Strong Spin-orbit Coupling Effects Research Articles

Wafer-scale synthesis of 2D PtTe2 thin films with high spin–orbit torque efficiency

Spintronic devices have become a crucial technology for overcoming the power consumption bottleneck in integrated circuits, due to their low power consumption, high-speed processing capability. Two-dimensional materials offer potential for performance enhancement and device miniaturization in spintronics because of their unique electronic and spin properties. Specifically, two-dimensional transition metal dichalcogenides (2D TMDs) are favored in the field of spintronics for their strong spin–orbit coupling effects, enabling effective control over the electron spin state. However, the preparation techniques for 2D TMDs are still in the exploratory stage. In this work, we explore novel preparation method combining magnetron sputtering and molecular beam epitaxy, leading to wafer-scale high-quality monocrystalline PtTe2 thin films. Further, Spin-Orbit Torque (SOT) efficiency is investigated in PtTe2-based heterostructures, which reveals a significant spin Hall angle of over 0.094. Our work provides a new way to fabricate the wafer-scale PtTe2 thin films and confirms a large SOT efficiency, which indicates the great promise for spintronic applications.

Orbital-Selectivity-Induced Robust Quantum Anomalous Hall Effect in Hund's Metals MgFeP.

Ferromagnetic (FM) states with high Curie temperatures (Tc) and strong spin-orbit coupling (SOC) are indispensable for the long-sought room-temperature quantum anomalous Hall (QAH) effects. Here, we propose a two-dimensional (2D) iron-based monolayer MgFeP that exhibits a notably high FM Tc (about 1525 K) along with exceptional structural stabilities. The unique multiorbital nature in MgFeP, where localized and dxz/yz orbitals coexist with itinerant dxy and dz2 orbitals, renders the monolayer a Hund's metal and in an orbital-selective Mott phase (OSMP). This OSMP triggers an FM double exchange mechanism, rationalizing the high Tc in the Hund's metal. This material transitions to a QAH insulator upon consideration of the SOC effect. By leveraging orbital selectivity, the QAH band gap can be enlarged by more than two times (to 137 meV). Our findings showcase Hund's metals as a promising material platform for realizing high-performance quantum topological electronic devices.

Dzyaloshinsky–Moriya Interaction Induced Anomalous g Behavior of Sr2IrO4 Probed by Electron Spin Resonance

Among the 5d transition metal iridates, Sr2IrO4, which has a layered chalcogenide structure, has received much attention due to its strong spin–orbit coupling (SOC), which produces Mott insulating states and anomalous physical behaviors. In this paper, the microscopic magnetism of Sr2IrO4 is studied with electron spin resonance (ESR) measurements. The Lande factor g of the ferromagnetic resonance signal of Sr2IrO4 shows anomalous behavior compared to typical ferromagnets. It gradually decreases, and the corresponding resonance field Hr increases, with decreasing temperature. The various physical parameters. including the saturated magnetic field Hs derived from M-H, Hr, ΔHpp, the g factor and the intensity I extracted from ESR spectra, are analyzed in detail. Eventually, it is revealed that the anomalous behavior of the g-factor is induced by in-plane Dzyaloshinsky–Moriya interaction (DMI) rather than the SOC effect.

First-principles investigations on the electronic structure, optical properties, and giant magnetic-optical Kerr effect in double-perovskite Ba2NiBO6 (B = Os, Ir)

