Orbital Texture Research Articles

Large Chiral Orbital Texture and Orbital Edelstein Effect in Co/Al Heterostructure.

Recent experiments by S. Krishnia et al. [Nano Lett. 2023, 23, 6785] reported an unprecedentedly large enhancement of torques upon inserting thin Al layer in Co/Pt heterostructure that suggested the presence of a Rashba-like interaction at the metallic Co/Al interface. Based on first-principles calculations, we reveal the emergence of a large helical orbital texture in reciprocal space at the interfacial Co layer, whose origin is attributed to the orbital Rashba effect due to the formation of the surface states at the Co/Al interface and where spin-orbit coupling is found to produce smaller contributions with a higher-order winding of the orbital moments. Our results unveil that the orbital texture gives rise to a nonequilibrium orbital accumulation producing large current-induced torques, thus providing an essential theoretical background for the experimental data and advancing the use of orbital transport phenomena in all-metallic magnetic systems with light elements.

Excited State Band Mapping and Ultrafast Nonequilibrium Dynamics in Topological Dirac Semimetal 1T-ZrTe2.

We performed time- and polarization-resolved extreme ultraviolet momentum microscopy on the topological Dirac semimetal candidate 1T-ZrTe2. Excited state band mapping uncovers the previously inaccessible linear dispersion of the Dirac cone above the Fermi level. We study the orbital texture of bands using linear dichroism in photoelectron angular distributions. These observations provide hints about the topological character of 1T-ZrTe2. Time-, energy-, and momentum-resolved nonequilibrium carrier dynamics reveal that intra- and interband scattering processes play a major role in the relaxation mechanism, leading to multivalley electron-hole accumulation near the Fermi level. We also show that electrons' inverse lifetime has a linear dependence as a function of their excess energy. Our time- and polarization-resolved XUV photoemission results shed light on the excited state electronic structure of 1T-ZrTe2 and provide valuable insights into the relatively unexplored field of quantum-state-resolved ultrafast dynamics in 3D topological Dirac semimetals.

Controllable orbital angular momentum monopoles in chiral topological semimetals

AbstractThe emerging field of orbitronics aims to generate and control orbital angular momentum for information processing. Chiral crystals are promising orbitronic materials because they have been predicted to host monopole-like orbital textures, where the orbital angular momentum aligns isotropically with the electron’s crystal momentum. However, such monopoles have not yet been directly observed in chiral crystals. Here, we use circular dichroism in angle-resolved photoelectron spectroscopy to image orbital angular momentum monopoles in the chiral topological semimetals PtGa and PdGa. The spectra show a robust polar texture that rotates around the monopole as a function of photon energy. This is a direct consequence of the underlying magnetic orbital texture and can be understood from the interference of local atomic contributions. Moreover, we also demonstrate that the polarity of the monopoles can be controlled through the structural handedness of the host crystal by imaging orbital angular moment monopoles and antimonopoles in the two enantiomers of PdGa, respectively. Our results highlight the potential of chiral crystals for orbitronic device applications, and our methodology could enable the discovery of even more complicated nodal orbital angular momentum textures that could be exploited for orbitronics.

Chiral orbital texture in nonlinear electrical conduction

Chiral orbital texture in nonlinear electrical conduction

Nonlinear orbital and spin Edelstein effect in centrosymmetric metals

Nonlinear spintronics combines nonlinear dynamics with spintronics, opening up new possibilities beyond linear responses. A recent theoretical work [Xiao et al. Phys. Rev. Lett.130, 166302 (2023)] predicts the nonlinear generation of spin density [nonlinear spin Edelstein effect (NSEE)] in centrosymmetric metals based on symmetry analysis combined with first-principle calculation. This paper focuses on the fundamental role of orbital degrees of freedom for the nonlinear generation in centrosymmetric systems. Using a combination of tight-binding model and density functional theory calculations, we demonstrate that nonlinear orbital density can arise independently of spin–orbit coupling. In contrast, spin density follows through spin–orbit coupling. We further elucidate the microscopic mechanism responsible for this phenomenon, which involves the NSEE induced by electric-field-induced orbital Rashba texture. In addition, we also explore the potential applications of the nonlinear orbital and spin Edelstein effect for magnetic-field-free switching of magnetization.

