Substantial Spin-orbit Coupling Research Articles

Six-Coordinated CoII Single-Molecule Magnets: Synthetic Strategy, Structure and Magnetic Properties.

The pursuit of molecule-based magnetic memory materials contributes significantly to high-density information storage research in the frame of the ongoing information technologies revolution. Remarkable progress has been achieved in both transition metal (TM) and lanthanide based single-molecule magnets (SMMs). Notably, six-coordinated CoII SMMs hold particular research significance owing to the economic and abundant nature of 3d TM ions compared to lanthanide ions, the substantial spin-orbit coupling of CoII ions, the potential for precise control over coordination geometry, and the air-stability of coordination-saturated structures. In this review, we will summarize the progress made in six-coordinated CoII SMMs, organized by their coordination geometry and molecular structure similarity. Valuable insights, principles, and new mechanism gleaned from this research and remaining issues that need to be addressed will also be discussed to guide future optimization.

Probing the Mott insulating behavior of Ba2MgReO6 with DFT+DMFT

We investigate the interplay of spin-orbit coupling, electronic correlations, and lattice distortions in the 5d1 double perovskite Ba2MgReO6. Combining density-functional theory (DFT) and dynamical mean-field theory (DMFT), we establish the Mott insulating character of Ba2MgReO6 in both its cubic and tetragonal paramagnetic phases. Despite substantial spin-orbit coupling, its impact on the formation of the insulating state is minimal, consistent with theoretical expectations for d1 systems. We further characterize the electronic properties of the cubic and tetragonal phases by analyzing spectral functions and local occupations in terms of multipole moments centered on the Re sites. Our results confirm the presence of ferroically ordered z2 quadrupoles in addition to the antiferroic x2−y2-type order. We compare two equivalent but complementary descriptions in terms of either effective Re-t2g frontier orbitals or more localized atomiclike Re-d and O-p orbitals. The former maps directly on a physically intuitive picture in terms of nominal d1 Re cations, while the latter explicitly demonstrates the role of hybridization with the ligands in the spin-orbit splitting and the formation of the charge quadrupoles around the Re sites. Finally, we compare our DFT+DMFT results with a previous DFT+U study of the tetragonal paramagnetic state. We find good qualitative agreement for the dominant charge quadrupoles, but also notable differences in the corresponding spectral functions, underscoring the need for more comparative studies between these two methods. Published by the American Physical Society 2024

Triplet proximity effects in superconductor/ferromagnet hybrid structures exhibiting intrinsic spin–orbit coupling

The conventional spin–singlets with momentum zero can be transformed into spin-polarized triplet states with non-zero momentum at the superconductor/ferromagnet interface by an inhomogeneous magnetic exchange field. While the decaying spectrum of triplet pairs in ferromagnetic metals has received significant attention, less is known about the decay of these pairs in ferromagnets with intrinsic spin–orbit coupling (SOC) present at the superconductor/ferromagnet interface. We have performed simulations to study the triplet proximity effects in hybrid structures composed of a BCS superconductor and ferromagnet with intrinsic spin orbit coupling (SOC) in the diffusive limit where the quasiclassical boundary conditions have been modified to incorporate the effect of SO coupling in Usadel equations and the self-consistent equation. We laid emphasis on the modification of the density of states inside the ferromagnet near the Fermi energy. The generated short ranged triplets (SRTs) present themselves in the form of zero energy gap in the density of states (DOS) even in the presence of comparatively larger values of the exchange field oriented either in plane or out of plane of the hybrid structure and the Long ranged triplets (LRTs) present themselves in the form of zero energy peak in the DOS for feasible magnitude and orientation of the exchange field. Understanding and modeling these observations is important as it is difficult to model such hybrid structures experimentally. Where earlier research has focused on the scenario of substantial spin orbit coupling in the ballistic threshold/clean limit, in this paper we provide conclusions that are applicable to the diffusive transport/dirty limit regime. Also, the findings reveal that the SO coupling generates a distinct imprint in the DOS, which exhibits extremely nonmonotonic behavior with magnetization orientations.