The hybrid 3d–5d transition-metal oxides have been frequently studied for their novel electronic and magnetic properties, in which the strong spin-orbit coupling (SOC) effect is added to the interplay among charge, spin, and orbital degrees of freedom. Recently, perfectly ordered 3d–5d double-perovskite oxides of Ba2NiOsO6 and Ba2NiIrO6 were synthesized: Ba2NiOsO6 was measured to be a rare ferromagnetic semiconductor and predicted to have a giant magneto-optical Kerr effect (MOKE); and Ba2NiIrO6 showed a competition between antiferromagnetic and ferromagnetic interactions. In this work, we systematically investigated the magnetic, electronic, and optical properties, as well as the MOKE of Ba2NiBO6 (B = Os, Ir) using density functional theory. The long-ranged B–B interaction was found to play a key role in determining the magnetism of the compounds. For Ba2NiOsO6, the experimentally observed semiconductive nature was reproduced only by taking into account both the electron correlation and SOC effect. In Ba2NiIrO6, however, the SOC effect on 5d Ir was weak. Owing to the d→d or p→d interband transitions, both materials had a strong absorption in the ultraviolet–visible spectral region. In particular, the absorption spectrum of Ba2NiIrO6 covered almost the entire visible region. They also exhibited considerable MOKE in the visible region. The maximum of Kerr rotation for Ba2NiOsO6 and Ba2NiIrO6 could reach 5.3° and 4.1°, respectively. The characteristics of the Kerr spectra were primarily dominated by the off-diagonal optical conductivity, which reflects the contributions of band exchange splitting and SOC to MOKE. The Ba2NiBO6 (B = Os, Ir) are very promising optoelectronic and magneto-optical materials.

Enhanced Rashba Spin Orbit Coupling and Magnetic Behavior at Oxide Heterointerfaces by Optical Gating.

Complex oxide heterointerfaces have been a hot research spot due to their rich physical phenomena and broad quantum coherence that respond to multiple external stimuli. Among these external stimuli, light is a very powerful one to manipulate properties such as carrier density and spin characteristics. However, achieving a light-magnetic correlation is in high demand for multifield responding devices, and its intrinsic mechanism remains unclear. Here, by illuminating Nd0.86Sr0.14Al0.86Ni0.14O3-SrTiO3 heterointerfaces using 360 nm light, we observe a series of interesting physical phenomena, like enhanced magnetoresistance (MR). More interestingly, a band splitting and strong Rashba spin-orbit coupling (SOC) effect occur after illumination, accompanied by a magnetic feature and thus leading to an anomalous Hall effect (AHE). Upon optical gating, the magnetism can be caused by Rashba SOC induced spin-orbit torque (SOT). The work will be sure to have great importance in both theoretical studies and all-oxide devices.

The Role of Polaronic States on the Spin Dynamics in Solution-Processed Two-Dimensional Layered Perovskite with Different Layer Thickness.

2D lead halide perovskites (LHPs) show strong excitonic and spin-orbit coupling effects, generating a facile spin injection. Besides, they possess a polaron character due to the soft crystal lattice, which can prolong the spin lifetime, making them favorable materials for spintronic applications. Here, the spin dynamics of 2D PEA2 PbI4 (MAPbI3 )n -l thin films with different layers by temperature- and pump fluence-dependent circularly polarization-resolved transient absorption (TA) measurements is studied. These results indicate that the spin depolarization mechanism is gradually converted from the Maialle-Silva-Sham (MSS) mechanism to the polaronic states protection mechanism with the layer number increasing from <n> = 1 to 3, which is determined by the interplay between the strength of Coulomb exchange interaction and the strength of polaronic effect. While for <n> ≥ 4, the Elliot-Yafet (EY) impurities mechanism is proposed, in which the formed polaronic states with free charge carriers no longer play the protective role.

Chiral Hybrid Perovskites (R-/S-CLPEA)4Bi2I10 with Enhanced Chirality and Spin–Orbit Coupling Splitting for Strong Nonlinear Optical Circular Dichroism and Spin Selectivity Effects

Chiral hybrid halide perovskites have attracted considerable attention in optoelectronics and spintronics owing to their unique optical, electric, and spin–orbit coupling (SOC) properties. In this article, with focus on the design scheme to increase the nonlinear optical (NLO) circular dichroism (CD) and spin selectivity effects by assembling chlorine-modified chiral R-/S-CLPEA [CLPEA = 1-(4-chlorophenyl)ethylamine] into bismuth-based perovskites, a pair of chiral hybrid perovskites (R-/S-CLPEA)4Bi2I10 were synthesized and characterized experimentally. A large NLO CD effect and strong spin-dependent charge transport were confirmed by the experimental measurements. The unique chirality-induced spin textures were illustrated in the SOC band structures from first-principles simulations. The combined theoretical and experimental results demonstrate that it is the synergic effect of large chirality of CLPEA and strong SOC effect of the Bi2I10 dimer that endows these perovskites with unique chiral spin textures, strong NLO CD effect, and remarkable spin-dependent charge transport properties, which are of importance for the functional design of chiral perovskites in nonlinear optics and spintronics.