Monopole-like orbital-momentum locking and the induced orbital transport in topological chiral semimetals

The interplay between chirality and topology nurtures many exotic electronic properties. For instance, topological chiral semimetals display multifold chiral fermions that manifest nontrivial topological charge and spin texture. They are an ideal playground for exploring chirality-driven exotic physical phenomena. In this work, we reveal a monopole-like orbital-momentum locking texture on the three-dimensional Fermi surfaces of topological chiral semimetals with B20 structures (e.g., RhSi and PdGa). This orbital texture enables a large orbital Hall effect (OHE) and a giant orbital magnetoelectric (OME) effect in the presence of current flow. Different enantiomers exhibit the same OHE which can be converted to the spin Hall effect by spin-orbit coupling in materials. In contrast, the OME effect is chirality-dependent and much larger than its spin counterpart. Our work reveals the crucial role of orbital texture for understanding OHE and OME effects in topological chiral semimetals and paves the path for applications in orbitronics, spintronics, and enantiomer recognition.

Optoelectronic Manifestation of Orbital Angular Momentum Driven by Chiral Hopping in Helical Se Chains.

Chiral materials have garnered significant attention in the field of condensed matter physics. Nevertheless, the magnetic moment induced by the chiral spatial motion of electrons in helical materials, such as elemental Te and Se, remains inadequately understood. In this work, we investigate the development of quantum angular momentum enforced by chirality by using static and time-dependent density functional theory calculations for an elemental Se chain. Our findings reveal the emergence of an unconventional orbital texture driven by the chiral geometry, giving rise to a nonvanishing current-induced orbital moment. By incorporating spin-orbit coupling, we demonstrate that current-induced spin accumulation arises in the chiral chain, which fundamentally differs from the conventional Edelstein effect. Furthermore, we demonstrate optoelectronic detection of the orbital angular momentum in the chiral Se chain, providing an alternative to the interband Berry curvature, which is ill-defined in low dimensions.

Orbital-selective charge-density wave in TaTe4

TaTe4, a metallic charge-density wave (CDW) material discovered decades ago, has attracted renewed attention due to its rich interesting properties, such as pressure-induced superconductivity and candidate nontrivial topological phase. Here, using high-resolution angle-resolved photoemission spectroscopy and ab initio calculation, we systematically investigate the electronic structure of TaTe4. At 26 K, we observe a CDW gap as large as 290 meV, which persists up to 500 K. The CDW-modulated band structure shows a complex reconstruction that closely correlates with the lattice distortion. Inside the CDW gap, there exist highly dispersive energy bands contributing to the remnant Fermi surface and metallic behavior in the CDW state. Interestingly, our ab initio calculation reveals that the large CDW gap mainly opens in the electronic states with out-of-plane orbital components, while the in-gap metallic states originate from in-plane orbitals, suggesting an orbital texture that couples with the CDW order. Our results shed light on the interplay between electron, lattice, and orbital in quasi-one-dimensional CDW materials.

Alternative Structure Model of Correlated Charge Density Wave in Monolayer 1T-Nb(Ta)Se2.

The putative Mott charge density wave (CDW) phases of monolayer 1T-NbSe2 and 1T-TaSe2 have attracted a lot of recent interest due to the unexpected orbital texture of their Mott-Hubbard states and the superstructure related to an exotic possibility of a quantum spin liquid with a spinon Fermi surface. The origins of the orbital texture and the superstructure have been, however, elusive. We find by using density functional theory calculations that these CDW phases can have an alternative metastable structure, an anion (Se) centered cluster, in contrast to the prevailing model of a cation (Nb or Ta) centered David star cluster. This structure can be stabilized by the charge transfer from the bilayer graphene/SiC substrate used commonly in the experiments. The anion-centered structure has a similar electronic band structure of a charge transfer insulator to that of DS clusters but naturally explains the orbital texture of the upper Hubbard band from simply its atomic structure. Moreover, this band structure exhibits a Fermi surface nesting to possibly break the symmetry spontaneously into a -R30° superstructure observed experimentally. The resulting ground state of the superstructure is shown to be a trivial band insulator, in contrast to exotic proposals. This result emphasizes the huge structural flexibility of these heteroexpitaxial monolayers, for which careful studies on atomic structures and interactions with substrates are highly requested.