Antipolar transitions in GaNb4Se8 and GaTa4Se8

We present dielectric, polarization, resistivity, specific heat, and magnetic susceptibility data on single crystals of the lacunar spinels GaNb4Se8 and GaTa4Se8, tetrahedral cluster-based materials with substantial spin-orbit coupling. We concentrate on the possible occurrence of antipolar order in these compounds, as previously reported for the isoelectronic GaNb4S8, where spin-orbit coupling plays a less important role. Our broadband dielectric-spectroscopy investigations reveal clear anomalies of the intrinsic dielectric constant at the magneto-structural transitions in both systems that are in accord with the expectations for antipolar transitions. A similar anomaly is also observed at the cubic-cubic transition of the Nb compound leading to an intermediate phase. Similar to other polar and antipolar lacunar spinels, we find indications for dipolar relaxation dynamics at low temperatures. Polarization measurements on GaNb4Se8 reveal weak ferroelectric ordering below the magneto-structural transition, either superimposed to antipolar order or emerging at structural domain walls. The temperature-dependent dc resistivity evidences essentially thermally-activated charge transport with different activation energies in the different phases. A huge step-like increase of the resistivity at the magneto-structural transition of the Ta compound points to a fundamental change in the electronic structure or the mechanism of the charge transport. At low temperatures, charge transport is governed by in-gap impurity states, as also invoked to explain the resistive switching in these compounds.

Glide symmetry protected higher-order topological insulators from semimetals with butterfly-like nodal lines

Most topological insulators (TIs) discovered today in spinful systems can be transformed from topological semimetals (TSMs) with vanishing bulk gap via introducing the spin-orbit coupling (SOC), which manifests the intrinsic links between the gapped topological insulator phases and the gapless TSMs. Recently, we have discovered a family of TSMs in time-reversal invariant spinless systems, which host butterfly-like nodal-lines (NLs) consisting of a pair of identical concentric intersecting coplanar ellipses (CICE). In this Communication, we unveil the intrinsic link between this exotic class of nodal-line semimetals (NLSMs) and a {{mathbb{Z}}}_{4} = 2 topological crystalline insulator (TCI), by including substantial SOC. We demonstrate that in three space groups (i.e., Pbam (No.55), P4/mbm (No.127), and P42/mbc (No.135)), the TCI supports a fourfold Dirac fermion on the (001) surface protected by two glide symmetries, which originates from the intertwined drumhead surface states of the CICE NLs. The higher order topology is further demonstrated by the emergence of one-dimensional helical hinge states, indicating the discovery of a higher order topological insulator protected by a glide symmetry.

Nonlinear anomalous Nernst effect in strained graphene induced by trigonal warping

It has recently been reported that a nonlinear anomalous Nernst current (NANC), induced by Berry curvature near the Fermi surface, can be generated as a second-order response to a longitudinal temperature gradient in a wide variety of time-reversal invariant and noncentrosymmetric materials. So far, NANC in two-dimensional Dirac systems has been reported to be finite only in materials with substantial spin-orbit coupling and titled Dirac cones formed from low-energy Dirac quasiparticles. Here, we prove that NANC can also emerge in two-dimensional Dirac materials even in the complete absence of titled Dirac cones and spin-orbit coupling. It's found that the NANC has a quantum origin from the trigonal warping of the Fermi surface. NANC in both trigonal-warping monolayer and bilayer graphene in the presence of uniaxial strain is theoretically investigated. The magnitude of NANC in trigonal-warping bilayer graphene is comparable to those reported which originated from tilted mechanisms in strained ${\mathrm{MoS}}_{2}$ and bilayer ${\mathrm{WTe}}_{2}$.

