Helical Spin Research Articles

Spin Spiral State at a Ferromagnetic Gd Vacuum Interface.

Centrosymmetric bulk magnets made of layered Gd intermetallics had been discovered recently to exhibit helical spin spirals with a wavelength of ≈2 nm that transform into skyrmion lattices at certain magnetic fields. Here we report on the observation of a spin spiral state at the Gd(0001) surface. Spin-polarized scanning tunneling microscopy images show striped regions with a periodicity of about 2nm. These stripes rearrange upon application of an external magnetic field, thereby unambiguously confirming their magnetic origin. Density functional theory calculations explain that competing exchange interactions in the surface layer of Gd(0001) together with a magnetovolume fine-tuning of the exchange interaction to the next Gd layer favor a chiral 2nm conical spin spiral at the surface, arising as a general behavior of the Gd monolayer.

Selective Rashba spin–orbit coupling manipulation in triple quantum wells

We explore the Rashba (α) spin–orbit coupling (SOC) manipulation in AlInSb/InSb triple quantum wells (QWs) with three subbands occupied in the presence of the external gate voltage V b . Diverse behaviors of α can be demonstrated by adjusting the structural parameters of the wells, which is greatly desirable for the design of multifunctional QW-based spintronic devices. Specifically, the first (lowest) subband always has larger Rashba coupling against the variations in the structural parameters and V b than the other subbands, conducive to spin detection. α ν s (ν = 1, 2, 3 is the subband index) of the second and third subbands take on dual (magnitude and sign) change owing to the regulation of the inner barrier height δ, may facilitating the realization of stretchable persistent spin helix in multiple QWs. Strikingly, α 3 can keep essentially zero in a wide gate range corresponding to asymmetrical QW structural configurations, by adjusting δ. However, when widening the well to a certain extent the δ-dependence of α become fixed, i.e. ∣α 1∣ > ∣α 2∣ > ∣α 3∣ maintains in wide triple-well systems. All these findings may shed light on selective and precise SOC control in QW systems for experiments.

Visualization of Unconventional Rashba Bands and Vortex Zero Mode in the Topological Superconductor Candidate AuSn4.

The noble metal alloy AuSn4 has recently been identified as an intrinsic surface topological superconductor, promisingly hosting the Majorana zero mode (MZM) for topological quantum computing. However, the atomic visualization of its nontrivial surface states and MZM remains elusive. Here, we report the direct observation of unconventional surface states and vortex zero mode in AuSn4 by scanning tunneling microscopy/spectroscopy. Unlike the trivial metallic bulk states of Sn-terminated surfaces, the Au-terminated surfaces exhibit pronounced surface states near the Fermi level, arising from unconventional Rashba bands characterized by shared helical spin textures. In the superconducting state, the Sn-terminated surfaces exhibit conventional Caroli-de Gennes-Matricon bound states, while the Au-terminated surfaces display sharp zero-energy core states resembling MZMs in a nonquantum-limit condition. This distinction may result from the dominant contribution of unconventional Rashba bands on the Au-terminated surface. Our results provide a new platform for studying termination-dependent topological surface states and MZM in noble-metal-based superconductors.

Spontaneous reversal of spin chirality and competing phases in the topological magnet EuAl4

AbstractMaterials exhibiting a spontaneous reversal of spin chirality have the potential to drive the widespread adoption of chiral magnets in spintronic devices. Unlike the majority of chiral magnets that require the application of an external field to reverse the spin chirality, we observe the spin chirality to spontaneously reverse in the topological magnet EuAl4. Using resonant elastic x-ray scattering we demonstrate that all four magnetic phases in EuAl4 are single-k, where the first two magnetic phases are characterized by spin density wave order and the last two by helical spin order. A single spin chirality was stabilised across the 1mm2 sample, and the reversal of spin chirality occurred whilst maintaining a helical magnetic structure. At the onset of the helical magnetism, the crystal symmetry lowers to a chiral monoclinic space group, explaining the asymmetry in the chiral spin order, and establishing a mechanism by which the spin chirality could reverse via magnetostructural coupling.