Origin of Subgap States in Normal-Insulator-Superconductor van der Waals Heterostructures.

Superconductivity in van der Waals materials, such as NbSe2 and TaS2, is fundamentally novel due to the effects of dimensionality, crystal symmetries, and strong spin-orbit coupling. In this work, we perform tunnel spectroscopy on NbSe2 by utilizing MoS2 or hexagonal boron nitride (hBN) as a tunnel barrier. We observe subgap excitations and probe their origin by studying various heterostructure designs. We show that the edge of NbSe2 hosts many defect states, which strongly couple to the superconductor and form Andreev bound states. Furthermore, by isolating the NbSe2 edge we show that the subgap states are ubiquitous in MoS2 tunnel barriers but absent in hBN tunnel barriers, suggesting defects in MoS2 as their origin. Their magnetic nature reveals a singlet- or a doublet-type ground state, and based on nearly vanishing g factors or avoided crossings of subgap excitations, we highlight the role of strong spin-orbit coupling.

Effects of strong spin-orbit coupling on Shiba states from magnetic adatoms using first-principles theory

Magnetic impurities at surfaces of superconductors can induce bound states referred to as Yu–Shiba–Rusinov states (i.e. Shiba states) within superconducting (SC) gaps. For superconductors with strong spin–orbit coupling (SOC), Shiba states arising from even single magnetic adatoms are too complex to be fully understood using effective models alone because SOC cannot be treated perturbatively and multiple orbitals are strongly mixed with spin projections. Here we investigate Shiba states of single magnetic adatoms at the surface of strongly spin-orbit coupled SC Pb, by solving the fully relativistic Dirac–Bogoliubov–de Gennes equations using multiple scattering Green’s function methods. For Fe and Co adatoms on Pb(110), we show that the Shiba states are better characterized by total angular momentum, J, and its projections on the z axis, m J . As a hallmark of the SOC effect, the Shiba states show a strong dependence of the orientation of the adatom moment. As the orientation of the Fe/Co moment changes, the deepest Shiba states merge at zero energy. This zero-energy state disappears with an additional non-magnetic adatom next to the magnetic adatom, although the other Shiba states unchange. For a Mn adatom on Pb, our Shiba states overall agree with experiments. The characteristics of our Shiba states are also observed with the similar energies and characters in the experiments. The deepest Shiba states that we compute, however, do not appear as close to the Fermi level as the experimental data. It would be interesting to compute the Shiba states with continuously varying vertical distances of the Mn adatom from the surface or with varying the charge state of the adatom, and to calculate the spatial dependence of the spectral density. Our findings will be also useful for understanding of Shiba states for dimers and longer spin chains on the Pb surface considering noncollinear magnetic structures in them.

Role of spin-orbit coupling effects in rare-earth metallic tetra-borides: a first principle study

We have investigated the electronic structure of rare-earth tetraborides, $\textrm{RB}_{4}$, using first-principle electronic structure methods (DFT) implemented in Quantum Espresso (QE). In this article we have studied heather-to neglected strong spin-orbit coupling (SOC) effects present in these systems on the electronic structure of these system in the non-magnetic ground state. The calculations were done under GGA and GGA+SO approximations using ultrasoft pseudopotentials and fully relativistic ultrasoft pseudopotentials (for SOC case). Perdew-Burke-Ernzerhof generalized gradient approximation (PBE-GGA) exchange-correlation functionals within the linearized plane-wave (LAPW) method as implemented in QE were used. The projected density of states consists of 3 distinct spectral peaks well below the Fermi energy and separated from the continuum density of states around the Fermi energy. The discrete peaks arises due to rare-earth $s$-orbital, rare-earth $p$ + B $p$ and B $p$-orbitals while the continuum arises due to hybridized B $p$, rare-earth $d$ orbitals. Upon inclusion of SOC the peak arising due to rare-earth $p$-orbitals gets split into two peaks corresponding to $j=0.5$ and $j=1.5$ configurations. In case of $\textrm{LaB}_{4}$, in the presence of SOC, spin-split $4f$ orbitals contributes to density of states at the Fermi level while the density of states at the Fermi level largely remains unaffected for all other materials under consideration.