Large 3D anisotropy of magnetoresistance in MoAlB

Materials with large three-dimensional (3D) anisotropic magnetoresistance (MR) have very important applications in anisotropic magnetoresistance sensors and magnetometers. Herein, we have observed a large 3D anisotropy of MR in nonmagnetic MoAlB single crystal. Specially, the MR ratio (MRa: MRb: MRc) reaches up to 140.5 : 1: 22, when electric current is along a-/b-/c-axis with an applied magnetic field of 8.5 T at 5 K. To clarify the origins of 3D anisotropic MR, angular MR and direction-dependent Hall coefficient measurements as well as first-principles calculations were performed. The nearly electron-hole compensation and the mixed d-p orbital texture are the important origins of the MR effect along a-/c-axis, and the anisotropy of MR originates from the anisotropic Fermi surface and carrier scattering along a-/c-axis in MoAlB. Whereas, the open orbit is a dominant origin along b-axis of MoAlB. Furthermore, the factors affecting the magnitude of MR are given by using two-band model, and possible control strategies are proposed. This work not only proposes a new idea for exploring single-phase nonmagnetic 3D anisotropic MR material, but also provides a key material for the design and development of new 3D anisotropic magnetoresistance sensors and magnetometers in the future.

Microscopic study of orbital textures

Many interesting spin and orbital transport phenomena originate from orbital textures, referring to k-dependent orbital states. Most of previous works are based on symmetry analysis to model the orbital texture and analyze its consequences. However the microscopic origins of orbital texture and its strength are largely unexplored. In this work, we derive the orbital texture Hamiltonians from microscopic tight-binding models for various situations. To form an orbital texture, k-dependent hybridization of orbital states are necessary. We reveal two microscopic mechanisms for the hybridization: (i) lattice structure effect and (ii) mediation by other orbital states. By considering the orbital hybridization, we not only reproduce the orbital Hamiltonian obtained by the symmetry analysis but also reveal previously unreported orbital textures like orbital Dresselhaus texture and anisotropic orbital texture. The orbital Hamiltonians obtained here would be useful for analyzing the orbital physics and designing the materials suitable for spin-orbitronic applications.

Quantum Hall spin textures far beyond the skyrmion limit

In strongly correlated quantum Hall ferromagnets with noninteger filling factors between $\ensuremath{\nu}=1$ and $\ensuremath{\nu}=3/2$, evidence of offbeat spin textures is obtained. The platforms for the study are two-dimensional electron systems based on MgZnO/ZnO heterostructures, in which the parameters of Zeeman and exchange energies are inconsistent with ordinary skyrmions. Experimental probing of magnetic order is fulfilled via exploration of the spectra of collective spin excitations by means of inelastic light scattering. In addition to the ferromagnetic spin exciton, a low-energy spin mode is observed, bearing witness to broken spin-rotational symmetry in the ground state. The two spin modes exhibit a pronounced anticrossing behavior, depending on the two-dimensional momentum, electron concentration, filling factor, and magnetic field tilt. The properties of the electron system are simulated using the exact diagonalization technique, showing that Landau level mixing and crossing play a key role in the nontrivial spin configuration. The corresponding spin textures emerging between $\ensuremath{\nu}=1$ and $\ensuremath{\nu}=3/2$ involve the orbital degree of freedom and are qualitatively different from skyrmions. Experiments at elevated temperatures show the destruction of this orbital spin texture phase with critical temperature far below the Zeeman energy. On the other side of $\ensuremath{\nu}=1$ the textures are absent.

