Anisotropic Spin Relaxation Research Articles

Spectroscopic Signatures of Phonon Character in Molecular Electron Spin Relaxation.

Spin-lattice relaxation constitutes a key challenge for the development of quantum technologies, as it destroys superpositions in molecular quantum bits (qubits) and magnetic memory in single molecule magnets (SMMs). Gaining mechanistic insight into the spin relaxation process has proven challenging owing to a lack of spectroscopic observables and contradictions among theoretical models. Here, we use pulse electron paramagnetic resonance (EPR) to profile changes in spin relaxation rates (T 1) as a function of both temperature and magnetic field orientation, forming a two-dimensional data matrix. For randomly oriented powder samples, spin relaxation anisotropy changes dramatically with temperature, delineating multiple regimes of relaxation processes for each Cu(II) molecule studied. We show that traditional T 1 fitting approaches cannot reliably extract this information. Single-crystal T 1 anisotropy experiments reveal a surprising change in spin relaxation symmetry between these two regimes. We interpret this switch through the concept of a spin relaxation tensor, enabling discrimination between delocalized lattice phonons and localized molecular vibrations in the two relaxation regimes. Variable-temperature T 1 anisotropy thus provides a unique spectroscopic method to interrogate the character of nuclear motions causing spin relaxation and the loss of quantum information.

Twist- and gate-tunable proximity spin-orbit coupling, spin relaxation anisotropy, and charge-to-spin conversion in heterostructures of graphene and transition metal dichalcogenides

Twist- and gate-tunable proximity spin-orbit coupling, spin relaxation anisotropy, and charge-to-spin conversion in heterostructures of graphene and transition metal dichalcogenides

Spin-valley coupling and spin-relaxation anisotropy in all-CVD Graphene- MoS2 van der Waals heterostructure

Two-dimensional (2D) van der Waals (vdW) heterostructures fabricated by combining 2D materials with unique properties into one ultimate unit can offer a plethora of fundamental phenomena and practical applications. Recently, proximity-induced quantum and spintronic effects have been realized in heterostructures of graphene (Gr) with 2D semiconductors and their twisted systems. However, these studies are so far limited to exfoliated flake-based devices, limiting their potential for scalable practical applications. Here, we report spin-valley coupling and spin-relaxation anisotropy in Gr-${\mathrm{MoS}}_{2}$ heterostructure devices prepared from scalable chemical vapor-deposited (CVD) 2D materials. Spin precession and dynamics measurements reveal an enhanced spin-orbit coupling strength in the Gr-${\mathrm{MoS}}_{2}$ heterostructure in comparison with pristine Gr at room temperature. Consequently, large spin-relaxation anisotropy is observed in the heterostructure, providing a method for spin filtering due to spin-valley coupling. These findings open a scalable platform for all-CVD 2D vdW heterostructures design and their device applications.

Illuminating Ligand Field Contributions to Molecular Qubit Spin Relaxation via T1 Anisotropy.

Electron spin relaxation in paramagnetic transition metal complexes constitutes a key limitation on the growth of molecular quantum information science. However, there exist very few experimental observables for probing spin relaxation mechanisms, leading to a proliferation of inconsistent theoretical models. Here we demonstrate that spin relaxation anisotropy in pulsed electron paramagnetic resonance is a powerful spectroscopic probe for molecular spin dynamics across a library of highly coherent Cu(II) and V(IV) complexes. Neither the static spin Hamiltonian anisotropy nor contemporary computational models of spin relaxation are able to account for the experimental T1 anisotropy. Through analysis of the spin-orbit coupled wave functions, we derive an analytical theory for the T1 anisotropy that accurately reproduces the average experimental anisotropy of 2.5. Furthermore, compound-by-compound deviations from the average anisotropy provide a promising approach for observing specific ligand field and vibronic excited state coupling effects on spin relaxation. Finally, we present a simple density functional theory workflow for computationally predicting T1 anisotropy. Analysis of spin relaxation anisotropy leads to deeper fundamental understanding of spin-phonon coupling and relaxation mechanisms, promising to complement temperature-dependent relaxation rates as a key metric for understanding molecular spin qubits.

