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Layered material α-RuCl 3 has caught wide attention due to its possible realization of Kitaev's spin liquid and its electronic structure that involves the interplay of electron-electron correlations and spin-orbit effects. Several DFT+U studies have suggested that both electron-electron correlations and spin-orbit effects are crucial for accurately describing the band gap. This work studies the importance of these two effects using fixed-node and fixed-phase diffusion Monte Carlo calculations both in spin-averaged and explicit spin-orbit formalisms. In the latter, the Slater-Jastrow trial function is constructed from two-component spin orbitals using our recent quantum Monte Carlo (QMC) developments and thoroughly tested effective core potentials. Our results show that the gap in the ideal crystal is already accurately described by the spin-averaged case, with the dominant role being played by the magnetic ground state with significant exchange and electron correlation effects. We find qualitative agreement between hybrid DFT, DFT+U, and QMC. In addition, QMC results agree very well with available experiments, and we identify the values of exact Fock exchange mixing that provide comparable gaps. Explicit spin-orbit QMC calculations reveal that the effect of spin-orbit coupling on the gap is minor, of the order of 0.2 eV, which corresponds to the strength of the spin orbit of the Ru atom.
Spin relaxation and decoherence is at the heart of spintronics and spin-based quantum information science. Currently, theoretical approaches that can accurately predict spin relaxation of general solids including necessary scattering pathways and are capable of nanosecond to millisecond simulation time are urgently needed. We present a first-principles real-time density-matrix approach based on Lindblad dynamics to simulate ultrafast spin dynamics for general solid-state systems. Through the complete first-principles descriptions of pump, probe, and scattering processes including electron-phonon, electron-impurity, and electron-electron scatterings with self-consistent electronic spin-orbit couplings, our method can directly simulate the ultrafast pump-probe measurements for coupled spin and electron dynamics over nanoseconds at any temperatures and doping levels. We first apply this method to a prototypical system GaAs and obtain excellent agreement with experiments. We found that the relative contributions of different scattering mechanisms and phonon modes differ considerably between spin and carrier relaxation processes. In sharp contrast to previous work based on model Hamiltonians, we point out that the electron-electron scattering is negligible at room temperature but becomes dominant at low temperatures for spin relaxation in n-type GaAs. We further examine ultrafast dynamics in novel spin-valleytronic materials: monolayer and bilayer WSe 2 with realistic defects. We find that spin relaxation is highly sensitive to local symmetry and chemical bonds around defects. For the bilayer WSe 2 , we identify the scattering pathways in ultrafast dynamics and determine relevant dynamical properties, essential to its utilization of unique spin-valley-layer locking effects. In conclusion, our work provides a predictive computational platform for spin dynamics in solids, which has potential for designing new materials ideal for spintronics and quantum information technology.
Here, using density functional theory calculations, we investigated possible Weyl semimetal (WSM) phases in antimony arsenide ordered alloys Sb 1-x As x (x=0, 1/6, 1/3, 1/2, 2/3, 5/6, 1). We find WSM phases for all As compositions of Sb 1-x As x with broken inversion symmetry, in contrast to Bi 1-x Sb x where only compositions x=1/2 and 5/6 were predicted to exhibit WSM phases. The WSM phases in Sb 1-x As x are characterized by the presence of 12 Weyl points, located within 55 meV from the Fermi level in the case of x = 1/2. The robust spin-orbit coupling strength and Berry curvature in these alloys produce large spin-Hall conductivity in the range of 176–602 ($\hslash$/e)(S/cm), comparable to that in the BiSb alloys. Finally, Sb 0.5 As 0.5 is predicted to be almost lattice matched to GaAs(111), with the Fermi level within the gap of the semiconductor, facilitating growth and characterization, and thus, offering promising integration with conventional semiconductors.
The hexagonal antiferromagnet MnTe has attracted enormous interest as a prototypical example of a spin-compensated magnet in which the combination of crystal and spin symmetries lifts the spin degeneracy of the electron bands without the need for spin-orbit coupling, a phenomenon called nonrelativistic spin splitting (NRSS). Subgroups of NRSS are determined by the specific spin-interconverting symmetry that connects the two opposite-spin sublattices. In MnTe, this symmetry is rotation, leading to the subgroup with spin splitting away from the Brillouin zone center, often called altermagnetism. MnTe also has the largest spontaneous magnetovolume effect of any known antiferromagnet, implying strong coupling between the magnetic moment and volume. This magnetostructural coupling offers a potential knob for tuning the spin-splitting properties of MnTe. Here, we use neutron diffraction with in situ applied pressure to determine the effects of pressure on the magnetic properties of MnTe and further explore this magnetostructural coupling. We find that applying pressure significantly increases the Néel temperature, but decreases the ordered magnetic moment. We explain this as a consequence of strengthened magnetic exchange interactions under pressure, resulting in higher 𝑇 N , with a simultaneous reduction of the local moment of individual Mn atoms, described here via density functional theory. This reflects the increased orbital hybridization and electron delocalization with pressure. In conclusion, these results shed light on the competition between magnetic exchange interactions and the strength of individual magnetic moments and show that the magnetic properties of MnTe can be controlled by pressure, opening the door to improved properties for spintronic applications through tuning via physical or chemical pressure.