Magnetic properties and helical spin structure of another compound Ca3SbFe3Si2O14 from the family of iron-containing langasites

A strong interest is attracted to the langasite-type compounds containing magnetic 3d ions. Coexistence of electric and magnetic order parameters in such materials can provide a new variety of multiferroics. In our work, another Fe-based langasite with a nearly stoichiometric composition Ca3SbFe3Si2O14 was synthesized. X-ray diffraction and X-ray fluorescence analyses, studies of magnetic susceptibility, specific heat and Mössbauer spectroscopy were performed. The crystal structure of Ca3SbFe3Si2O14 (CSFS) was found to be hexagonal, space group P321. From full-profile analysis by the Le Bail method, the lattice parameters a = 8.115(1) Å, c = 5.058(1) Å, V = 288.4(1) Å3 were determined. The temperature dependence of magnetic susceptibility χ(Т) indicates the formation of long-range magnetic order at temperatures below TN = 34 K. The negative value of Weiss temperature θCW indicates the domination of antiferromagnetic exchange interaction. From the value of the Curie constant, the effective magnetic moment per Fe3+ ion µeff = 6.12 µB was estimated, which is slightly higher than the expected value 5.9 µB for the 3d5 - S = 5/2 state of iron. Measurements of the specific heat allowed a Debye temperature value ΘD = 390(10) K to be obtained. Based on the assessment of the magnetic contribution to the specific heat, the value of magnetic entropy ΔSmag ∼ 47.8 ± 5.6 J/mol K was determined. Hyperfine interaction parameters obtained from Mössbauer spectra indicate a helical magnetic ordering of iron moments in langasite Ca3SbFe3Si2O14. The period of a magnetic helicoid is about five periods of the crystal structure along the c axis. The calculated value of the angle (α) between the main axis of the electric field gradient Z′ at iron nuclei and the crystallographic c axis (67.2°) is significantly greater than in other langasites Ba3SbFe3Si2O14 (28.8°), Ba3NbFe3Si2O14 (36°), Ba3TaFe3Si2O14 (34.8°). This may be due to the more contracted FeO4 tetrahedra in CSFS compared to those in the other compositions.

A foray on SCFT3 via super spinor-helicity and Grassmann twistor variables

In this paper, we develop a momentum super space formalism for N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1, 2 superconformal field theories in three dimensions. First, we solve for super-correlators in the usual momentum superspace variables. However, we found that expressing quantities in super space spinor helicity variables greatly simplifies the analysis. Further, by performing a “half” Fourier transform of the Grassmann coordinates which is analogous to the Twistor transform, an even more remarkable simplification occurs. Using this formalism, we first compute all three point correlation functions involving conserved super-currents with arbitrary spins in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1, 2 theories. We discover interesting double copy relations in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 super-correlators. Further, we discovered super double copy relations that take us from N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 to N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 super-correlators. We also extend our results to correlators involving scalars as well as to higher points. Further, we comment on the connection of our results with the flat space super amplitudes in one higher dimension.

Multimodal Approach Reveals the Symmetry-Breaking Pathway to the Broken Helix in EuIn2As2

Understanding and manipulating emergent phases, which are themes at the forefront of quantum-materials research, rely on identifying their underlying symmetries. This general principle has been particularly prominent in materials with coupled electronic and magnetic degrees of freedom, in which magnetic order influences the electronic band structure and can lead to exotic topological effects. However, identifying symmetry of a magnetically ordered phase can pose a challenge, particularly in the presence of small domains. Here we introduce a multimodal approach for determining magnetic structures, which combines symmetry-sensitive optical probes, scattering, and group-theoretical analysis. We apply it to EuIn2As2, a material that has received attention as a candidate axion insulator. While first-principles calculations predict this state on the assumption of a simple collinear antiferromagnetic structure, subsequent neutron-scattering measurements reveal a much more intricate magnetic ground state characterized by two coexisting magnetic wave vectors reached by successive thermal phase transitions. The proposed high- and low-temperature phases are a spin helix and a state with interpenetrating helical and Néel antiferromagnetic order termed a “broken helix,” respectively. Employing a multimodal approach, we identify the magnetic structure associated with these two phases of EuIn2As2. We find that the higher-temperature phase is characterized by a variation of the magnetic moment amplitude from layer to layer, with the moment vanishing entirely in every third Eu layer. The lower-temperature structure is similar to the broken helix, with one important difference: Because of local strain, the relative orientation of the magnetic structure and the lattice is not fixed. Consequently, the symmetry required to protect the axion phase is not generically protected in EuIn2As2, but we show that it can be restored if the magnetic structure is tuned with uniaxial strain. Finally, we present a spin Hamiltonian that identifies the spin interactions that account for the complex magnetic order in EuIn2As2. Our work highlights the importance of a multimodal approach in determining the symmetry of complex order parameters. Published by the American Physical Society 2024