Nonlinear transport without spin-orbit coupling or warping in two-dimensional Dirac semimetals

It has recently been realized that the first-order moment of the Berry curvature, namely, the Berry curvature dipole (BCD), can give rise to nonlinear current in a wide variety of time-reversal invariant and non-centrosymmetric materials. While the BCD in two-dimensional Dirac systems is known to be finite only in the presence of either substantial spin-orbit coupling where low-energy Dirac quasiparticles form tilted cones or higher order warping of the Fermi surface, we argue that the low-energy Dirac quasiparticles arising from the merging of a pair of Dirac points without any tilt or warping of the Fermi surface can lead to a nonzero BCD. Remarkably, in such systems, the BCD is found to be independent of Dirac velocity as opposed to the Dirac dispersion with a tilt or warping effects. We further show that the proposed systems can naturally host helicity-dependent photocurrent due to their linear momentum-dependent Berry curvatures. Finally, we discuss an important byproduct of this work, i.e., nonlinear anomalous Nernst effect as a second-order thermal response.

Coexistence of large conventional and planar spin Hall effect with long spin diffusion length in a low-symmetry semimetal at room temperature.

The spin Hall effect (SHE) is usually observed as a bulk effect in high-symmetry crystals with substantial spin-orbit coupling (SOC), where the symmetric spin-orbit field imposes a widely encountered trade-off between spin Hall angle (θSH) and spin diffusion length (Lsf), and spin polarization, spin current and charge current are constrained to be mutually orthogonal. Here, we report a large θSH of 0.32 accompanied by a long Lsf of 2.2 μm at room temperature in a low-symmetry few-layered semimetal MoTe2, thus identifying it as an excellent candidate for simultaneous spin generation, transport and detection. In addition, we report that longitudinal spin current with out-of-plane polarization can be generated by both transverse and vertical charge current, due to the conventional and a newly observed planar SHE, respectively. Our study suggests that manipulation of crystalline symmetries and strong SOC opens access to new charge-spin interconversion configurations and spin-orbit torques for spintronic applications.

Berry Curvature Dipole in Strained Graphene: A Fermi Surface Warping Effect.

It has been recently established that optoelectronic and nonlinear transport experiments can give direct access to the dipole moment of the Berry curvature in nonmagnetic and noncentrosymmetric materials. Thus far, nonvanishing Berry curvature dipoles have been shown to exist in materials with substantial spin-orbit coupling where low-energy Dirac quasiparticles form tilted cones. Here, we prove that this topological effect does emerge in two-dimensional Dirac materials even in the complete absence of spin-orbit coupling. In these systems, it is the warping of the Fermi surface that triggers sizable Berry dipoles. We show indeed that uniaxially strained monolayer and bilayer graphene, with substrate-induced and gate-induced band gaps, respectively, are characterized by Berry curvature dipoles comparable in strength to those observed in monolayer and bilayer transition metal dichalcogenides.

Linear and nonlinear optical and spin-optical response of gapped and proximitized graphene

The properties of graphene can be significantly modified by interaction with a commensurate substrate. Via proximity effects, both band gaps and substantial spin-orbit coupling can be induced, opening a route to novel applications. In this work, we ask whether the linear and nonlinear optical response can be applied to probe the underlying symmetry of gapped and proximitized graphene. Answering in the affirmative, we show that, in particular, optical second-harmonic generation is a highly sensitive tool for characterization. Importantly, the spin-orbit sublattice symmetry is clearly revealed by the optical spectra. In addition, the topological phase of the materials is revealed via linear and nonlinear spin-optical effects.

Nearest-neighbor Kitaev exchange blocked by charge order in electron-doped α−RuCl3

The long search for materials carrying quantum spin liquid states has recently led to $\ensuremath{\alpha}$-RuCl${}_{3}$, a layered honeycomb Mott insulator with substantial spin-orbit coupling. Often, controlled doping of materials with strong 2D character generates new exotic properties as well as a better understanding of the parent compound. This paper shows that the intercalation compound K${}_{0.5}$RuCl${}_{3}$ sustains a peculiar charge disproportionation into formally Ru${}^{2+}$ and Ru${}^{3+}$. Every Ru${}^{3+}$ with one hole in the t${}_{2g}$ shell is surrounded by Ru${}^{2+}$ where the t${}_{2g}$ level is full and magnetically inert. Thus each type of Ru sites forms a triangular lattice and nearest-neighbor interactions of the original honeycomb are blocked.

