Helical Spin Research Articles

The Loop Momentum Amplituhedron

In this paper we focus on scattering amplitudes in maximally supersymmetric Yang-Mills theory and define a long sought-after geometry, the loop momentum amplituhedron, which we conjecture to encode tree and (the integrands of) loop amplitudes in spinor helicity variables. Motivated by the structure of amplitude singularities, we define an extended positive space, which enhances the Grassmannian space featuring at tree level, and a map which associates to each of its points tree-level kinematic variables and loop momenta. The image of this map is the loop momentum amplituhedron. Importantly, our formulation provides a global definition of the loop momenta. We conjecture that for all multiplicities and helicity sectors, there exists a canonical logarithmic differential form defined on this space, and provide its explicit form in a few examples.

All plus four point (A)dS graviton function using generalized on-shell recursion relation

This paper presents a calculation of the four gravitons amplitude in (Anti)-de Sitter space, focusing specifically on external gravitons with positive helicity. To achieve this, we employ a generalized recursion method that involves complexifying all external momentum of the graviton function, which results in the factorization of AdS graviton amplitudes and eliminates the need for Feynman-Witten diagrams. Our calculations were conducted in three boundary dimensions, with a particular emphasis on exploring cosmology and aiding the cosmological bootstrap program. To compute the expression, we utilized the three-dimensional spinor helicity formalism. The final expression was obtained by summing over residues of physical poles, and we present both symbolic and numerical results. Additionally, we discuss the advantages and limitations of this approach, and highlight potential opportunities for future research.

Two copies of spin helices with stretching pitch and compensating helicity

Persistent spin helix (PSH) manifests itself as an effective knob to tackle spin decay inevitably occurring in disordered two-dimensional electron gases. Here, for ordinary (110)-oriented two-subband GaInAs wells subjected to top and back gate voltages, we theoretically achieve adjusting the Dresselhaus terms of the two bands while meanwhile consistently pinning the system at symmetric configuration [i.e., locking the Rashba spin-orbit (SO) terms to zero], thus enabling simultaneous formation of two copies of PSHs of flexible control. Strikingly, we are able to stretch the pitch---spin density wave length---of PSH by far more than one period, enabling helix-stretch functional spin field-effect transistor (FET), with both on and off states protected by the PSH symmetry. Moreover, we attain a scenario in which the helicities of the two copies of PSHs are sufficiently compensated. This makes possible a new concept: ``orbit (band) filter,'' which resembles spin FET while with novel functionality of orbit filtering, opening up a new route towards spintronic and orbitronic combined applications.

Tuning spin-orbit coupling and realizing inverse persistent spin helix by an extra above-barrier radiation in a GaAs/Al0.3Ga0.7As heterostructure.

A persistent spin helix with equal strength of the Rashba and Dresselhaus spin-orbit coupling (SOC) is expected for future spintronic devices due to the suppression of spin relaxation. In this work we investigate the optical tuning of the Rashba and Dresselhaus SOC by monitoring the spin-galvanic effect (SGE) in a GaAs/Al0.3Ga0.7As two dimensional electron gas. An extra control light above the bandgap of the barrier is introduced to tune the SGE excited by a circularly polarized light below the bandgap of GaAs. We observe different tunability of the Rashba- and Dresselhaus-related SGE currents and extract the ratio of the Rashba and Dresselhaus coefficients. It decreases monotonously with the power of the control light and reaches a particular value of ∼-1, implying the formation of the inverse persistent spin helix state. By analyzing the optical tuning process phenomenologically and microscopically, we reveal greater optical tunability of the Rashba SOC than that of the Dresselhaus SOC.