Giant chiral magnetoelectric oscillations in a van der Waals multiferroic

Helical spin structures are expressions of magnetically induced chirality, entangling the dipolar and magnetic orders in materials1–4. The recent discovery of helical van der Waals multiferroics down to the ultrathin limit raises prospects of large chiral magnetoelectric correlations in two dimensions5,6. However, the exact nature and magnitude of these couplings have remained unknown so far. Here we perform a precision measurement of the dynamical magnetoelectric coupling for an enantiopure domain in an exfoliated van der Waals multiferroic. We evaluate this interaction in resonance with a collective electromagnon mode, capturing the impact of its oscillations on the dipolar and magnetic orders of the material with a suite of ultrafast optical probes. Our data show a giant natural optical activity at terahertz frequencies, characterized by quadrature modulations between the electric polarization and magnetization components. First-principles calculations further show that these chiral couplings originate from the synergy between the non-collinear spin texture and relativistic spin–orbit interactions, resulting in substantial enhancements over lattice-mediated effects. Our findings highlight the potential for intertwined orders to enable unique functionalities in the two-dimensional limit and pave the way for the development of van der Waals magnetoelectric devices operating at terahertz speeds.

Large-Gap and Topological Crystalline Insulating Phase in RbZnBi and CsZnBi.

Topological insulators (TIs) are a new class of materials with gapless boundary states inside the bulk insulating gap. This metallic boundary state hosts intriguing phenomena such as helical spin textures and Dirac crossing points. Here, we theoretically propose RbZnBi and CsZnBi as a new family of TIs exhibiting large bulk band gaps and unique gapless surface states. Our first-principles density functional calculations show that two materials can be stabilized in two different structures depending on the stacking order of hexagonal ZnBi layers. While both materials in the AA-stacked structure become TI, the AB-stacked RbZnBi and CsZnBi are topological crystalline insulators with hourglass-shaped Fermion surface states protected by nonsymmorphic glide symmetry. The calculated bulk gap is about 1.5-1.8 times larger than that of Bi2Se3, which makes RbZnBi and CsZnBi promising candidates for future applications.

Ward identities for superamplitudes

We introduce Ward identities for superamplitudes in D-dimensional N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document}-extended supergravities. These identities help to clarify the relation between linearized superinvariants and superamplitudes. The solutions of these Ward identities for an n-partice superamplitude take a simple universal form for half BPS and non-BPS amplitudes. These solutions involve arbitrary functions of spinor helicity and Grassmann variables for each of the n superparticles. The dimension of these functions at a given loop order is exactly the same as the dimension of the relevant superspace Lagrangians depending on half-BPS or non-BPS superfields, given by (D − 2)L + 2 − N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} or (D − 2)L + 2 − 2N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ 2\\mathcal{N} $$\\end{document}, respectively. This explains why soft limits predictions from superamplitudes and from superspace linearized superinvariants agree.

Spinor-helicity representations of particles of any mass in dS4 and AdS4 spacetimes

The spinor-helicity representations of massive and (partially) massless particles in four-dimensional (anti–)de Sitter (A)dS spacetime are studied within the framework of the dual pair correspondence. We show that the dual groups (also known as “little groups”) of the anti–de Sitter and de Sitter groups are, respectively, O(2N) and O*(2N). For N=1, the generator of the dual algebra so(2)≅so*(2)≅u(1) corresponds to the helicity operator, and the spinor-helicity representation describes massless particles in (A)dS4. For N=2, the dual algebra is composed of two ideals, s and mΛ. The former ideal s≅so(3) fixes the spin of the particle, while the mass is determined by the latter ideal mΛ, which is isomorphic to so(2,1), iso(2), or so(3) depending on the cosmological constant being positive, zero, or negative. In the case of a positive cosmological constant, namely dS4, the spinor-helicity representation contains all massive particles corresponding to the principal series representations and the partially massless particles corresponding to the discrete series representations leaving out only the light massive particles corresponding to the complementary series representations. The zero and negative cosmological constant cases, which had been addressed in earlier references, are also discussed briefly. Finally, we consider the multilinear form of helicity spinors invariant under (A)dS group, which can serve as the (A)dS counterpart of the scattering amplitude, and discuss technical differences and difficulties of the (A)dS cases compared to the flat spacetime case. Published by the American Physical Society 2024