Visualizing the evolution from Mott insulator to Anderson insulator in Ti-doped 1T-TaS2

The electronic evolution of doped Mott insulators has been extensively studied for decades in search of exotic physical phases. The proposed Mott insulator 1T-TaS2 provides an intriguing platform to study the electronic evolution via doping. Here we apply scanning tunneling microscopy (STM) to study the evolution in Ti-doped 1T-TaS2 at different doping levels. The doping Ti atom locally perturbs the electronic and spin state inside the doped star of David and induces a clover-shaped orbital texture at low-doping levels (x < 0.01). The insulator to metal transition occurs around a critical point x = 0.01, in which small metallic and large insulating domains coexist. The clover-shaped orbital texture emerges at a broader energy range, revealing a competition with the electron correlation. It transforms to a disorder-induced Anderson insulating behavior as doping increases. We directly visualize the trapped electrons in dI/dV conductance maps. The comprehensive study of the series of Ti-doped 1T-TaS2 deepens our understanding of the electronic state evolution in a doped strong-correlated system.

Reconciling the bulk metallic and surface insulating state in 1T−TaSe2

The origin of different electronic states of $1T\ensuremath{-}{\mathrm{TaS}}_{2}$ and $1T\ensuremath{-}{\mathrm{TaSe}}_{2}$ remains controversial due to the complicated correlated electronic properties. We apply scanning tunneling microscopy to study the electronic state of bulk $1T\ensuremath{-}{\mathrm{TaSe}}_{2}$. Both insulating and metallic states are identified in different areas of the same sample. The insulating state is similar to that in $1T\ensuremath{-}{\mathrm{TaS}}_{2}$, concerning both the $dI/dV$ spectrum and the orbital texture. With detailed investigations in single-step areas, the electronic state measured on the upper-layer surface is found to be associated with different stacking orders and the lower layer's electronic state. The insulating state is most possibly a single-layer property, perturbed to a metallic state by particular stacking orders. Both the metallic and large-gap insulating spectra, together with their corresponding stacking orders, are stable states in $1T\text{\ensuremath{-}}{\mathrm{TaSe}}_{2}$. The connected metallic areas lead to the metallic transport behavior. We then reconcile the bulk metallic and surface insulating state in $1T\ensuremath{-}{\mathrm{TaSe}}_{2}$. The rich phenomena in $1T\ensuremath{-}{\mathrm{TaSe}}_{2}$ deepen our understanding of the correlated electronic state in bulk $1T\ensuremath{-}{\mathrm{TaSe}}_{2}$ and $1T\ensuremath{-}{\mathrm{TaS}}_{2}$.

Unveiling the orbital texture of 1T-TiTe2 using intrinsic linear dichroism in multidimensional photoemission spectroscopy

The momentum-dependent orbital character in crystalline solids, referred to as orbital texture, is of capital importance in the emergence of symmetry-broken collective phases, such as charge density waves as well as superconducting and topological states of matter. By performing extreme ultraviolet multidimensional angle-resolved photoemission spectroscopy for two different crystal orientations linked to each other by mirror symmetry, we isolate and identify the role of orbital texture in photoemission from the transition metal dichalcogenide 1T-TiTe2. By comparing our experimental results with theoretical calculations based on both a quantitative one-step model of photoemission and an intuitive tight-binding model, we unambiguously demonstrate the link between the momentum-dependent orbital orientation and the emergence of strong intrinsic linear dichroism in the photoelectron angular distributions. Our results represent an important step towards going beyond band structure (eigenvalues) mapping and learning about electronic wavefunction and orbital texture of solids by exploiting matrix element effects in photoemission spectroscopy.

