Spin Components Research Articles

An Algorithm to Compute the Fundamental Classes of Spin Components of Strata of Differentials

Abstract We construct an algorithm for computing the cycle classes of the spin components of a stratum of differentials in the moduli space of stable curves $\overline {\mathcal {M}}_{g,n}$. In addition, we implement it within the Sage package admcycles. Our main strategy is to reconstruct these cycles by their restrictions to the boundary of $\overline {\mathcal {M}}_{g,n}$ via clutching maps. These restrictions can be computed recursively by smaller dimensional spin classes and determine the original class via a certain system of linear equations. To study the spin parities on the boundary of a stratum of differentials of even type, we make use of the moduli space of multi-scale differentials introduced in [4]. As an application of our algorithm, one can verify a conjecture on spin double ramification cycles stated in [18] in many examples, by using the results computed by our algorithm.

Spin-resonant tunneling in ferromagnetic conductor/ semiconductor heterostructure for spin-filter application

Spin-dependent tunneling in a ferromagnetic conductor/ semiconductor is analyzed with zero external fields. The barrier transparency, dwell time, tunneling time of electrons through heterostructure and the degree of polarization efficiency are calculated in Fe/GaAs double barrier heterostructure. The polarization efficiency of Fe/GaAs and Fe/InAs double-barrier heterostructures are compared. The Fe/GaAs has a high degree spin-polarization than Fe/InAs structure. The barrier transparency peak is sharper at the high width of the barrier. The results show that the polarization efficiency is maximum when the barrier width is maximum. The tunneling lifetime of electrons is evaluated using Heisenberg’s uncertainty principle. The spin components are completely separated at high barrier width and hence can be used effectively as a spin filter.

Revisiting the structure and dynamics of hydrated Cd2+ in aqueous solutions: Insights from the RI‐SCS‐MP2/MM molecular dynamics simulation

AbstractThe spin component scale MP2/molecular mechanics molecular dynamics simulation investigated the hydration shell formation and hydrated Cd2+ dynamics in the water environment. At the first hydration shell, six water molecules with 2.27 Å for the average distance between water and Cd2+. Dynamical properties were analyzed by computing the water molecule's mean residence time (MRT) in its first and second hydration shells. The MRT of each shell was determined to be 31.8 and 1.92 ps, suggesting the strong influence of Cd2+ in the first hydration shell. The second shell was labile, with an average number of water molecules being 18. Despite the strong interaction between Cd2+ and water molecules in the first shell, the influence of ions in the second hydration shell remained weak.