Effects of spin-orbit coupling on zero-energy bound states localized at magnetic impurities in multiband superconductors

We investigate the effect of spin-orbit coupling on the in-gap bound states localized at magnetic impurities in multi-band superconductors with unconventional (sign-changed) and conventional (sign-unchanged) $s$-wave pairing symmetry, which may be relevant to iron-based superconductors. Without spin-orbit coupling, for spin-singlet superconductors it is known that such bound states cross zero energy at a critical value of the impurity scattering strength and acquire a finite spin-polarization. Moreover, the degenerate, spin-polarized, zero energy bound states are unstable to applied Zeeman fields as well as deviation of the impurity scattering strength away from criticality. Using a T-matrix formalism as well as analytical arguments, we show that, in the presence of spin-orbit coupling, the zero-energy bound states localized at magnetic impurities in unconventional, sign-changed, $s$-wave superconductors acquire surprising robustness to applied Zeeman fields and variation in the impurity scattering strength, an effect which is absent in the conventional, sign-unchanged, $s$-wave superconductors. Given that the iron-based multi-band superconductors may possess a substantial spin-orbit coupling as seen in recent experiments, our results may provide one possible explanation to the recent observation of surprisingly robust zero bias scanning tunneling microscope peaks localized at magnetic impurities in iron-based superconductors provided the order parameter symmetry is sign changing $s_{+-}$-wave.

The vicinity of hyper-honeycomb β-Li2IrO3 to a three-dimensional Kitaev spin liquid state.

Due to the combination of a substantial spin-orbit coupling and correlation effects, iridium oxides hold a prominent place in the search for novel quantum states of matter, including, e.g., Kitaev spin liquids and topological Weyl states. We establish the promise of the very recently synthesized hyper-honeycomb iridate β-Li2IrO3 in this regard. A detailed theoretical analysis reveals the presence of large ferromagnetic first-neighbor Kitaev interactions, while a second-neighbor antiferromagnetic Heisenberg exchange drives the ground state from ferro to zigzag order via a three-dimensional Kitaev spin liquid and an incommensurate phase. Experiment puts the system in the latter regime but the Kitaev spin liquid is very close and reachable by a slight modification of the ratio between the second- and first-neighbor couplings, for instance via strain.

Na3Bi: A Robust Material Offering Dirac Electrons for Device Applications

Na3Bi, a three dimensional (3D) Dirac semimetal, has been studied by use of density functional theory. The computed lattice constants were in agreement with experimental values. Calculation of the electron density of states and band structure revealed substantial spin–orbit coupling in this compound. This spin–orbit coupling, however, has a negligible effect on relaxed atomic positions obtained by use of force minimization. We also computed the pressure variation of the lattice constants of this compound. From the values obtained for the lattice constants at different pressures we calculated the electronic properties at different pressures up to 2 GPa. At ambient pressure the compound is a Dirac semimetal with linear E(k) dispersion in the conduction band around the Dirac point located at $${\hbox{D}}(0, 0,\sim 0.14\frac{2\pi }{c})$$ , between Γ and A in the Brillouin zone (BZ). With increasing pressure the lattice constants decrease, with a decreasing less than c. The Dirac point is observed at all the pressures studied and the location of the Dirac point shifts toward the Γ point with increasing pressure. The electronic structure of Na3Bi was found to be robust to the effects of external or chemical pressure.

α−RuCl3: A spin-orbit assisted Mott insulator on a honeycomb lattice

We examine the role of spin-orbit coupling in the electronic structure of $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$, in which Ru ions in $4{d}^{5}$ configuration form a honeycomb lattice. Our x-ray absorption spectroscopy measurements at the Ru $L$ edges exhibit distinct spectral features associated with the presence of substantial spin-orbit coupling, as well as an anomalously large branching ratio. Furthermore the measured optical spectra can be described very well with first-principles electronic structure calculations obtained by taking into account both spin-orbit coupling and electron correlations. We propose that $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$ is a spin-orbit assisted Mott insulator, and that the bond-dependent Kitaev interaction may be important for understanding magnetism of this compound.