Electronic, spintronic, and piezoelectric properties of new Janus ZnAXY ( A=Si,Ge,Sn , and X,Y=S,Se,Te ) monolayers

Two-dimensional (2D) Janus materials due to their asymmetric structures show fascinating spintronic and piezoelectric properties making them a research hot spot in recent years. In this work, inspired by Janus group-III monochalcogenides, we propose $\mathrm{Zn}AXY$ ($A=\mathrm{Si}$, Ge, Sn, and $X/Y=\mathrm{S}$, Se, Te, $X&lt;Y$) monolayers as a novel structure with broken inversion and mirror symmetry. By calculating cohesive energy and phonon dispersion, eight of nine possible $\mathrm{Zn}AXY$ monolayers are proved to be dynamically stable. In addition, thermal stability of these eight structures is confirmed by ab initio molecular dynamics simulations. The electronic band structures of $\mathrm{Zn}AXY$ monolayers indicate that all of them are indirect semiconductors with strong spin-orbit coupling effects. Lack of inversion symmetry gives rise to Zeeman-type spin splitting at the $K$ point of the conduction band with the highest value of 136 meV for ZnSiSeTe. Furthermore, out-of-plane asymmetry results in Rashba spin splitting (RSS) at the \ensuremath{\Gamma} point of the valence and conduction bands in the most compositions of Janus $\mathrm{Zn}AXY$ monolayers. Among them, ZnGeSTe with ${\ensuremath{\alpha}}_{R}^{{\mathrm{\ensuremath{\Gamma}}}_{V}}$ of $1.79\phantom{\rule{0.28em}{0ex}}\mathrm{eV}\phantom{\rule{0.28em}{0ex}}\AA{}$ and ${\ensuremath{\alpha}}_{R}^{{\mathrm{\ensuremath{\Gamma}}}_{c}}$ of $0.862\phantom{\rule{0.28em}{0ex}}\mathrm{eV}\phantom{\rule{0.28em}{0ex}}\AA{}$ and ZnSiSTe with ${\ensuremath{\alpha}}_{R}^{{\mathrm{\ensuremath{\Gamma}}}_{V}}$ of $1.537\phantom{\rule{0.28em}{0ex}}\mathrm{eV}\phantom{\rule{0.28em}{0ex}}\AA{}$ and ${\ensuremath{\alpha}}_{R}^{{\mathrm{\ensuremath{\Gamma}}}_{c}}$ of $0.756\phantom{\rule{0.28em}{0ex}}\mathrm{eV}\phantom{\rule{0.28em}{0ex}}\AA{}$ are found to be great materials for future spintronic applications. Interestingly, in addition to large RSS, Mexican hat dispersion is observed at the \ensuremath{\Gamma} point of the topmost valence band in these materials. Moreover, the calculated elastic coefficients for the hexagonal $\mathrm{Zn}AXY$ monolayers confirm the mechanical stability of the predicted structures. Finally, Janus $\mathrm{Zn}AXY$ monolayers possess high in-plane (up to 7.46 pm/V) and out-of-plane (up to 0.67 pm/V) piezoelectric coefficients making them appealing alternatives for prevalent piezoelectric materials.

Interplay of charge ordering and superconductivity in two-dimensional 2H group V transition-metal dichalcogenides