Accurate Torque Evaluation in Elongated Ultra-Scaled STT-MRAM Devices

Emerging spin-transfer torque magnetoresistive random access memory (STT-MRAM) is attractive for stand-alone and embedded applications. STT-MRAM is nonvolatile, operates fast, and possesses excellent endurance. STT-MRAM is compatible with CMOS technology and can be integrated during the back-end-of-line process. This makes STT-MRAM promising for automotive and IoT applications, microcontrollers, frame buffer memory, and last level cache. The core of modern STT-MRAM cells consists of a magnetic tunnel junction (MTJ), which is a sandwich of two ferromagnetic (FM) layers separated by a tunnel barrier (TB). The FM layers are referred to as reference layer (RL) and free layer (FL). The magnetization of the RL is fixed, while the magnetization of the FL can be reversed. The use of MTJs with perpendicular magnetic anisotropy (PMA) permits to obtain better scalability and lower switching currents. When the magnetization vectors of the FL and RL are parallel (P), the electrical resistance is lower than when the vectors are anti-parallel (AP), which provides a way to store binary information. Importantly, the switching between these two stable configurations is achieved by purely electrical means.To reduce the footprint and benefit from shape-induced anisotropy, an ultra-scaled MRAM cell with a composite FL made of several elongated ferromagnetic pieces, separated by multiple MgO barriers, was proposed and demonstrated [1]. In elongated FLs, shown in Fig.1a, domain walls or magnetization textures can be generated during switching. In this case, additional spin torques created by the presence of magnetization gradients inside the ferromagnetic parts must be considered. This type of torque is typically modeled by the Zhang-Li expression [2]. If the spin dephasing length correctly describes the coupled charge and spin transport through the device, the expression for bulk torque must be generalized [3].In MTJs, however, there exists another torque acting on a FL close to the interface with MgO. This torque, predicted by Slonczewski [4] and Berger [5], was utilized to flip the magnetization in traditional MTJs with a FL fabricated as a flat and thin disk. It is due to the spin-polarized current coming across the TB from the RL. Electrons tunneling from the RL become spin-polarized. When entering the FL, the spin polarized electrons interact with the magnetization via the exchange interaction. When the magnetization vectors in the RL and FL are not aligned, the spin current components normal to the FL magnetization are quickly absorbed. Due to conservation of the angular momentum, the absorption of the normal component of the spin current results in a torque acting on the FL magnetization in the opposite sense. If the current is sufficiently strong, the magnetization of the FL can be switched between the two stable P and AP configurations relative to the RL.As the Slonczewski torque is localized at the interface and Zhang-Li (ZL) torque is acting in the bulk, the two torques are usually assumed to be independent. However, this is not correct [5]. Although the spin component normal to the FL magnetization is indeed quickly absorbed, the interface-polarization induced spin current parallel to the magnetization propagates into the FL at a longer distance determined by the spin-flipping length. This length is about 10nm in typical FL materials. As the interface-polarization induced spin current hits the spin texture, it modifies the ZL torque value determined by the spin polarization in the bulk. The FL in ultra-scaled MRAM cells contains a TB on both interfaces. Here, we compare the ZL torque acting on the domain wall (Fig.1b) for the case, when the interface polarization at the second TB is lower than the spin polarization in the bulk (Fig.1c) or higher (Fig.1d). It is demonstrated that the torque acting on the domain wall can be enhanced compared to the ZL value for the case of larger interface polarization than spin polarization in the bulk. B. Jinnai, J. Igarashi, K. Watanabe et al. High-performance shape-anisotropy magnetic tunnel junctions down to 2.3 nm, in Proc. IEDM Conf., 2020, pp. 24.6.1-24.6.4, doi: 10.1109/IEDM13553.2020.9371972S. Zhang and Z. Li. Roles of nonequilibrium conduction electrons on the magnetization dynamics of ferromagnets. Phys. Rev. Lett., vol. 93, 127204, 2004 doi: 10.1103/PhysRevLett.93.127204J. C. Slonczewski. Current-driven excitation of magnetic multilayers, J. Magn.Magn. Mater., vol. 159, no. 1, pp. L1 - L7, 1996, doi: 10.1016/0304-8853(96)00062-5L. Berger. Emission of spin waves by a magnetic multilayer traversed by a current, Phys. Rev. B, vol. 54, pp. 9353-9358, 1996, doi: 10.1103/PhysRevB.54.9353S. Fiorentini, M. Bendra, J. Ender et al. Spin and charge drift-diffusion in ultra-scaled MRAM cells, Sci. Rep., vol. 12, 20958, pp.1-13, 2022, doi: 10.1038/s41598-022-25586-4 Figure 1

Isotropic Spin Hall Effect in an Epitaxial Ferromagnet.

We report the observation of the isotropic spin Hall effect in a ferromagnet. We show that the spin Hall effect in an epitaxially grown Fe_{3}Si generates a sizable spin current with a spin direction that is noncollinear with the magnetization. Furthermore, we find that the spin Hall current is independent of the relative orientation between its spin direction and the magnetization; the spin Hall effect is isotropic. This observation demonstrates that the intrinsically generated transverse spin component is protected from dephasing, providing fundamental insights into the generation and transport of spin currents in ferromagnets.