Enhanced emergent electromagnetic inductance in Tb5Sb3 due to highly disordered helimagnetism

In helimagnetic metals, ac current-driven spin motions can generate emergent electric fields acting on conduction electrons, leading to emergent electromagnetic induction (EEMI). Recent experiments reveal the EEMI signal generally shows a strongly current-nonlinear response. In this study, we investigate the EEMI of Tb5Sb3, a short-period helimagnet. Using small angle neutron scattering we show that Tb5Sb3 hosts highly disordered helimagnetism with a distribution of spin-helix periodicity. The current-nonlinear dynamics of the disordered spin helix in Tb5Sb3 indeed shows up as the nonlinear electrical resistivity (real part of ac resistivity), and even more clearly as a nonlinear and huge EEMI (imaginary part of ac resistivity) response. The magnitude of the EEMI reaches as large as several tens of μH for Tb5Sb3 devices on the scale of several tens of μm, originating to noncollinear spin textures possibly even without long-range helimagnetic order.

Chiral Jahn-Teller Distortion in Quasi-Planar Boron Clusters.

In this work, we have observed that some chiral boron clusters (B16-, B20-, B24-, and B28-) can simultaneously have helical molecular orbitals and helical spin densities; these seem to be the first compounds discovered to have this intriguing property. We show that chiral Jahn-Teller distortion of quasi-planar boron clusters drives the formation of the helical molecular spin densities in these clusters and show that elongation/enhancement in helical molecular orbitals can be achieved by simply adding more building blocks via a linker. Aromaticity of these boron clusters is discussed. Chiral boron clusters may find potential applications in spintronics, such as molecular magnets.

Generators of the Poincaré Group for arbitrary tensors and spinor-tensors

In this work, we systematically derive explicit expressions for the Poincaré Group generators on arbitrary-rank tensors and spinor-tensors in D=3+1 and D=2+1 spacetimes, thus generalizing previous works in the literature for the groups ISO(3,1) and ISO(2,1). From the Casimir eigenvalue equations, we demonstrate in a model-independent way the Fierz-Pauli constraints for massive particles for spins s=5/2, 3, and 4 in D=3+1 and helicities α=5/2, 3, and 4 in D=2+1 dimensions. We also comment on the demonstration of the Fierz-Pauli constraints for the general case of arbitrary spin (helicity).

Topological signatures of Mo2TiC2O2

Mo2TiC2 is the Ordered Double Transitional Metal Layered Carbides (ODTMLC) derived from its parent MAX phases Mo2TiAlC2 by a wet chemical etching. Its oxidation was done by a new ablated plasma thrust method in which the MXenes were at 750 °C under an oxygen background in the pulsed laser deposition chamber. The reflective high electron energy diffraction technique assures the oxidation at the ambient gas pressure p = 0.1 mbar, which was described in the previous paper. The obtained Mo2TiC2O2 was transferred for their topological test under angle-resolved photoemission spectroscopy, circular dichroism test, and Chemical Potential (CP) analysis. An indirect energy bandgap of 125 meV was obtained. The sine function of α along with period π and β with period 2π shows that there is a possibility of helical spin textures in both α (electron-like pocket around Γ̄) and β (elliptical electron-like pocket around M̄). The CP analysis shows the possibility of at least 100 meV bandgap creation on a single surface so that the surface charges will flow without any effect of bulk. The Mo2TiC2O2 can be used as topological insulating material.

Giant magnetoresistance resulting from superzone gap in spin-frustrated rare-earth-based aluminide: DyFe2Al10.

The magnetic properties of orthorhombic aluminides have recently been the subject of investigation, revealing several intriguing phenomena within this class of materials. However, the exploration of their magnetic and electrical transport phenomena has remained somewhat limited. In this study, we delve into the magnetic and electrical transport characteristics of one such material from that group which is DyFe2Al10(DFA). Our findings go beyond classifying this material as a simple antiferromagnet; but it posses a short range ferromagnetic ordering apart from helical spin structure of Dy3+. It exhibits a metamagnetic transition and spin glass behavior below its Néel temperature (TN). Our analysis of electrical magnetotransport behavior indicates the emergence of an antiferromagnetic superzone gap, resulting in a significant enhancement in magnetoresistance effect. This discovery paves the way for a class of materials with complex interactions and notable magnetoresistance properties.