Layered $2H\text{\ensuremath{-}}T{X}_{2}$ with $T=\mathrm{Nb}$, Ta and $X=\mathrm{S}$, Se exhibit rich dimensionality effects on charge density wave (CDW) order and superconductivity, but comprehensive understanding of these correlated quantum phases in the two-dimensional limit of $2H\text{\ensuremath{-}}T{X}_{2}$ is still lacking, hindering their practical applications. Here, I calculate from first principles the phonon linewidth and bare susceptibility to study the origin of CDW formation in ${\mathrm{NbSe}}_{2}$, ${\mathrm{TaS}}_{2}$, ${\mathrm{TaSe}}_{2}$, and ${\mathrm{NbS}}_{2}$ monolayers, analyze their relative CDW strength, and evaluate electron-phonon superconductivity within the fully anisotropic Migdal-Eliashberg theory. A peaked linewidth of the longitudinal acoustic branch and no Fermi-surface nesting around ${\mathbf{q}}_{\mathrm{CDW}}$ indicate CDW instability driven by the wave-vector-dependent electron-phonon coupling. The $3\ifmmode\times\else\texttimes\fi{}3$ CDW ground state favors a distinct hollow-centered clustering of transition-metal atoms, with larger distortion amplitude in ${\mathrm{NbSe}}_{2}$ and ${\mathrm{TaSe}}_{2}$ than in ${\mathrm{TaS}}_{2}$ and ${\mathrm{NbS}}_{2}$. Superconducting results of the monolayer CDW phase prove that strong spin-orbit coupling effects are dominant in determining the critical temperature ${T}_{\mathrm{c}}$ of each system via modifying both the strength and anisotropic extent of electron-phonon interactions. I also recapitulate measured opposite thickness dependencies of ${T}_{\mathrm{c}}$ in $\mathrm{Nb}{X}_{2}$ and $\mathrm{Ta}{X}_{2}$, and show that whether superconductivity is weakened or enhanced in monolayer limit relies on specific evolution of CDW-modulated Fermi-level density of states and electron-phonon matrix elements under reduced dimensionality. This work lays the foundation for applications of $2H$ group V transition-metal dichalcogenides in versatile nanoscale quantum devices.

Bloch-type magnetic skyrmions in two-dimensional lattices.

Magnetic skyrmions in two-dimensional lattices are a prominent topic of condensed matter physics and materials science. Current research efforts in this field are exclusively constrained to Néel-type and antiskyrmions, while Bloch-type magnetic skyrmions are rarely explored. Here, we report the discovery of Bloch-type magnetic skyrmions in a two-dimensional lattice of MnInP2Te6, using first-principles calculations and Monte-Carlo simulations. Arising from the joint effect of broken inversion symmetry and strong spin-orbit coupling, monolayer MnInP2Te6 presents large Dzyaloshinskii-Moriya interaction. This, along with ferromagnetic exchange interaction and out-of-plane magnetic anisotropy, gives rise to skyrmion physics in monolayer MnInP2Te6, in the absence of a magnetic field. Remarkably, different from all previous works on two-dimensional lattices, the resultant magnetic skyrmions feature Bloch-type magnetism, which is protected by D3 symmetry. Furthermore, Bloch-type magnetic bimerons are also identified in monolayer MnTlP2Te6. The phase diagrams of these Bloch-type topological magnetisms under a magnetic field, temperature and strain are mapped out. Our results greatly enrich the research on magnetic skyrmions in two-dimensional lattices.

The tunable anisotropic Rashba spin-orbit coupling effect in Pb-adsorbed Janus monolayer WSeTe.

The spin-splitting properties of Pb-adsorbed monolayer Janus WSeTe are investigated based on first-principles calculations. The adsorbed system shows large Rashba splitting (the Rashba parameter is up to 0.75 eV Å), and we find that different adsorption layers (Te/Se adsorption layers) exhibit different significant features under spin-orbit coupling. Zeeman splitting and Rashba splitting co-exist at the high symmetry Γ point of the Te adsorption layer, while the Se adsorption layer exhibits anisotropic Rashba spin-orbit coupling. It was determined using k·p perturbation theory that Pb atom adsorption reduces the initial symmetry of the 2H-WSeTe monolayer and induces a strong spin-orbit coupling effect, so as to induce the anisotropic Rashba effect. Furthermore, the tunability of Rashba splitting was demonstrated by varying the adsorption concentration, adjusting the adsorption distance, and applying biaxial strain. This predicted adsorption system has potential value in spintronic devices.