How to perform the coherent measurement of a curved phase space by continuous isotropic measurement. I. Spin and the Kraus-operator geometry of SL(2,C)

The generalized Q-function of a spin system can be considered the outcome probability distribution of a state subjected to a measurement represented by the spin-coherent-state (SCS) positive-operator-valued measure (POVM). As fundamental as the SCS POVM is to the 2-sphere phase-space representation of spin systems, it has only recently been reported that the SCS POVM can be performed for any spin system by continuous isotropic measurement of the three total spin components [E. Shojaee, C. S. Jackson, C. A. Riofrio, A. Kalev, and I. H. Deutsch, Phys. Rev. Lett. 121, 130404 (2018)]. This article develops the theoretical details of the continuous isotropic measurement and places it within the general context of curved-phase-space correspondences for quantum systems. The analysis is in terms of the Kraus operators that develop over the course of a continuous isotropic measurement. The Kraus operators of any spin j are shown to represent elements of the Lie group SL(2,C)≅Spin(3,C), a complex version of the usual unitary operators that represent elements of SU(2)≅Spin(3,R). Consequently, the associated POVM elements represent points in the symmetric space SU(2)∖SL(2,C), which can be recognized as the 3-hyperboloid. Three equivalent stochastic techniques, (Wiener) path integral, (Fokker-Planck) diffusion equation, and stochastic differential equations, are applied to show that the continuous isotropic POVM quickly limits to the SCS POVM, placing spherical phase space at the boundary of the fundamental Lie group SL(2,C) in an operationally meaningful way. Two basic mathematical tools are used to analyze the evolving Kraus operators, the Maurer-Cartan form, modified for stochastic applications, and the Cartan, decomposition associated with the symmetric pair SU(2) ⊂ SL(2,C). Informed by these tools, the three schochastic techniques are applied directly to the Kraus operators in a representation-independent – and therefore geometric – way (independent of any spectral information about the spin components).The Kraus-operator-centric, geometric treatment applies not just to SU(2) ⊂ SL(2,C), but also to any compact semisimple Lie group and its complexification. The POVM associated with the continuous isotropic measurement of Lie-group generators thus corresponds to a type-IV globally Riemannian symmetric space and limits to the POVM of generalized coherent states. This generalization is the focus of a sequel to this article.

Spin alignment of vector mesons from quark dynamics in a rotating medium* *Supported in part by the National Natural Science Foundation of China (NSFC) (12235016, 12221005), the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB34030000), the start-up funding from the University of Chinese Academy of Sciences (UCAS), and the Fundamental Research Funds for the Central Universities

Vorticities in heavy-ion collisions (HICs) are supposed to induce spin alignment and polarization phenomena of quarks and mesons. In this work, we analyze the spin alignment of vector mesons ϕ and ρ induced by rotation from quark dynamics in the framework of the Nambu-Jona-Lasinio (NJL) model. The rotating angular velocity induces mass splitting of spin components for vector mesons . This behavior contributes to the spin alignment of vector mesons in an equilibrium medium and naturally explains the negative deviation of for vector mesons. Incidentally, the positive deviation of under the magnetic field can also be easily understood from quark dynamics.

Tuning the spin of Dirac fermions on the surface of topological insulators in proximity to a helical spin density wave

We investigate the spin tunability of Dirac fermions on the surface of a 3D topological insulator in proximity to a helical spin density wave, acting as an applied one-dimensional periodic potential for spins produced by spiral multiferroic oxide. It is observed that the spin mean values of Dirac fermion undergo oscillations under the influence of such a periodic potential created by the exchange field of magnetization. The tunability of spin is strongly affected by the strength, orientation and period of the exchange field. In particular, the mean values of spin are anisotropic around the Dirac point, depending strongly on the amplitude and spatial period of the periodic potential. We also find that the spin expectation values change significantly by changing the plane of magnetization. Interestingly, the in-plane components of spin mean values perform pronounced oscillations, whereas the out of plane component does not oscillate at all. The oscillations of planar components of spin are originated from the spin-momentum locking on the surface of topological insulator.