Tailoring magnetism in spinel vanadate CoV2O4 epitaxial thin films

Near itinerant cubic bulk CoV2O4 is at variance with other spinel vanadates by not showing orbital ordering down to low temperature, albeit it displays fragile anomalies related to spin, and lattice structure, signaling a spin/orbital glass transition around 95 K. We investigate tetragonal-like epitaxial CoV2O4 films on SrTiO3 and (La0.3Sr0.7)(Al0.65Ta0.35)O3 substrates that exhibit pronounced signature of spin reorientation transition from to a/b plane around 90 K unlike its bulk counterpart. Using in-plane and out-of-plane magnetic measurements, we demonstrate the intricate link between Co2+ and V3+ sublattice magnetizations that give rise to anisotropic magnetic switching. In-plane magnetic measurements reveal a wasp-waist shaped M(H) loop below reorientation transition temperature, while the out-of-plane follows antiferromagnet-like M(H) response. The wasp-waist shaped feature could be linked to in-plane spin-canted (anti)ferromagnetism induced by canting away of V-spins away from antiferromagnetically coupled Co-spin direction below reorientation transition temperature. Further, we uncover the evidence for slow relaxation over a period of ∼104 s at 20 K and memory effect that indicates the possible existence for magnetic glassy phase in the low temperature regime. Using epitaxial strain as a control knob, our results inspire future study to manipulate orbital states, spin texture and itinerant electron character in tailored CoV2O4 films away from cubic lattice symmetry.

Author Correction: Strong correlations and orbital texture in single-layer 1T-TaSe2

Author(s): Chen, Y; Ruan, W; Wu, M; Tang, S; Ryu, H; Tsai, HZ; Lee, RL; Kahn, S; Liou, F; Jia, C; Albertini, OR; Xiong, H; Jia, T; Liu, Z; Sobota, JA; Liu, AY; Moore, JE; Shen, ZX; Louie, SG; Mo, SK; Crommie, MF | Abstract: In the version of this Article previously published, co-author Ryan L. Lee was missing the middle initial. This has now been corrected in the online versions.

Profiling spin and orbital texture of a topological insulator in full momentum space

We investigate the coupled spin and orbital textures of the topological surface state in ${\mathrm{Bi}}_{2}$(Te,${\mathrm{Se})}_{3}$(0001) across full momentum space using spin- and angle-resolved photoelectron spectroscopy and relativistic one-step photoemission theory. For an approximately isotropic Fermi surface in ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{2}\mathrm{Se}$, the measured intensity and spin momentum distributions, obtained with linearly polarized light, qualitatively reflect the orbital composition and the orbital-projected in-plane spin polarization, respectively. In ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$, the in-plane lattice potential induces a hexagonal anisotropy of the Fermi surface, which manifests in an out-of-plane photoelectron spin polarization with a strong dependence on light polarization, excitation energy, and crystallographic direction.

Quasiparticle interference and quantum confinement in a correlated Rashba spin-split 2D electron liquid.

Exploiting inversion symmetry breaking (ISB) in systems with strong spin-orbit coupling promises control of spin through electric fields-crucial to achieve miniaturization in spintronic devices. Delivering on this promise requires a two-dimensional electron gas with a spin precession length shorter than the spin coherence length and a large spin splitting so that spin manipulation can be achieved over length scales of nanometers. Recently, the transition metal oxide terminations of delafossite oxides were found to exhibit a large Rashba spin splitting dominated by ISB. In this limit, the Fermi surface exhibits the same spin texture as for weak ISB, but the orbital texture is completely different, raising questions about the effect on quasiparticle scattering. We demonstrate that the spin-orbital selection rules relevant for conventional Rashba system are obeyed as true spin selection rules in this correlated electron liquid and determine its spin coherence length from quasiparticle interference imaging.

Orbital Rashba effect in a surface-oxidized Cu film

Recent experimental observation of unexpectedly large current-induced spin-orbit torque in surface oxidized Cu on top of a ferromagnet suggested a possible role of the orbital Rashba effect (ORE). With this motivation, we investigate the ORE from first principles by considering an oxygen monolayer on top of a Cu(111) film. We show that surface oxidization of Cu film leads to gigantic enhancement of the ORE for states near the Fermi surface. The resulting chiral orbital texture in the momentum space is exceptionally strong, reaching $\sim 0.5\hbar$ in magnitude. We find that resonant hybridization between O $p$-states and Cu $d$-states is responsible for the emergence of the ORE. We demonstrate that application of an external electric field generates huge orbital Hall current, which is an order of magnitude larger than the spin Hall current found in heavy metals. This implies that "orbital torque" mechanism may be significant in surface oxidized Cu/ferromagnet structures. It also encourages experimental verification of the orbital texture in surface oxidized Cu through optical measurements such as angle-resolved photoemission spectroscopy.