Oxygen-deficient Europium monoxide EuO 1-x shows a metal-to-insulator transition near the Curie temperature (T C ). A systematic transport study of EuO 1-x thin films as a function of exposure time in air reveals a gradually decreased T C from 140 K to 70 K as the concentration of the oxygen vacancies decreases, which is accompanied by a drastic increase in the resistance. Here we also find an unusual enhancement of magnetic anisotropy in the transport measurements, which results from the strong spin-orbit coupling at the interface between the film and substrate and possible presence of spin-textures like skyrmions in EuO 1-x .
Lanthanide-based single-molecule magnets (SMMs) are promising building blocks for quantum memory and spintronic devices. Designing lanthanide-based SMMs with long spin relaxation time requires a detailed understanding of their electronic structure, including the crucial role of the spin-orbit coupling (SOC). While traditional calculations of SOC using the perturbation theory applied to a solution of the non-relativistic Schrödinger equation are valid for light atoms, this approach is questionable for systems containing heavy elements such as lanthanides. We investigate the accuracy of the perturbation estimates of SOC by variationally solving the Dirac equation for the [DyO] + molecule, a prototype of a lanthanide-based SMM. We show that the energy splittings between the M J states involved in spin relaxation depend on the interplay between strong SOC and dynamic electron correlations. Here, we demonstrate that this interplay affects the resonances between the spin and vibrational transitions, and, therefore, the spin relaxation time.
A localized Zeeman field, intensified at heterostructure interfaces, could play a crucial role in a broad area including spintronics and unconventional superconductors. Conventionally, the generation of a local Zeeman field is achieved through magnetic exchange coupling with a magnetic material. However, magnetic elements often introduce defects, which could weaken or destroy superconductivity. Alternatively, the coupling between a superconductor with strong spin-orbit coupling and a nonmagnetic chiral material could serve as a promising approach to generate a spin-active interface. Here, we leverage an interface superconductor, namely, induced superconductivity in noble metal surface states, to probe the spin-active interface. Our results unveil an enhanced interface Zeeman field, which selectively closes the surface superconducting gap while preserving the bulk superconducting pairing. The chiral material, i.e., trigonal tellurium, also induces Andreev bound states (ABS) exhibiting spin polarization. The field dependence of ABS manifests a substantially enhanced interface Landég-factor (g eff ~ 12), thereby corroborating the enhanced interface Zeeman energy.
Plumbene, a two-dimensional (2D) material consisting of a single layer of lead (Pb) atoms in a honeycomb lattice, stands as a pioneering addition to the elemental 2D material family. Here, this comprehensive review encapsulates the theoretical predictions and experimental advancements that underscore its potential. With properties shaped by significant spin-orbit coupling and structural buckling, plumbene offers a playground for phenomena like the quantum spin Hall effect, superconductivity, and topological phase transitions. Despite promising theoretical insights, experimental realization has encountered challenges, primarily due to high reactivity of Pb and the need for precise fabrication conditions. This paper critically examines the electronic, thermal, mechanical, and topological attributes of plumbene, alongside synthesis methods, functionalization techniques, and substrate effects. It further proposes directions for addressing synthesis challenges and integrating plumbene into advanced technologies, particularly in electronic, spintronic, and quantum computing applications. This review aims to bridge the gap between theoretical potential and experimental progress, fostering a deeper understanding of this intriguing material.
Here, recent studies show the nonrelativistic antiferromagnetic ordering could generate momentum-dependent spin splitting analogous to the Rashba effect but free from the requirement of relativistic spin-orbit coupling. Whereas the classification of such compounds can be illustrated by different spin-splitting prototypes (SSTs) from symmetry analysis and density-functional-theory calculations, the huge variation in chemical bonding and structures of these diverse compounds possibly clouds the issue of how much of the variation in spin splitting can be traced back to the symmetry-defined characteristics, rather to the underlining chemical and structural diversity. The alternative model Hamiltonian approaches do not confront the issues of chemical and structural complexity but often consider only the magnetic sublattice, dealing with the all-important effects of the nonmagnetic ligands via renormalizing the interactions between the magnetic sites. To this end, we constructed a DFT model Hamiltonian that allows us to study SSTs at constant chemistry while retaining the realistic atomic-scale structure including ligands. This is accomplished by using a single, universal magnetic skeletal lattice (Ni 2+ ions in rocksalt NiO) and designing small displacements of the nonmagnetic (oxygen) sublattice which produce, by design, the different SST magnetic symmetries. We show that (i) even similar crystal structures having very similar band structures can lead to contrasting behavior of spin splitting vs momentum, and (ii) even subtle deformations of the nonmagnetic ligand sublattice could cause a giant spin splitting in AFM-induced SST. This is a paradigm shift relative to the convention of modeling magnets without considering the nonmagnetic ligand that mediates indirect magnetic interaction (e.g., superexchange).