Optimizing Floquet engineering for non-equilibrium steady states with gradient-based methods

Non-equilibrium steady states are created when a periodically driven quantum system is also incoherently interacting with an environment - as it is the case in most realistic situations. The notion of Floquet engineering refers to the manipulation of the properties of systems under periodic perturbations. Although it more frequently refers to the coherent states of isolated systems (or to the transient phase for states that are weakly coupled to the environment), it may sometimes be of more interest to consider the final steady states that are reached after decoherence and dissipation take place. In this work, we demonstrate how those final states can be optimally tuned with respect to a given predefined metric, such as for example the maximization of the temporal average value of some observable, by using multicolor periodic perturbations. We show a computational framework that can be used for that purpose, and exemplify the concept using a simple model for the nitrogen-vacancy center in diamond: the goal in this case is to find the driving periodic magnetic field that maximizes a time-averaged spin component. We show that, for example, this technique permits to prepare states whose spin values are forbidden in thermal equilibrium at any temperature.

Spin and orbital angular momentum of coherent photons in a waveguide

Spin angular momentum of a photon corresponds to a polarisation degree of freedom of lights, and such that various polarisation properties are coming from macroscopic manifestation of quantum-mechanical properties of lights. An orbital degree of freedom of lights is also manipulated to form a vortex of lights with orbital angular momentum, which is also quantised. However, it is considered that spin and orbital angular momentum of a photon cannot be split from the total orbital angular momentum in a gauge-invariant way. Here, we revisit this issue for a coherent monochromatic ray from a laser source, propagating in a waveguide. We obtained the helical components of spin and orbital angular momentum by the correspondence with the classical Ponyting vector. By applying a standard quantum field theory using a coherent state, we obtained the gauge-independent expressions of spin and orbital angular momentum operators. During the derivations, it was essential to take a finite cross-sectional area into account, which leads the finite longitudinal component along the direction of the propagation, which allows the splitting. Therefore, the finite mode profile was responsible to justify the splitting, which was not possible as far as we were using plane-wave expansions in a standard theory of quantum-electrodynamics (QED). Our results suggest spin and orbital angular momentum are well-defined quantum-mechanical freedoms at least for coherent photons propagating in a waveguide and in a vacuum with a finite mode profile.

Triggered Superradiance and Spin Inversion Storage in a Hybrid Quantum System.

We study the superradiant emission of an inverted spin ensemble strongly coupled to a superconducting cavity. After fast inversion, we detune the spins from the cavity and store the inversion for tens of milliseconds, during which the remaining transverse spin components disappear. Switching back on resonance enables us to study the onset of superradiance. A weak trigger pulse of a few hundred photons shifts the superradiant burst to earlier times and imprints its phase onto the emitted radiation. For long hold times, the inversion decreases below the threshold for spontaneous superradiance. There, the energy stored in the ensemble can be used to amplify microwave pulses passing through the cavity.

Collective dynamics of polarized spin-half fermions in relativistic heavy-ion collisions

Standard relativistic hydrodynamics has been successful in describing the properties of the strongly interacting matter produced in the heavy-ion collision experiments. Recently, there has been a significant theoretical advancement in this field to explain spin polarization of hadrons emitted in these processes. Although current models have successfully explained some of the experimental data based on the coupling between spin polarization and vorticity of the medium, they still lack a clear understanding of the differential measurements. This is commonly interpreted as an indication that the spin needs to be treated as an independent degree of freedom whose dynamics is not entirely bound to flow circulation. In particular, if the spin is a macroscopic property of the system, in equilibrium its dynamics should follow hydrodynamic laws. Here, we develop a framework of relativistic hydrodynamics which includes spin degrees of freedom from the quantum kinetic theory for Dirac fermions and use it for modeling the dynamics of matter. Following experimental observations, we assume that the polarization effects are small and derive conservation laws for the net baryon current, the energy–momentum tensor and the spin tensor based on the de Groot–van Leeuwen–van Weert definitions of these currents. We present various properties of the spin polarization tensor and its components, analyze the propagation properties of the spin polarization components, and derive the spin-wave velocity for arbitrary statistics. We find that only the transverse spin components propagate, analogously to the electromagnetic waves. Finally, using our framework, we study the space–time evolution of the spin polarization for the systems respecting certain space–time symmetries and calculate the mean spin polarization per particle, which can be compared to the experimental data. We find that, for some observables, our spin polarization results agree qualitatively with the experimental findings and other model calculations.