Extrinsic spin-valley Hall effect and spin-relaxation anisotropy in magnetized and strained graphene

The implementation of the quantum spin-valley Hall effect is a critical challenge for the spintronics and valleytronic experimentalists because it requires breaking both time-reversal symmetry ($\mathcal{T}$) and spatial inversion symmetry ($\mathcal{P}$) while preserving the joint symmetry $\mathcal{O}=\mathcal{T}\mathcal{P}$. Here, we demonstrate an extrinsic spin-valley Hall effect by the magnetic field and temperature modulation of the nonlocal resistance in a Hall bar device consisting of magnetized and strained graphene. Besides, we achieve a striking crossover from positive to negative nonlocal magnetoresistance owing to the magnetic field dependence of spin-valley relaxation instead of the usual Hanle spin precession. Moreover, we microscopically derive a large and tunable spin-relaxation anisotropy of the magnetized graphene within the Born-Markov and the Weiss-field approximations. Our findings offer fascinating opportunities to manipulate the spin and valley degrees of freedom and design novel electronic devices.

Spin relaxation in copper channels with submicron cross sections

• We review our recent experimental studies of the spin relaxation processes in the submicron copper channels of nonlocal spin valves (NLSV). Long spin relaxation lengths up to 3.0 μm at low temperatures are demonstrated in highly conductive copper channels with residual resistivity ratios up to 6. An unexpected anisotropy of spin relaxation is observed and can be attributed to the surface spin-orbit effects. An unusual scaling of the Kondo spin relaxation is established experimentally and can be explained by overlapping Kondo screening clouds. Our results demonstrate the technological potential of copper as a spin transport channel in spintronics and highlights unanswered fundamental questions related to the spin relaxation processes. We review our recent experimental studies of the spin relaxation processes in the submicron copper channels of nonlocal spin valves (NLSV). Long spin relaxation lengths up to 3.0 μm at low temperatures are demonstrated in highly conductive copper channels with residual resistivity ratios up to 6. An unexpected anisotropy of spin relaxation is observed and can be attributed to the surface spin-orbit effects. An unusual scaling of the Kondo spin relaxation is established experimentally and can be explained by overlapping Kondo screening clouds. Our results demonstrate the technological potential of copper as a spin transport channel in spintronics and highlights unanswered fundamental questions related to the spin relaxation processes.

Polarization Effect in Electron Paramagnetic Resonance with Anisotropic Effective G-Tensor and Anisotropic Spin Relaxation

Polarization Effect in Electron Paramagnetic Resonance with Anisotropic Effective G-Tensor and Anisotropic Spin Relaxation

Observation of an anisotropic ultrafast spin relaxation process in large-area WTe2 films

Weyl semimetal Td-WTe2 hosts the natural broken inversion symmetry and strong spin–orbit coupling, which contains profound spin-related physics within a picosecond timescale. However, the comprehensive understanding of ultrafast spin behaviors in WTe2 is lacking due to its limited quality of large-scale films. Here, we report on an anisotropic ultrafast spin dynamics in highly oriented Td-WTe2 films using a femtosecond pump–probe technique at room temperature. A transient spin polarization-flip transition as fast as 0.8 ps is observed upon photoexcitation. The inversed spin is subsequently scattered by defects with a duration of about 5.9 ps. The whole relaxation process exhibits an intriguing dual anisotropy of sixfold and twofold symmetries, which stems from the energy band anisotropy of the WTe2 crystalline structure and the matrix element effect, respectively. Our work enriches the insights into the ultrafast opto-spintronics in topological Weyl semimetals.

Anisotropic spin dynamics in semiconductor narrow wires from the interplay between spin-orbit interaction and planar magnetic field

The anisotropic spin dynamics in wires based on a [001]-oriented semiconductor quantum well were investigated to determine the effect of applying an in-plane magnetic field both parallel to and perpendicular to the spin-orbit magnetic field, and the interaction between them. In one-dimensional spin motion where the wire width is less than the spin-precession length, it is known that the global spin precession is essentially determined by the spin-orbit induced precession along the wire direction. In this study, our objective is to investigate the nature of anisotropic spin dynamics in such narrow semiconductor wires along various crystal orientations. We proposed an analytic expression for the anisotropic spin-relaxation rates and the Larmor-precession frequencies for the arbitrary magnetic field orientation based on a theoretical understanding of the spin dynamics in the narrow wire structure. This expression describes the interaction between the spin-orbit field and all orientations of the in-plane magnetic field. We experimentally investigated the spin dynamics for lithographically defined 800-nm-width wires oriented along the $[\overline{1}10]$, [100], and [110] crystal orientations using a [001] GaAs/AlGaAs quantum well. Time-resolved Kerr rotation microscopy measurements indicated that the spin-relaxation time was the longest for the in-plane magnetic field perpendicular to the spin-orbit field, whereas the parallel configuration was found to be the shortest among all the directions. The precession frequency was found to have the opposite symmetry. These relations are well explained by the theoretical considerations developed in this work. Because the Rashba and Dresselhaus spin-orbit fields are mutually orthogonal in the [100] crystal orientation, it is possible to evaluate both spin-orbit coefficients from the precession anisotropy. These findings suggest that it is possible to control the spin state in narrow wires approaching the one-dimensional state and evaluate the spin-orbit coefficient. This has the potential to provide a greater understanding of quantum and topological information in semiconductor one-dimensional wires.