4D flat-space scattering amplitude/CFT3 correlator correspondence revisited

In this paper, we make connection between CFT3 three point correlation function of conserved currents and 4D three point amplitude of general spin massless gauge field explicit. We do so by taking flat space limit of momentum space CFT correlation function and show how they reproduce flat space amplitudes. We then point out a mismatch between number of independent structures in 3D CFT correlator of conserved currents and 4D flat space covariant vertex of massless higher spin fields. This is in contrast with general expectation that counting of 3d CFT correlator and 4d flat space amplitude should match. This mismatch is even more pronounced in spinor helicity variables.We also point out an interesting relation between parity even and parity odd flat space amplitude in momentum space. This observation helps us to construct a new momentum space CFT structure which accounts for the mismatch. However we should mention that this extra CFT structure can't be constructed out of conserved currents and hence counting mismatch between CFT correlation of conserved currents and flat space amplitude of massless gauge field persists. Story in spinor helicity variable is more complicated and is discussed in detail. We further comment on the connection of CFT correlation function in spinor helicity variables to AdS amplitudes in spinor helicity variables and light cone variables.

Magnetic excitations in the helical Rashba superconductor

We investigate the magnetic excitation spectrum in the helical state of a noncentrosymmetric superconductor with inversion symmetry breaking and strong Rashba spin–orbit coupling. For this purpose we derive the general expressions of the dynamical spin response functions under the presence of strong Rashba splitting of conduction bands, superconducting gap and external field which lead to stabilization of Cooper pairs with finite overall momentum in a helical state. The latter is characterized by momentum space regions of paired and unpaired states with different quasiparticle dispersions. The magnetic response is determined by i) excitations within and between both paired and unpaired regions ii) anomalous coherence factors and iii) additional spin matrix elements due to helical Rashba spin texture of bands. We show that as a consequence typical correlated real space and spin space anisotropies appear in the dynamical susceptibility which would be observable as a characteristic fingerprint for a helical superconducting state in inelastic neutron scattering investigations.

Topological dynamical quantum phase transition in a quantum skyrmion phase

The quantum skyrmionic phase is modeled in a two-dimensional helical spin lattice. This topological skyrmionic phase retains its nature in a large parameter space before moving to a ferromagnetic phase. Next-nearest-neighbor interaction improves the stability and it also causes a shift of the topological phase in the parameter space. Nonanalytic behavior of the rate function observed, when the system which is initially in a quantum skyrmion phase is quenched to a trivial quantum ferromagnetic phase, indicates a dynamical quantum phase transition. Dynamical quantum phase transition is absent when the system initially in a skyrmion phase is quenched to a helical phase.

Stripe helical magnetism and two regimes of anomalous Hall effect in NdAlGe

We report the magnetic and electronic transport properties of the inversion and time-reversal symmetry breaking Weyl semimetal NdAlGe. This material is analogous to NdAlSi, whose helical magnetism presents a rare example of a Weyl-mediated collective phenomenon, but with a larger spin-orbit coupling. Our neutron diffraction experiments revealed that NdAlGe, similar to NdAlSi, supports an incommensurate Ising spin density wave ($T_{\text{inc}}=6.8$ K) with a small helical spin canting of 3$^\circ$ and a long-wavelength of $\sim$ 35 nm, which transitions to a commensurate ferrimagnetic state below $T_{\text{com}}=5.1$ K. Using small-angle neutron scattering, we showed that the zero-field cooled ferrimagnetic domains form stripes in real space with characteristic length scales of 18 nm and 72 nm parallel and perpendicular to the [110] direction, respectively. Interestingly, for the transport properties, NdAlSi does not exhibit an anomalous Hall effect (AHE) that is commonly observed in magnetic Weyl semimetals. In contrast to NdAlSi, we identify two different AHE regimes in NdAlGe that are respectively governed by intrinsic Berry curvature and extrinsic disorders/spin fluctuations. Our study suggests that Weyl-mediated magnetism prevails in this group of noncentrosymmetric magnetic Weyl semimetals NdAl$X$, but transport properties including AHE are affected by material-specific extrinsic effects such as disorders, despite the presence of prominent Berry curvature.

Imprinting Spatial Helicity Structure of Vector Vortex Beam on Spin Texture in Semiconductors

We present the transfer of the spatially variant polarization of topologically structured light to the spatial spin texture in a semiconductor quantum well. The electron spin texture, which is a circular pattern with repeating spin-up and spin-down states whose repetition rate is determined by the topological charge, is directly excited by a vector vortex beam with a spatial helicity structure. The generated spin texture efficiently evolves into a helical spin wave pattern owing to the spin-orbit effective magnetic fields in the persistent spin helix state by controlling the spatial wave number of the excited spin mode. By tuning the repetition length and azimuthal angle, we simultaneously generate helical spin waves with opposite phases by a single beam.