When a Poincaré-invariant system spontaneously breaks continuous internal symmetries, Goldstones’ theorem demands the existence of massless, spin-zero excitations in a one-to-one correspondence with the broken symmetry generators. When a system spontaneously breaks Poincaré symmetry, however, the kinds of excitations that satisfy Goldstone’s theorem can be quite unusual. In particular, they may have any spin and need not be particles or even quasiparticles. The standard coset construction used to formulate effective actions of Goldstones, however, is rather restrictive and is incapable of generating the full spectrum of possibilities allowed by Goldstone’s theorem. We propose a (partial) remedy to this problem by postulating a novel coset construction for systems that spontaneously break Poincaré symmetry. This new construction is capable of generating effective actions with a wide range of Goldstone excitations — including fermionic degrees of freedom — even when all symmetries are bosonic. To demonstrate its utility, we focus on constructing effective actions for point particles of various spins. We recover the known result that a particle of spin s requires an \( \mathcal{N} \) = 2 s supersymmetric worldline reparameterization gauge symmetry, which we implement at the level of the coset construction. In the process, we discover that massless particles require a novel kind of inverse Higgs constraint that bears some resemblance to the dynamical inverse Higgs constraints that appear in certain fermi liquid effective field theories. We then consider particles that, in addition to quantum spin, have finite spatial extent and are free to rotate. We derive a novel action for such particles and find a ‘spin-orbital’ coupling between the intrinsic quantum spin and the physical-rotation degrees of freedom.
Potential energy curves (PECs) for the spin-free (ΛS) and spin–orbit (Ω) states associated with the four lowest-lying dissociation channels of Na 2 and K 2 were calculated at the SA-CASSCF/SO-CASPT2/aug-cc-pwCVQZ-DK level. The PECs of Na 2 were consistent with the experimental data and with the FS-CCSD (2,0) calculations, reproducing the double-well and the “shelf” character for some of the potentials of the excited states. For K 2 , the PECs behaved in a similar way and the spectroscopic parameters for the ground and the excited states are in good agreement with the available experimental values. The dissociation energy of K 2 was predicted to be D e = 4454 cm −1 , within an agreement of 5 cm −1 with the experiments. For Na 2 , D e = 5789 cm −1 compared to the experimental value of 6022 cm −1 . The inclusion of spin–orbit coupling effects resulted in avoided crossings, which affect the PECs. Spin–orbit changes the predicted curves for some excited Ω states arising from ΛS states that overlap each other, affecting their associated vibrational frequencies and bond distances. Here, the current studies of the low-lying states in K 2 reveal a similar structure to those of Na 2 , which suggests the accessibility of long-lived energy storing reservoir states and possible population inversions in K 2 following prior experimental work on the reaction of halogen atoms with Na 3 to produce excited states of Na 2 .
Zintl phases, containing strongly covalently bonded frameworks with separate ionically bonded ions, have emerged as a critical materials family in which to couple magnetism and strong spin-orbit coupling to drive diverse topological phases of matter. Here we report the single-crystal synthesis, magnetic, thermodynamic, transport, and theoretical properties of the Zintl compound EuZn 2 P 2 that crystallizes in the anti-La 2 O 3 (CaAl 2 Si 2 ) P-3m1 structure, containing triangular layers of Eu 2+ ions. In-plane resistivity measurements reveal insulating behavior with an estimated activation energy of E g = 0.11eV. Specific heat and magnetization measurements indicate antiferromagnetic ordering at T N = 23K. Curie-Weiss analysis of in-plane and out of plane magnetic susceptibility from T = 150 to 300 K yields p eff = 8.61 for μ 0 H⊥c and p eff = 7.74 for μ 0 H//c, close to the expected values for the 4f 7 J = S = 7/2 Eu 2+ ion and indicative of weak anisotropy. Below T N , a significant anisotropy of χ ⊥ /χ // ≈ 2.3 develops, consistent with A-type magnetic order as observed in isostructural analogs and as predicted by the density functional theory calculations reported herein. The positive Weiss temperatures of θ W =19.2K for μ 0 H⊥c and θ W =41.9K for μ 0 H//c show a similar anisotropy and suggest competing ferromagnetic and antiferromagnetic interactions. Comparing Eu magnetic ordering temperatures across trigonal EuM 2 X 2 (M= divalent metal, X= pnictide) shows that EuZn 2 P 2 exhibits the highest ordering temperature, with variations in T N correlating with changes in expected dipolar interaction strengths within and between layers and independent of the magnitude of electrical conductivity. These results provide experimental validation of the crystochemical intuition that the cation Eu 2+ layers and the anionic (M 2 X 2 ) 2– framework can be treated as electronically distinct subunits, enabling further predictive materials design.