Electrically triggered spin reversal and precise control of spin polarization for electron transport at the single-molecule level

Different from conventional ferromagnetic methods, producing a spin-polarized current through electrical ways in spintronic devices can greatly increase operating speed, reduce power consumption, and improve device integration. Inspired by recent experimental progress on the synthesis of a heptauthrene molecule, we investigate its spin-dependent transport contacted with Au electrodes through first-principles calculations. By applying a gate voltage, the transmission can be switched between completely spin-up and spin-down polarized states, achieving an electrically controlled dual-spin filter. Furthermore, a fine tuning on the spin polarization, between 100% and −100%, can also be realized, where the transport with any ratio of spin-up to spin-down electron quantities can be realized beyond the traditional devices. The peculiar transmission spectra and their shift are found to play crucial roles, where transmission peaks distribute on both sides of the Fermi level with opposite spin components. Such a spin-polarization modulating effect is found to be robust to the molecule-electrode contacting site, indicating it is an intrinsic feature of such systems. Moreover, the dimension of the device is at the single-molecule level, suggesting great application potential.

Methods for Obtaining One Single Larmor Frequency, Either v1 or v2, in the Coherent Spin Dynamics of Colloidal Quantum Dots.

The coexistence of two spin components with different Larmor frequencies in colloidal CdSe and CdS quantum dots (QDs) leads to the entanglement of spin signals, complicating the analysis of dynamic processes and hampering practical applications. Here, we explored several methods, including varying the types of hole acceptors, air or anaerobic atmosphere and laser repetition rates, in order to facilitate the obtention of one single Larmor frequency in the coherent spin dynamics using time-resolved ellipticity spectroscopy at room temperature. In an air or nitrogen atmosphere, manipulating the photocharging processes by applying different types of hole acceptors, e.g., Li[Et3BH] and 1-octanethiol (OT), can lead to pure spin components with one single Larmor frequency. For as-grown QDs, low laser repetition rates favor the generation of the higher Larmor frequency spin component individually, while the lower Larmor frequency spin component can be enhanced by increasing the laser repetition rates. We hope that the explored methods can inspire further investigations of spin dynamics and related photophysical processes in colloidal nanostructures.

Spin contribution to the inverse Faraday effect of nonmagnetic metals

We formulate the spin contribution to the inverse Faraday effect of non-magnetic metals. We deal with the role of the inversion symmetry, which forces all electronic bands to be at least twice degenerate at every point in the Brillouin zone. We show both analytically and numerically that our formulation of the inverse Faraday effect is invariant under unitary rotation within the doubly degenerate set of bands. In addition, we show the importance of resonance-like features in the band structure for the inverse Faraday effect. Our first-principles computed spin component of the inverse Faraday effect in a simple metal such as Au is reminiscent of its optical absorption, with a characteristic d-s resonance in the optical spectrum.

Spin polarization induced by decoherence in a tunneling one-dimensional Rashba model

Basic questions on the nature of spin polarization in two terminal systems and the way in which decoherence breaks Time-Reversal Symmetry (TRS) are analyzed. We exactly solve several one-dimensional models of tunneling electrons and show the interplay of spin precession and decay of the wavefunction in either a U(1)U(1) magnetic field or an effective Spin-Orbit (SO) magnetic field. Spin polarization is clearly identified as the emergence of a spin component parallel to either magnetic field. We show that Onsager’s reciprocity is fulfilled when time reversal symmetry is present and no spin polarization arises, no matter the barrier parameters or the SO strength. Introducing a Büttiker’s decoherence probe, that preserves unitarity of time evolution, we show that breaking of TRS results in a strong spin polarization for realistic SO, and barrier strengths. We discuss the significance of these results as a very general scenario for the onset of the Chiral-Induced Spin Selectivity effect (CISS).