Anisotropy of Transverse Spin Relaxation in H2O-D2O Liquid Entrapped in Nanocavities: Application to Studies of Connective Tissues.

The spin-spin relaxation in connective tissues is simulated using a model in which a connective tissue is represented by a set of nanocavities containing H2O-D2O liquid. Collagen fibrils in connective tissues form ordered hierarchical long structures of hydrated nano-cavities with characteristic diameter from 1 nm to several tens of nanometers and length of about 100 nm. We consider influence of the restricted Brownian motion of molecules inside a nano-cavity on spin-spin relaxation. The analytical expression for the transverse time T 2 for H2O-D2O liquid in contained a nanocavity was obtained. We show that the angular dependence of the transverse relaxation rate does not depend on the concentration of D2O. The theoretical results could explain the experimentally observed dependence of the degree of deuteration on the relaxation time T 2. Accounting the orientation distribution of the nanocavities well agreement with the experimental dependence of the relaxation for articular cartilage on the deuteration degree was obtained.

Bilayer graphene encapsulated within monolayers of WS2 or Cr2Ge2Te6 : Tunable proximity spin-orbit or exchange coupling

Van der Waals (vdW) heterostructures consisting of bilayer graphene (BLG) encapsulated within monolayers of strong spin-orbit semiconductor WS$_2$ or ferromagnetic semiconductor Cr$_2$Ge$_2$Te$_6$ (CGT), are investigated. By performing realistic first-principles calculations we capture the essential BLG band structure features, including layer- and sublattice-resolved proximity spin-orbit or exchange couplings. For different relative twist angles (0 or 60$^{\circ}$) of the WS$_2$ layers, and the magnetizations (parallel or antiparallel) of the CGT layers, with respect to BLG, the low energy bands are found and characterized by a series of fit parameters of model Hamiltonians. These effective models are then employed to investigate the tunability of the relevant energy dispersions by a gate field. For WS$_2$/BLG/WS$_2$ encapsulation we find that twisting allows to turn off the spin splittings away from the $K$ points, due to opposite proximity-induced valley-Zeeman couplings in the two sheets of BLG. Close to the $K$ points the electron spins are polarized out of the plane. This polarization can be flipped by applying a gate field. As for magnetic CGT/BLG/CGT structures, we realize the recently proposed spin-valve effect, whereby a gap opens for antiparallel magnetizations of the CGT layers. Furthermore, we find that for the antiferromagnetic orientation the electron states away from $K$ have vanishingly weak proximity exchange, while the states close to $K$ remain spin polarized in the presence of an electric field. The induced magnetization can be flipped by changing the gate field. These findings should be useful for spin transport, spin filtering, and spin relaxation anisotropy studies of BLG-based vdW heterostructures.

Strongly anisotropic spin dynamics in magnetic topological insulators

The recent discovery of magnetic topological insulators has opened new avenues to explore exotic states of matter that can emerge from the interplay between topological electronic states and magnetic degrees of freedom, be it ordered or strongly fluctuating. Motivated by the effects that the dynamics of the magnetic moments can have on the topological surface states, we investigate the magnetic fluctuations across the (MnBi$_{\text{2}}$Te$_{\text{4}}$)(Bi$_{\text{2}}$Te$_{\text{3}}$)$_{\text{n}}$ family. Our paramagnetic electron spin resonance experiments reveal contrasting Mn spin dynamics in different compounds, which manifests in a strongly anisotropic Mn spin relaxation in MnBi$_{\text{2}}$Te$_{\text{4}}$ while being almost isotropic in MnBi$_{\text{4}}$Te$_{\text{7}}$. Our density-functional calculations explain these striking observations in terms of the sensitivity of the local electronic structure to the Mn spin-orientation, and indicate that the anisotropy of the magnetic fluctuations can be controlled by the carrier density, which may directly affect the electronic topological surface states.