Large magnetostriction of heavy-metal-element doped Fe-based alloys

Using density functional theory calculation and rigid band model, we investigate the electronic structure and magnetostrictive properties of transition heavy-metal doped Fe-based (Fe–Al, Fe–Si, Fe–B, and Fe–Be) alloys. It is found that a small amount of addition of 4d/5d heavy-metal atoms greatly enhances the coefficient of tetragonal magnetostriction of Fe-based alloys, reaching up to about 1000 ppm in Fe87.5Al6.25Pt6.25 and Fe75Al18.75Rh6.25 alloys. The underlying mechanism is mainly ascribed to combined factors of band narrowing induced by non-bonded states in pure Fe layer, strong spin–orbit coupling effect by heavy metals, and improved mechanical properties, through analysis of the electronic density of states near Fermi level and k-mesh resolved magnetocrystalline anisotropy energy in momentum space. These results provide useful guidance for optimizing the magnetostrictive performance of Fe-based alloys for practical application.

Magnetic interactions in AB-stacked kagome lattices: Magnetic structure, symmetry, and duality

We present the results of an extensive study of the phase diagram and spin wave excitations for a general spin model on a hexagonal AB-stacked kagome system. The boundaries of the magnetic phases are determined via a combination of numerical (Monte Carlo) and analytical (Luttinger-Tisza) methods. We also determine the phase coexistence regions by considering the instabilities in the spin wave spectra. Depending on the strength of the spin-orbit coupling (SOC), some spin and lattice rotations become decoupled, leading to considerably larger symmetry groups than typical magnetic groups. Thus, we provide a detailed symmetry description of the magnetic Hamiltonian with negligible, weak, and intermediate strength of SOC. The spin symmetry in these three cases has a strong effect on the splittings observed in the spin excitation spectra. We further identify a number of self-duality transformations that map the Hamiltonian onto itself. These transformations describe the symmetry of the parameter space and provide an exact mapping between the properties of different magnetic orders and lead to accidental degeneracies. Finally, we discuss the physical relevance of our findings in the context of $\mathrm{Mn}_3X$ compounds.

Ruthenium-doping-induced strong electromagnetic loss in FeCo nanoparticles by orbital hybridization and electron transmission

Ferromagnetic metal/alloy particles are widely used in the field of electromagnetic wave absorption. Doping is an effective means of modulating the electromagnetic properties of magnetic metals and alloys. In this study, (Fe3Co7)1−xRux nanoparticles with different Ru doping contents are prepared using a polyvinylpyrrolidone (PVP)-assisted liquid-phase reduction process. First-principles calculations reveal that strong electron-orbit hybridization occurs between Ru-4d and Fe/Co-3d owing to the strong spin-orbit coupling effect of Ru-4d orbital electrons. This generates a space charge distribution and carries a magnetic moment of 1.80 hbar/2. The use of Ru doping results in a reduction in FeCo alloy particle size from 1.5 µm to 200 nm, slight decrease in the saturation magnetization from 179 to 152 emu/g, and increase in the electrical conductivity from 2.79 × 10-4 to 6.62 × 10-4 S·cm-1. The dielectric and magnetic loss values vary from 0.22 to 0.95 and 0.06–0.37, respectively, in the 2–18 GHz frequency range. Ru doping-induced dipole polarization relaxation, exchange resonance, and increased conductivity loss are the primary reasons for the enhanced electromagnetic loss of the material. When the level of Ru doping x reaches 0.10, the minimum reflection loss (RLmin) increases from − 21.5 to − 41.9 dB. Thus, (Fe3Co7)1−xRux is a promising material for electromagnetic loss due to its tunable composition, size, conductivity, magnetic properties, and excellent electromagnetic loss capability.

Momentum microscopy of Pb-intercalated graphene on SiC: Charge neutrality and electronic structure of interfacial Pb

Intercalation is an established technique for tailoring the electronic structure of epitaxial graphene. Moreover, it enables the synthesis of otherwise unstable two-dimensional (2D) layers of elements with unique physical properties compared to their bulk versions due to interfacial quantum confinement. In this work, we present uniformly Pb-intercalated quasi-freestanding monolayer graphene on SiC, which turns out to be essentially charge neutral with an unprecedented $p$-type carrier density of only $(5.5\pm2.5)\times10^9$ cm$^{-2}$. Probing the low-energy electronic structure throughout the entire first surface Brillouin zone by means of momentum microscopy, we clearly discern additional bands related to metallic 2D-Pb at the interface. Low-energy electron diffraction further reveals a $10\times10$ Moir\'e superperiodicity relative to graphene, counterparts of which cannot be directly identified in the available band structure data. Our experiments demonstrate 2D interlayer confinement and associated band structure formation of a heavy-element superconductor, paving the way towards strong spin-orbit coupling effects or even 2D superconductivity at the graphene/SiC interface.