Transformation from Magnetic Soliton to Skyrmion in a Monoaxial Chiral Magnet.

Topological spin textures are of great interest for both fundamental physics and applications in spintronics. The Dzyaloshinskii-Moriya interaction underpins the formation of single-twisted magnetic solitons or multi-twisted magnetic skyrmions in magnetic materials with different crystallographic symmetries. However, topological transitions between these two kinds of topological objects have not been verified experimentally. Here, the direct observation of transformations from a chiral soliton lattice (CSL) to magnetic skyrmions in a nanostripe of the monoaxial chiral magnet CrNb3 S6 using Lorentz transmission electron microscopy is reported. In the presence of an external magnetic field, helical spin structures first transform into CSLs and then evolve into isolated elongated magnetic skyrmions. The detailed spin textures of the elongated magnetic skyrmions are resolved using off-axis electron holography and are shown to comprise two merons, which enclose their ends and have unit total topological charge. Magnetic dipolar interactions are shown to play a key role in the magnetic soliton-skyrmion transformation, which depends sensitively on nanostripe width. The findings here, which are consistent with micromagnetic simulations, enrich the family of topological magnetic states and their transitions and promise to further stimulate the exploration of their emergent electromagnetic properties.

Surface-induced ferromagnetism and anomalous Hall transport at Zr2S(001)

Two-dimensional layered electrides possessing anionic excess electrons in the interstitial spaces between cationic layers have attracted much attention due to their promising opportunities in both fundamental research and technological applications. Using first-principles calculations, we predict that the layered bulk electride ${\mathrm{Zr}}_{2}\mathrm{S}$ is nonmagnetic with massive Dirac nodal-line states arising from $\mathrm{Zr}\text{\ensuremath{-}}4d$ cationic and interlayer anionic electrons. However, the ${\mathrm{Zr}}_{2}\mathrm{S}(001)$ surface increases the density of states at the Fermi level due to the surface potential, thereby inducing a ferromagnetic order at the outermost Zr layer via the Stoner instability. Consequently, the time-reversal symmetry breaking at the surface not only generates spin-polarized topological surface states with intricate helical spin textures but also hosts an intrinsic anomalous Hall effect originating from the Berry curvature generated by spin-orbit coupling. Our findings offer a playground to investigate the emergence of ferromagnetism and anomalous Hall transport at the surface of nonmagnetic topological electrides.

Raman laser induced self-organization with topology in a dipolar condensate.

We investigate the ground states of a dipolar Bose-Einstein condensate (BEC) subject to Raman laser induced spin-orbit coupling with mean-field theory. Owing to the interplay between spin-orbit coupling and atom-atom interactions, the BEC presents remarkable self-organization behavior and thus hosts various exotic phases including vortex with discrete rotational symmetry, stripe with spin helix, and chiral lattices with C4 symmetry. The peculiar chiral self-organized array of square lattice, which spontaneously breaks both U(1) and rotational symmetries, is observed when the contact interaction is considerable in comparison with the spin-orbit coupling. Moreover, we show that the Raman-induced spin-orbit coupling plays a crucial role in forming rich topological spin textures of the chiral self-organized phases by introducing a channel for atoms to turn on spin flipping between two components. The self-organization phenomena predicted here feature topology owing to spin-orbit coupling. In addition, we find long-lived metastable self-organized arrays with C6 symmetry in the case of strong spin-orbit coupling. We also present a proposal to observe these predicted phases in ultracold atomic dipolar gases with laser-induced spin-orbit coupling, which may stimulate broad theoretical as well as experimental interest.

Anisotropy of Electronic Spin Texture in the High-Temperature Cuprate Superconductor Bi2Sr2CaCu2O8+δ

Seeking new order parameters and the related broken symmetry and studying their relationship with phase transition have been important topics in condensed matter physics. Here, by using spin- and angle-resolved photoemission spectroscopy, we confirm the helical spin texture caused by spin-layer locking in the nodal region in the cuprate superconductor Bi2Sr2CaCu2O8+δ and discover the anisotropy of spin polarizations at nodes along Γ–X and Γ–Y directions. The breaking of C 4 rotational symmetry in electronic spin texture may give deeper insights into understanding the ground state of cuprate superconductors.