Many-body correlations in one-dimensional optical lattices with alkaline-earth(-like) atoms

We explore the rich nature of correlations in the ground state of ultracold atoms trapped in state-dependent optical lattices. In particular, we consider interacting fermionic ytterbium or strontium atoms, realizing a two-orbital Hubbard model with two spin components. We analyze the model in one-dimensional setting with the experimentally relevant hierarchy of tunneling and interaction amplitudes by means of exact diagonalization and matrix product states approaches, and study the correlation functions in density, spin, and orbital sectors as functions of variable densities of atoms in the ground and metastable excited states. We show that in certain ranges of densities these atomic systems demonstrate strong density-wave, ferro- and antiferromagnetic, as well as antiferroorbital correlations.

Modelling, control and simulation of a single rotor UAV with swashplateless torque modulation

Single rotor-base unmanned aerial vehicles (UAVs) represent the most minimalistic design to implement an aerial vehicle. We describe here a mono-rotor UAV, also named mono-spinner, that uses torque modulation (also called swashplateless mechanism) to provide roll and pitch control without the need of a complicated swashplate mechanism. A full non-linear model of the mono-spinner based on the Euler-Poincaré theoretical framework is given including a description of the structure of the drone and its rotor control system. Mechanical properties, kinetic energy and all of the external forces of interest to derive the equations of motion are described. A novel, Lyapunov-stable, quaternion-based nonlinear control law based on the decomposition of the orientation quaternion into a spin component and a reduced orientation component is provided. Finally, simulation results based on parameters measured from a real implementation of a mono-spinner are produced.

Spin-orbit optical Hall effect in π-vector fields.

Given the tremendous increase of data in digital era, vector vortex light with strongly coupled spin and orbital angular momenta of photons have attracted great attention for high-capacity optical applications. To fully utilize such rich degrees of freedom of light, it is highly anticipated to separate the coupled angular momentum with a simple but powerful method, and the optical Hall effect becomes a promising scheme. Recently, the spin-orbit optical Hall effect has been proposed in terms of general vector vortex light using two anisotropic crystals. However, angular momentum separation for π-vector vortex modes, another important part in vector optical fields, have not been explored and it remains challenging to realize broadband response. Here, the wavelength-independent spin-orbit optical Hall effect in π-vector fields has been analyzed based on Jones matrices and verified experimentally using a single-layer liquid-crystalline film with designed holographic structures. Every π-vector vortex mode can be decoupled into spin and orbital components with equal magnitude but opposite signs. Our work could enrich the fields of high-dimensional optics.

Spin-statistics relation and Abelian braiding phase for anyons in the fractional quantum Hall effect

Quasihole excitations in fractional quantum Hall (FQH) systems exhibit fractional statistics and fractional spin, but how the spin-statistics relation emerges from many-body physics remains poorly understood. Here we prove a spin-statistics relation using only FQH wave functions, on both the sphere and disk geometry. In particular, the proof on the disk generalizes to all quasiholes in realistic systems, which have a finite size and could be deformed into arbitrary shapes. Different components of the quasihole spins are linked to different conformal Hilbert spaces (CHS), which are nullspaces of model Hamiltonians that host the respective FQH ground states and quasihole states. Understanding how the intrinsic spin of the quasiholes is linked to different CHS is crucial for the generalized spin-statistics relation that takes into account the effect of metric deformation. In terms of the experimental relevance, this enables us to study the effect of deformation and disorder that introduces an additional source of Berry curvature, an aspect of anyon braiding that has been largely neglected in previous literature.