Spin-Orbit-Torque Efficiency and Current-Driven Coherent Magnetic Dynamics in a Pt / Ni /Py Trilayer-Based Spin Hall Nano-Oscillator

We experimentally study the current-induced effective spin-orbit torque (SOT) efficiency and the spectral characteristics of current-driven coherent magnetic dynamics in spin Hall nano-oscillators (SHNOs) based on the $\mathrm{Pt}$/$\mathrm{Ni}$/Py trilayer. We determine that the $\mathrm{Pt}$/$\mathrm{Ni}$/Py trilayer structure has an effective dampinglike torque efficiency ${\ensuremath{\xi}}_{\mathrm{DL}}\ensuremath{\sim}0.055$, comparable with the $\mathrm{Pt}$/$\mathrm{Co}$ and $\mathrm{Pt}$/$\mathrm{Fe}$ bilayer systems with a strong interfacial spin-orbit coupling and magnetic proximity effect. Furthermore, the microwave-generation spectra show that the $\mathrm{Pt}$/$\mathrm{Ni}$/Py-based SHNOs exhibit a single nonlinear self-localized bullet mode with a frequency below ${f}_{\mathrm{FMR}}$ and a significant current-dependent frequency red shift due to its strong nonlinear effect, which is very similar to that in $\mathrm{Pt}$/Py-based SHNOs, at low oblique angles $\ensuremath{\varphi}\ensuremath{\le}\phantom{\rule{0.2em}{0ex}}{50}^{\ensuremath{\circ}}$. In contrast, at high oblique angles $\ensuremath{\varphi}\ensuremath{\ge}\phantom{\rule{0.2em}{0ex}}{55}^{\ensuremath{\circ}}$, the spectra show two oscillating peaks with very similar field-, current-, and temperature-dependent behaviors, which suggests the spatial coexistence of two same-type nonlinear self-localized bullet modes at certain currents and magnetic fields. Additionally, the observed linear temperature dependence of the minimum line width, which resembles the thermal broadening of single-mode oscillation, further confirms that two localized bullet modes are independent, spatially separated, and lack thermally activated mode-transition behavior. Our results provide valuable information for the electronic control of coherent magnetic dynamics by combining bulk and interfacial spin-orbit coupling effects in the magnetic heterostructures.

Bi Layer Properties in the Bi–FeNi GMR-Type Structures Probed by Spectroscopic Ellipsometry

Bismuth (Bi) having a large atomic number is characterized by a strong spin–orbit coupling (SOC) and is a parent compound of many 3D topological insulators (TIs). The ultrathin Bi films are supposed to be 2D TIs possessing a nontrivial topology, which opens the possibility of developing new efficient technologies in the field of spintronics. Here we aimed at studying the dielectric function properties of ultrathin Bi/FeNi periodic structures using spectroscopic ellipsometry. The [Bi(d)–FeNi(1.8 nm)]N GMR-type structures were grown by rf sputtering deposition on Sitall-glass (TiO2) substrates. The ellipsometric angles Ψ(ω) and Δ(ω) were measured for the grown series (d = 0.6, 1.4, 2.0, and 2.5 nm, N = 16) of the multilayered film samples at room temperature for four angles of incidence of 60∘, 65∘, 70∘, and 75∘ in a wide photon energy range of 0.5–6.5 eV. The measured ellipsometric angles, Ψ(ω) and Δ(ω), were simulated in the framework of the corresponding multilayer model. The complex (pseudo)dielectric function spectra of the Bi layer were extracted. The GMR effects relevant for the studied Bi–FeNi MLF systems were estimated from the optical conductivity zero-limit (optical GMR effect). The obtained results demonstrated that the Bi layer possessed the surface metallic conductivity induced by the SOC effects, which was strongly enhanced on vanishing the semimetallic-like phase contribution on decreasing the layer thickness, indicating its nontrivial 2D topology properties.