Coexistence of Quantum-Spin-Hall and Quantum-Hall-Topological-Insulating States in Graphene/hBN on SrTiO3 Substrate.

SrTiO3 (STO) substrate, a perovskite oxide material known for its high dielectric constant (ɛ), facilitates the observation of various (high-temperature) quantum phenomena. A quantum Hall topological insulating (QHTI) state, comprising two copies of QH states with antiparallel two ferromagnetic edge-spin overlap protected by the U(1) axial rotation symmetry of spin polarization, has recently been achieved in low magnetic field (B) even as high as ≈100 K in a monolayer graphene/thin hexagonal boron nitride (hBN) spacer placed on an STO substrate, thanks to the high ɛ of STO. Despite the use of the heavy STO substrate, however, proximity-induced quantum spin Hall (QSH) states in 2D TI phases, featuring a topologically protected helical edge spin phase within time-reversal-symmetry, is not confirmed. Here, with the use of a monolayer hBN spacer, it is revealed the coexistence of QSH (at B = 0T) and QHTI (at B ≠ 0) states in the same single graphene sample placed on an STO, with a crossover regime between the two at low B. It is also classified that the different symmetries of the two nontrivial helical edge spin phases in the two states lead to different interaction with electron-puddle quantum dots, caused by a local surface pocket of the STO, in the crossover regime, resulting in a spin dephasing only for the QHTI state. The results obtained using STO substrates open the doors to investigations of novel QH spin states with different symmetries and their correlations with quantum phenomena. This exploration holds value for potential applications in spintronic devices.

Frequency-independent optical spin injection in Weyl semimetals

We demonstrate that in Weyl semimetals, the momentum-space helical spin texture can couple to the chirality of the Weyl node to generate a frequency-independent optical spin injection. This frequency-independence is rooted in the topology of the Weyl node. Since the helicity and the chirality are always locked for Weyl nodes, the injected spin from a pair of Weyl nodes always add up, implying no symmetry requirements for Weyl semimetals. Finally, we show that such frequency-independent spin injection is robust against multiband corrections and lattice-regularization effect and capable of realizing all-optical magnetization switching in the THz regime.

Weyl metallic state induced by helical magnetic order

In the rapidly expanding field of topological materials there is growing interest in systems whose topological electronic band features can be induced or controlled by magnetism. Magnetic Weyl semimetals, which contain linear band crossings near the Fermi level, are of particular interest owing to their exotic charge and spin transport properties. Up to now, the majority of magnetic Weyl semimetals have been realized in ferro- or ferrimagnetically ordered compounds, but a disadvantage of these materials for practical use is their stray magnetic field which limits the minimum size of devices. Here we show that Weyl nodes can be induced by a helical spin configuration, in which the magnetization is fully compensated. Using a combination of neutron diffraction and resonant elastic x-ray scattering, we find that below TN = 14.5 K the Eu spins in EuCuAs develop a planar helical structure which induces two quadratic Weyl nodes with Chern numbers C = ±2 at the A point in the Brillouin zone.

Fast photochromism of helicene-bridged imidazole dimers.

The unique optical and magnetic properties of organic biradicaloids on polycyclic aromatic hydrocarbons are of fundamental interest in the development of novel organic optoelectronic materials. Open-shell π-conjugated molecules with helicity have recently attracted a great deal of attention due to the magnetic-field-dependence and spin-selectivity arising from the combination of helical chirality and electron spins. However, the molecular design for helical biradicaloids is limited due to the thermal instability and high reactivity. Herein, we achieved fast photochromic reactions and reversible photo-generation of biradical species using helicene-bridged imidazole dimers. A [9]helicene-bridged imidazole dimer exhibits reversible photochromism upon UV light irradiation. The transient species produced reversibly by UV light irradiation exhibited ESR spectra with a fine structure characteristic of a triplet radical pair, indicating the reversible generation of the biradical. The half-life of the thermal recombination reaction of the biradical was estimated to be 29 ms at 298 K. Conversely, a substantial activation energy barrier was confirmed for the intramolecular recombination reaction in the [7]helicene-bridged imidazole dimer, attributed to the extended pitch length of [7]helicene. The temperature dependence of the thermal back reactions revealed that the [7]helicene and [9]helicene moieties functioned as 'soft' and 'hard' molecular bridges, respectively. These findings pave the way for future advances in the development of photoswitchable helical biradicaloids.