Nb due to its strong spin-orbit interaction, the amount of which dramatically changes below or above the superconducting critical temperature (TC). The charge imbalance effect observed in the Cu/Nb interface ensures that superconducting Nb absorbs pure spin currents even below TC. Our analyses based on the density of states calculated using the Usadel equation can well reproduce the experimental results, implying that the strong spin-orbit interaction of Nb is still effective for the spin absorption even below TC. Most importantly, our method allows us to determine the intrinsic spin relaxation time in the superconducting Nb, which reaches more than 4 times greater than that in the normal state.

Anisotropic intrinsic spin relaxation in graphene due to flexural distortions

We propose an intrinsic spin scattering mechanism in graphene originated by the interplay of atomic spin-orbit interaction and the local curvature induced by flexural distortions of the atomic lattice. Starting from a multiorbital tight-binding Hamiltonian with spin-orbit coupling considered non-perturbatively, we derive an effective Hamiltonian for the spin scattering of the Dirac electrons due to flexural distortions. We compute the spin lifetime due to both flexural phonons and ripples and we find values in the microsecond range at room temperature. Interestingly, this mechanism is anisotropic on two counts. First, the relaxation rate is different for off-plane and in-plane spin quantization axis. Second, the spin relaxation rate depends on the angle formed by the crystal momentum with the carbon-carbon bond. In addition, the spin lifetime is also valley dependent. The proposed mechanism sets an upper limit for spin lifetimes in graphene and will be relevant when samples of high quality can be fabricated free of extrinsic sources of spin relaxation.

Intrinsic spin-relaxation induced negative tunnel magnetoresistance in a single-molecule magnet

We investigate theoretically the effects of intrinsic spin-relaxation on the spin-dependent transport through a single-molecule magnet (SMM), which is weakly coupled to ferromagnetic leads. The tunnel magnetoresistance (TMR) is obtained by means of the rate-equation approach including not only the sequential but also the cotunneling processes. It is shown that the TMR is strongly suppressed by the fast spin-relaxation in the sequential region and can vary from a large positive to slight negative value in the cotunneling region. Moreover, with an external magnetic field along the easy-axis of SMM, a large negative TMR is found when the relaxation strength increases. Finally, in the high bias voltage limit the TMR for the negative bias is slightly larger than its characteristic value of the sequential region; however, it can become negative for the positive bias caused by the fast spin-relaxation.

Intrinsic spin lifetime of conduction electrons in germanium

We investigate the intrinsic spin relaxation of conduction electrons in germanium due to electron-phonon scattering. We derive intravalley and intervalley spin-flip matrix elements for a general spin orientation and quantify the resulting anisotropy in spin relaxation. The form of the intravalley spin-flip matrix element is derived from the eigenstates of a compact spin-dependent $\mathbf{k}$$\cdot$$\mathbf{p}$ Hamiltonian in the vicinity of the $L$ point (where thermal electrons are populated in Ge). Spin lifetimes from analytical integrations of the intravalley and intervalley matrix elements show excellent agreement with independent results from elaborate numerical methods.

NMR Measurement of Exchange of Deuterium between Palladium–Deuteride and Deuterium Gas

Deuterium NMR is used to measure the rate of exchange of D between PdDx (x ≅ 0.7) and the surrounding D2 gas at thermal equilibrium. In the presence of exchange, the very rapid longitudinal spin relaxation rate of the gas provides an additional path for spin relaxation of the PdDx, beyond the mechanisms intrinsic to the solid deuteride. The measurements reported here extend from −100 to 100 °C, with exchange rates from the palladium phase to the gas varying from approximately 0.1 to 200 s–1. Compared to the PdHx/H2 system, the PdDx/D2 system allows a wider range of exchange rates to be probed because of the very low rate of intrinsic longitudinal spin relaxation in PdDx. The activation energy for the exchange rate is found to be 0.32 eV ± 10%. The data from PdHx is reanalyzed, and a nearly equal energy is found.