Graphene on two-dimensional hexagonal BN, AlN, and GaN: Electronic, spin-orbit, and spin relaxation properties

We investigate the electronic structure of graphene on a series of 2D hexagonal nitride insulators hXN, X = B, Al, and Ga, with DFT calculations. A symmetry-based model Hamiltonian is employed to extract orbital parameters and spin-orbit coupling (SOC) from the low-energy Dirac bands of proximitized graphene. While commensurate hBN induces a staggered potential of about 10 meV into the Dirac bands, less lattice-matched hAlN and hGaN disrupt the Dirac point much less, giving a staggered gap below 100 $\mu$eV. Proximitized intrinsic SOC surprisingly does not increase much above the pristine graphene value of 12 $\mu$eV; it stays in the window of (1-16) $\mu$eV, depending strongly on stacking. However, Rashba SOC increases sharply when increasing the atomic number of the boron group, with calculated maximal values of 8, 15, and 65 $\mu$eV for B, Al, and Ga-based nitrides, respectively. The individual Rashba couplings also depend strongly on stacking, vanishing in symmetrically-sandwiched structures, and can be tuned by a transverse electric field. The extracted spin-orbit parameters were used as input for spin transport simulations based on Chebyshev expansion of the time-evolution of the spin expectation values, yielding interesting predictions for the electron spin relaxation. Spin lifetime magnitudes and anisotropies depend strongly on the specific (hXN)/graphene/hXN system, and they can be efficiently tuned by an applied external electric field as well as the carrier density in the graphene layer. A particularly interesting case for experiments is graphene/hGaN, in which the giant Rashba coupling is predicted to induce spin lifetimes of 1-10 ns, short enough to dominate over other mechanisms, and lead to the same spin relaxation anisotropy as observed in conventional semiconductor heterostructures: 50\%, meaning that out-of-plane spins relax twice as fast as in-plane spins.

Control of spin relaxation anisotropy by spin-orbit-coupled diffusive spin motion

Spatiotemporal spin dynamics under spin-orbit interaction is investigated in a (001) GaAs two-dimensional electron gas using magneto-optical Kerr rotation microscopy. Spin polarized electrons are diffused away from the excited position, resulting in spin precession because of the diffusion-induced spin-orbit field. Near the cancellation between spin-orbit field and external magnetic field, the induced spin precession frequency depends nonlinearly on the diffusion velocity, which is unexpected from the conventional linear relation between the spin-orbit field and the electron velocity.This behavior originates from an enhancement of the spin relaxation anisotropy by the electron velocity perpendicular to the diffused direction. We demonstrate that the spin relaxation anisotropy, which has been regarded as a material constant, can be controlled via diffusive electron motion.

Electrical control of spin relaxation anisotropy during drift transport in a two-dimensional electron gas

Spin relaxation was studied in a two-dimensional electron gas confined in a wide GaAs quantum well. Recently, the control of the spin relaxation anisotropy by diffusive motion was first shown in D. Iizasa et al., arXiv:2006.08253 (2020). Here, we demonstrate electrical control by drift transport in a system with two-subbands occupied. The combined effect of in-plane and gate voltages was investigated using time-resolved Kerr rotation. The measured relaxation time present strong anisotropy with respect to the transport direction. For an in-plane accelerating electric field along $\left[110\right]$, the lifetime was strongly suppressed irrespective of the applied gate voltage. Remarkably, for transport along $\left[1\bar{1}0\right]$, the data shows spin lifetime that was gate-dependent and longer than in the $\left[110\right]$ direction regardless of the in-plane voltage. In agreement, independent results of anisotropic spin precession frequencies are also presented. Nevertheless, the long spin lifetime, strong anisotropy and drift response seen in the data are beyond the existing models for spin drift and diffusion.

Giant Anisotropy of Spin Relaxation and Spin-Valley Mixing in a Silicon Quantum Dot.

In silicon quantum dots (QDs), at a certain magnetic field commonly referred to as the "hot spot," the electron spin relaxation rate (T_{1}^{-1}) can be drastically enhanced due to strong spin-valley mixing. Here, we experimentally find that with a valley splitting of 78.2±1.6 μeV, this hot spot in spin relaxation can be suppressed by more than 2 orders of magnitude when the in-plane magnetic field is oriented at an optimal angle, about 9° from the [100] sample plane. This directional anisotropy exhibits a sinusoidal modulation with a 180° periodicity. We explain the magnitude and phase of this modulation using a model that accounts for both spin-valley mixing and intravalley spin-orbit mixing. The generality of this phenomenon is also confirmed by tuning the electric field and the valley splitting up to 268.5±0.7 μeV.