Anomalous Property of Ag(BO2)2 Hyperhalogen: Does Spin–Orbit Coupling Matter?

Hyperhalogens were recently identified as a new class of highly electronagative species which are composed of metals and superhalogens. In this work, high-level theoretical calculations and photoelectron spectroscopy experiments are systematically conducted to investigate a series of coinage-metal-containing hyperhalogen anions, Cu(BO(2))(2)(-), Ag(BO(2))(2)(-), and Au(BO(2))(2)(-). The vertical electron detachment energy (VDE) of Ag(BO(2))(2)(-) is anomalously higher than those of Au(BO(2))(2)(-) and Cu(BO(2))(2)(-). In quantitative agreement with the experiment, high-level ab initio calculations reveal that spin-orbit coupling (SOC) lowers the VDE of Au(BO(2))(2)(-) significantly. The sizable magnitude of about 0.5 eV of SOC effect on the VDE of Au(BO(2))(2)(-) demonstrates that SOC plays an important role in the electronic structure of gold hyperhalogens. This study represents a new paradigm for relativistic electronic structure calculations for the one-electron-removal process of ionic Au(I)L(2) complexes, which is characterized by a substantial SOC effect.

Singlet oxygen generation versus O–O homolysis in phenyl-substituted anthracene endoperoxides investigated by RASPT2, CASPT2, CC2, and TD-DFT methods

The electronic excited states corresponding to singlet oxygen generation versus O–O splitting in o-fluorine-phenyl-9-anthracene-9,10-endoperoxide 1 and its 9,10-bisarylanthracene analog 2 have been investigated using theoretical methods. In the case of the smaller endoperoxide 1, the recently developed second-order perturbation theory restricted active space (RASPT2) method has been employed and the results are compared to those from the complete active space (CASPT2), second-order approximated coupled cluster (CC2), and time-dependent density functional theory (TD-DFT) approaches. In addition to the vertical excited states, the photochemical path leading to homolytic O–O dissociation has been computed. This process is governed by a point, where four singlet and four triplet states are almost degenerate and show substantial spin-orbit coupling. The results obtained with RASPT2 indicate that the S 1 state is of π oo * σ oo * character, corresponding to the O–O homolytic dissociation, while higher excited states S n (n ≥ 2) correspond to local and charge transfer excitations and should be correlated to the generation of singlet molecular oxygen. A similar photochemical picture is obtained with CASPT2, although two different active spaces are required to describe different parts of the spectrum. The calculations carried out with CC2 as well as the functionals CAM-B3LYP and the B3LYP(32) containing 32 % of exact exchange show good agreement with the RASPT2 energies, but present a strong mixing of π oo * σ oo * and π oo * π an * excitations in the lowest S 1 state, contradicting the assignment of RASPT2/CASPT2. The use of BP86 is strongly discouraged since it misplaces a large number of charge transfer states below the π oo * σ oo * state. The excited states of 2, calculated with B3LYP(32) are very similar to those of 1, leading to the conclusion that both endoperoxides should show a similar photochemistry, that is, the O–O cleavage seems to be partially quenched and singlet oxygen generation is enhanced, in comparison with the parent compound, anthracene-9,10-endoperoxide. The different electronic excited states of o-fluorine-phenyl-9-anthracene-9,10-endoperoxide have been benchmarked with RASPT2. The lowest excited state corresponds to the homolytic O–O dissociation and higher excited states are connected to singlet oxygen generation.

Physics. Spinning holes in semiconductors.

The electron spin is emerging as a new powerful tool in the electronics and optics industries. Many proposed applications--including quantum computers--require the creation of spin currents. However, such currents have so far proven difficult to produce in semiconductors. In his Perspective, Fertig highlights a new theoretical analysis by Murakami et al., who show how spin currents might be achieved. The authors propose using holes rather than electrons in semiconductors with substantial spin-orbit coupling.