A New Route to Symmetries through the Extended Dirac Equation

A new route to the Dirac equation and its symmetries is outlined on the basis of the four-vector representation of the Lorentz group (LG). This way permits one to linearize the first Casimir operator of the LG in terms of the energy–momentum four-vector and enables one to derive an extended Dirac equation that naturally reveals the SU(2) symmetry in connection with an isospin associated with the LG. The procedure gives a spin-one-half fermion doublet, which we interpret as the electron and neutrino or the up-and-down quark doublet. Similarly, the second Casimir operator can be linearized by invoking an abstract isospin that is not connected with the LG, but with the two basic empirical fermion types. Application of the spinor helicity formalism yields two independent singlet and triplet fermion states—which we interpret as being related to U(1) and the lepton, respectively—to the SU(3) symmetry group of the three colors of the quarks. The way in which we obtain these results indicates the genuine yet very different physical natures of these basic symmetries. This new notion does not need the idea of grand unification. However, by still combining them in the product group SU(4)=SU(3)⊗U(1) and then further combining all groups into SU(2)⊗SU(4), one may get a symmetry scheme that perhaps supports the notion of unification by the group SU(8). We also argue that the simpler SO(4) group—instead of SU(4)—seems more appropriate for achieving unification.

Persistent spin helix on a diamond surface

Using first-principles calculations, we determine the impact of hydroxyl (OH) termination on the spin–orbit coupling (SOC) coefficient and spin texture of diamond surfaces. The persistent spin helix (PSH) state is revealed in the OH-terminated diamond (111) surface. The value of coefficient PSH α PSH was 14.2 meV·Å, which is larger than that of the zinc-blende n-type quantum well of GaAs/AlGaAs. The large α PSH is caused by the asymmetric charge density distribution near the surface rather than the size of the atomic SOC. The large α PSH will ensure the wavelength of PSH (λ PSH ), which will aid in the miniaturization of spintronic devices.

Strain engineering a persistent spin helix with infinite spin lifetime

Persistent spin textures (PSTs) in solid-state materials arise from a unidirectional spin-orbit field in momentum space and offer a route to deliver long carrier spin lifetimes sought for future quantum microelectronic devices. Nonetheless, few three-dimensional materials are known to host PSTs owing to crystal symmetry and chemical requirements. There are even fewer examples demonstrated experimentally. Here we report that high-quality persistent spin textures can be obtained in the polar point groups containing an odd number of mirror operations. We use representation theory analysis and electronic structure calculations to formulate general discovery principles to identify PSTs hidden in known complex ternary layered and perovskite structures with large electric polarizations. We then show some of these materials exhibit PSTs without requiring any special crystalline symmetries. This finding removes the limitation imposed by mirror-symmetry protected PSTs that has limited compound discovery. Our general design approach enables the pursuit of persistent spin helices in materials exhibiting the $C_{3v}$ crystal class adopted by many quantum materials exhibiting large Rashba coefficients.

Doping control of magnetism and emergent electromagnetic induction in high-temperature helimagnets

Ac current-driven motions of spiral spin textures can give rise to emergent electric fields acting on conduction electrons. This in turn leads to the emergent electromagnetic induction effect which may realize quantum inductor elements of micrometer size. ${\rm YMn}_{6}{\rm Sn}_{6}$ is a helimagnet with a short helical period (2-3 nm) that shows this type of emergent inductance beyond room temperature. To identify the optimized materials conditions for ${\rm YMn}_{6}{\rm Sn}_{6}$-type room-temperature emergent inductors, we have investigated emergent electromagnetic inductance (EEMI) as the magnetism is modified through systematic partial substitution of Y by Tb. By small angle neutron scattering and inductance measurements, we have revealed that the pinning effect on the spin-helix translational mode by Tb doping selectively and largely suppresses the negative component of EEMI, while sustaining the positive inductance arising from the spin tilting mode. We also find that in addition to the spin helix, even the spin-collinear antiferromagnetic structure can host the positive EEMI due to thermally enhanced spin fluctuations. The present study highlights the facile control of both the magnitude and sign of EEMI beyond room temperature, and thus suggests a route to expand the range of emergent inductor candidate materials.