Investigating the spin-orbit interaction in van der Waals heterostructures by means of the spin relaxation anisotropy

Graphene offers long spin propagation and, at the same time, a versatile platform to engineer its physical properties. Proximity-induced phenomena, taking advantage of materials with large spin-orbit coupling or that are magnetic, can be used to imprint graphene with large spin-orbit coupling and magnetic correlations. However, full understanding of the proximitized graphene and the consequences on the spin transport dynamics requires the development of unconventional experimental approaches. The investigation of the spin relaxation anisotropy, defined as the ratio of lifetimes for spins pointing out of and in the graphene plane, is an important step in this direction. This review discusses various methods for extracting the spin relaxation anisotropy in graphene-based devices. Within the experimental framework, current understanding on spin transport dynamics in single-layer and bilayer graphene is presented. Due to increasing interest, experimental results in graphene in proximity with high spin-orbit layered materials are also reviewed.

Comparison of spin photocurrent in devices based on in-plane or out-of-plane magnetized CoFeB spin detectors

We have measured a helicity-dependent photocurrent at zero external magnetic field in a device based on a semiconductor quantum well embedded in a p-i-n junction. The device is excited under vertical incidence with circularly polarized light. The spin filtering effect is evidenced in the temperature range 77--300 K owing to a CoFeB/MgO spin filter with out-of-plane magnetization in remanence. The helicity-dependent photocurrent is explored as a function of the temperature and bias. These characteristics are compared with those of a spin photocurrent device with in-plane magnetized CoFeB/MgO spin filter, excited under oblique incidence with circularly polarized light. In contrast to the in-plane spin filter device, the circularly polarized light asymmetry of the photocurrent in the out-of-plane device depends weakly on the external bias. The two devices are sensitive to the spin filtering of either the in-plane $({S}_{x})$ or out-of-plane $({S}_{z})$ photogenerated electron spin in the semiconductor quantum well. The helicity-dependent photocurrent results can be explained by the Dyakonov-Perel electron spin-relaxation mechanism. Our study reveals the giant spin relaxation anisotropy in III-V zinc-blende quantum wells in the presence of a vertical electric field.

Heterostructures of graphene and hBN: Electronic, spin-orbit, and spin relaxation properties from first principles

We perform extensive first-principles calculations for heterostructures composed of monolayer graphene and hexagonal boron nitride (hBN). Employing a symmetry-derived minimal tight-binding model, we extract orbital and spin-orbit coupling (SOC) parameters for graphene on hBN, as well as for hBN encapsulated graphene. Our calculations show that the parameters depend on the specific stacking configuration of graphene on hBN. We also perform an interlayer distance study for the different graphene/hBN stacks to find the corresponding lowest energy distances. For very large interlayer distances, one can recover the pristine graphene properties, as we find from the dependence of the parameters on the interlayer distance. Furthermore, we find that orbital and SOC parameters, especially the Rashba one, depend strongly on an applied transverse electric field, giving a rich playground for spin physics. Armed with the model parameters, we employ the Dyakonov-Perel formalism to calculate the spin relaxation in graphene/hBN heterostructures. We find spin lifetimes in the nanosecond range, in agreement with recent measurements. The spin relaxation anisotropy, being the ratio of out-of-plane to in-plane spin lifetimes, is found to be giant close to the charge neutrality point, decreasing with increasing doping, and being highly tunable by an external transverse electric field. This is in contrast to bilayer graphene in which an external field saturates the spin relaxation anisotropy.

Strongly anisotropic spin relaxation in the neutral silicon vacancy center in diamond

Color centers in diamond are a promising platform for quantum technologies, and understanding their interactions with the environment is crucial for these applications. We report a study of spin- lattice relaxation (T1) of the neutral charge state of the silicon vacancy center in diamond. Above 20 K, T1 decreases rapidly with a temperature dependence characteristic of an Orbach process, and is strongly anisotropic with respect to magnetic field orientation. As the angle of the magnetic field is rotated relative to the symmetry axis of the defect, T1 is reduced by over three orders of magnitude. The electron spin coherence time (T2) follows the same temperature dependence but is drastically shorter than T1. We propose that these observations result from phonon-mediated transitions to a low lying excited state that are spin conserving when the magnetic field is aligned with the defect axis, and we discuss likely candidates for this excited state.