Abstract The helical edge states of time-reversal invariant two-dimensional topological insulators are protected against backscattering in idealized models. In more realistic scenarios with a shallow confining potential at the sample boundary, additional strongly interacting edge states may arise, that could interfere with the topological protection of edge conduction. We find that interaction effects within the reconstructed edges are well described by the Luttinger liquid model. While interactions between this Luttinger liquid and the helical edge states can in principle give rise to dynamical spin polarization and the breaking of time-reversal symmetry, we demonstrate that random spin-orbit coupling strongly suppresses such dynamical spin polarization, resulting in the persistence of near quantized edge conduction.
Significance Although out-of-plane current-induced spin polarization (CISP) is important for perpendicular-magnetization reorientation, and it has been realized by the crystalline symmetry breaking, its material examples are relatively fewer compared with in-plane CISP in Rashba systems. With the help of intrinsic spin–orbit coupling, an intriguing out-of-plane CISP is designed in transition-metal dichalcogenides by the symmetry breaking in the spin space, which provides opportunities for out-of-plane magnetization rotation and electric control of valley splitting. Moreover, the spin polarization is associated with valley-dependent responses to electric current and adds a dimension, valley degree of freedom, to the study of CISP. The symmetry argument and non-Rashba effective model also helps to illuminate these physics and broaden the scope of the CISP.
The superconductor ThIrSi, with Tc=6.5K, is expected to show unusual features in view of its noncentrosymmetric structure and the presence of heavy elements featuring a sizable spin-orbit coupling. Here, we report a comprehensive study of its electronic properties by means of magnetization, muon-spin rotation and relaxation (μSR) and nuclear magnetic resonance (NMR) measurements. Both the superfluid density ρ sc (T) (determined via transverse-field μSR) and the spin-lattice relaxation rate T–1 1(T) (determined via NMR) suggest a nodeless superconductivity. Furthermore, the absence of spontaneous magnetic fields below T c , as evinced from zero-field μSR measurements, indicates a preserved time-reversal symmetry in the superconducting state of ThIrSi. Finally, temperature-dependent upper critical fields as well as field-dependent superconducting muon-spin relaxations suggest the presence of multiple superconducting gaps in ThIrSi.
The goal of this project is to gain theoretical insight into magnetism in the presence of spin-orbit coupling (SOC) for multi-orbital Mott insulators. Inspired by the exact solution of the Kitaev model that harbors a quantum spin liquid with novel excitations and struck by its relevance for materials with anisotropic orbital interactions, the PI will explore various new classes of 4d and 5d transition metal oxides. Starting with all electron Hamiltonians, the PI will derive minimal magnetic models. The aim will be to understand the role played by orbital frustration, even in the absence of any geometric frustration, in creating orbitally ordered as well as spin-orbital liquid phases. Orbital frustration arises primarily from the directional or anisotropic nature of d-orbitals in contrast to the isotropic nature of the spin degree of freedom. These models will be investigated by a variety of theoretical and numerical methods, including exact diagonalization, mean field theories, density matrix renormalization group and quantum Monte Carlo methods. Testable predictions for three experiments: nuclear magnetic resonance (NMR) and resonant x-ray scattering (RXS) to probe orbital ordering and pump-probe experiments to probe quantum dynamics will test the validity of these models for materials.
Monolayer semiconducting transition metal dichalcogenides possess broken inversion symmetry and strong spin-orbit coupling, leading to a unique spin-valley locking effect. In 2H stacked pristine multilayers, spin-valley locking yields an electronic superlattice structure, where alternating layers correspond to barriers and quantum wells depending on the spin-valley indices. Here, in this work, we show that the spin-valley locked superlattice hosts a kind of dipolar exciton with the electron and hole constituents separated in an every-other-layer configuration: that is, either in two even or two odd layers. Such excitons become optically bright via hybridization with intralayer excitons. This effect is also manifested by the presence of multiple anti-crossing patterns in the reflectance spectra, as the dipolar exciton is tuned through the intralayer resonance by an electric field. The reflectance spectra further reveal an excited state orbital of the every-other-layer exciton, pointing to a sizable binding energy in the same order of magnitude as the intralayer exciton. As layer thickness increases, the dipolar exciton can form a one-dimensional Bose–Hubbard chain displaying layer number-dependent fine spectroscopy structures.