Theoretical insight of origin of Rashba-Dresselhaus effect in tetragonal and rhombohedral phases of BiFeO3.

The inclusion of the spin-orbit coupling effect in ferroelectric materials with non-centrosymmetry leads to intriguing properties for spintronic applications. In the present work, a comparative study of spin splitting in the bulk electronic energy bands of the tetragonal and rhombohedral phases of BiFeO3 (BFO) in terms of the Rashba and Dresselhaus effects is carried out through first-principles calculations. The obtained spin splittings, particularly at the conduction band minima, are further supplemented with an effective k·p model analysis. For the tetragonal BFO, a dominating pure bulk-type Rashba effect with helical in-plane spin components shown through diagrams is observed, whereas the rhombohedral BFO shows a significant contribution from the out-of-plane spin components and an interplay between the Rashba and Dresselhaus effects is discussed. In addition, tunability of the Rashba parameters with the application of uniaxial strain (±5%) is obtained in tetragonal BFO, in which the Rashba coefficient (αR) doubles with a compressive 5% strain, making tetragonal BFO a suitable candidate for spintronic applications. More importantly, full reversal of the in-plane spin texture is obtained for the opposite polarization states in tetragonal BFO with an activation energy barrier of 1.13 eV.

Cooperativity and reactivity properties of medium-sized boron clusters: a combined density functional theory and information-theoretic approach study

In continuation of our previous work of small boron clusters [Phys. Chem. Chem. Phys. 23, 24118 (2021)], we systematically examined the neutral and negatively charged boron clusters B n /B − (nε{8–38}) with planar or quasi-planar conformations, whose exotic properties have aroused considerable interest in the literature. We make use of two total energy partition schemes, conceptual density functional theory, and the information-theoretic approach to appreciate the cooperativity and reactivity properties. We found that neutral boron clusters are positively cooperative, but negatively charged boron clusters are negatively cooperative. Our results show that the origin of the cooperativity effect for the negatively cooperative boron clusters is much more complicated than the neutral boron clusters. For chemical reactivity, we unveil that the reactive sites are around the cluster periphery and boron atoms can be both electrophilic and nucleophilic. Global and local aromaticity for the boron clusters can be totally different. For the first time, we have observed helical spin density distributions for negatively charged boron clusters (B16 – and B20 – ), which is reminiscent of helical molecular orbitals [Chem. Sci. 4, 4278 (2013)] in allenes, cumulenes, and oligoynes (polyalkynes). Collectively, our results should provide more insights to understand the exotic properties of boron clusters and henceforth yield novel potential applications.

Non-collinear magnetic configuration mediated exchange coupling at the interface of antiferromagnet and rare-earth nanolayers

Mn_{3}Ir/CoFe bilayer is a prototypical exchange-coupled antiferromagnet (AF)–ferromagnet (FM) system. Nevertheless, a strong exchange coupling between FM and rare-earth(RE) interfaces of Fe/Dy and Fe/Tb has been established earlier. Strong coupling at the FM–RE interface originates from the number of irreversible spins owing to the imbalance in the non-collinear configuration in RE. However, exchange coupling between AF–RE could not be established due to the minimal number of irreversible spins in AF and RE. A frustrated inter-domain magnetic interaction leads to the coexistence of spin-freezing-like ordering around the temperature range of helical spin modulation at the exchange-coupled interfaces of RE-based specimens. To overcome the lack of coupling between the AF–RE interface, we use a sandwich structure of AF–FM–RE layers (Mn_{3}Ir/CoFe/Dy) as we demonstrate establishing considerable exchange bias in the system. Changing the bias direction during field cooling introduces possible differences in non-collinear directions (helicities), which affects the number of irreversible spins and consequent exchange coupling differently for opposite directions. The non-collinear structures in RE are topologically stable; thus, their directions of orientation can be regarded as an additional degree of freedom, which can be manipulated in all-spin-based technology.