Recently, huge attention has been drawn to improve optical sensing devices based on photonic resonators in the presence of graphene. In this paper, based on the transfer matrix approach and TE polarization for the incident electromagnetic waves, we numerically evaluate the transmission and reflection spectra for one-dimensional photonic resonators and surface plasmon resonances with strained graphene, respectively. We proved that a relatively small strain field in graphene can modulate linearly polarized resonant modes within the photonic bandgap of the defective crystal. Moreover, we study the strain effects on the surface plasmon resonances created by the evanescent wave technique at the interference between a monolayer graphene and prism.
We report on the strain-induced switch between ferromagnetic (FM) and antiferromagnetic (AFM) orderings in 1T-CrX2 (X = Se, Te) monolayers based on the first-principles calculations. The CrSe2 and CrTe2 monolayers without strains are found to be AFM and FM, respectively. Under the biaxial tensile strain, the CrSe2 monolayer tends to be FM when the strain is larger than 2%. The FM state is further stabilized when the strain is increased. Moreover, the CrSe2 monolayer changes to be half-metallic when the tensile strain is larger than 10%. While for the CrTe2 monolayer, the critical strain at whi…
Recently, two-dimensional monolayer MoSi2N4 with hexagonal structure was successfully synthesized in experiment (Hong et al 2020 Science 369, 670). The fabricated monolayer MoSi2N4 is predicted to have excellent mechanical properties. Motived by the experiment, we perform first-principles calculations to investigate the mechanical properties of monolayer MoSi2N4, including its ideal tensile strengths, critical strains, and failure mechanisms. Our results demonstrate that monolayer MoSi2N4 can withstand stresses up to 51.6 and 49.2 GPa along zigzag and armchair directions, respectively. The cor…
Using first-principles calculations, we systematically investigate the electronic structures and band topologies of four kinds of group-V elemental (P, As, Sb and Bi) monolayers with buckled honeycomb structure. It is found that all these monolayers can change from semiconducting to semimetallic under compressive strain. If a tensile strain is however applied, the P, As and Sb monolayers undergo phase transition from topologically trivial to non-trivial regime, whereas the topological insulating nature of Bi monolayer remains unchanged. With tunability of the band gaps and band topologies, it …
Using first-principles full-potential density functional calculations, we predict that mechanically tunable band-gap is realizable in ZnS monolayer in graphene-like honeycomb structure by application of in-plane homogeneous biaxial strain. A transition point from direct-to-indirect gap-phase is predicted to exist for biaxial tensile strain lying in the interval (2.645%, 3.171%). In the two gap-phases, the band gap decreases with increasing strain and varies linearly with strain.
CdTe is a well known and widely used binary compound for optoelectronic applications. In this study, we propose the thinnest, free standing monolayer of CdTe which holds the tetragonal-PbO (alpha-PbO) symmetry. The structural, electronic, vibrational and strain dependent properties are investigated by means of first principles calculations based on density functional theory. Our results demonstrate that the monolayer alpha-CdTe is a dynamically stable and mechanically flexible material. It is found that the thinnest monolayer crystal of CdTe is a semiconductor with a direct band gap of 1.95 eV…
The appearance of single photon sources in atomically thin semiconductors holds great promises for the development of a flexible and ultra-compact quantum technology, in which elastic strain engineering can be used to tailor their emission properties. Here, we show a compact and hybrid 2D-semiconductor-piezoelectric device that allows for controlling the energy of single photons emitted by quantum emitters localized in wrinkled WSe2 monolayers. We demonstrate that strain fields exerted by the piezoelectric device can be used to tune the energy of localized excitons in WSe2 up to 18 meV in a re…
We report the influence of uniaxial tensile mechanical strain in the range 0-2.2% on the phonon spectra and bandstructures of monolayer and bilayer molybdenum disulfide (MoS2) two-dimensional crystals. First, we employ Raman spectroscopy to observe phonon softening with increased strain, breaking the degeneracy in the E' Raman mode of MoS2, and extract a Grüneisen parameter of ~1.06. Second, using photoluminescence spectroscopy we measure a decrease in the optical band gap of MoS2 that is roughly linear with strain, ~45 meV% strain for monolayer MoS2 and ~120 meV% strain for bilayer MoS2. Thir…
The increase of a thermoelectric material's figure of merit (ZT value) is limited by the interplay of the transport coefficients. Here we report the greatly enhanced thermoelectric performance of a ZrS2 monolayer by the biaxial tensile strain, due to the simultaneous increase of the Seebeck coefficient and decrease of the thermal conductivity. Based on the first-principles calculations combined with the Boltzmann transport theory, we predict the band gap of the ZrS2 monolayer can be effectively engineered by the strain and the Seebeck coefficient is significantly increased. The thermal conduct…
Using full-potential density functional calculations within local density approximation (LDA), we found mechanically tunable band-gap in ZnO monolayer (ML-ZnO) in graphene-like honeycomb structure, by simulated application of in-plane homogeneous biaxial strain. Unstrained ML-ZnO was found to have a direct band gap of energy 1.68 eV within LDA; the actual band gap would be more, since LDA is known to underestimate the gap. Within our simulated strain limit of about plus or minus 10%, the band gap remains direct and shows a strong non-linear variation with strain. The results may find applicati…
We study a gapped graphene monolayer in a combination of uniform magnetic field and strain-induced uniform pseudomagnetic field. The presence of two fields completely removes the valley degeneracy. The resulting density of states shows a complicated behaviour that can be tuned by adjusting the strength of the fields. We analyze how these features can be observed in the sublattice, valley and full density of states. The analytical expression for the valley DOS is derived.
Strain engineering applied to carbon monosulphide monolayers allows to control the bandgap, controlling electronic and thermoelectric responses. Herein, we study the semiconductor-metal phase transition of this layered material driven by strain control on the basis of first-principles calculations. We consider uniaxial and biaxial tensile strain and we find a highly anisotropic electronic and thermoelectonic responses depending on the direction of the applied strain. Our results indicate that strain-induced response could be an effective method to control the electronic response and the thermo…
We demonstrate the continuous and reversible tuning of the optical band gap of suspended monolayer MoS2 membranes by as much as 500 meV by applying very large biaxial strains. By using chemical vapor deposition (CVD) to grow crystals that are highly impermeable to gas, we are able to apply a pressure difference across suspended membranes to induce biaxial strains. We observe the effect of strain on the energy and intensity of the peaks in the photoluminescence (PL) spectrum, and find a linear tuning rate of the optical band gap of 99 meV/%. This method is then used to study the PL spectra of b…
We describe a facile technique based on polymer encapsulation to apply several percent controllable strains to monolayer and few-layer Transition Metal Dichalcogenides (TMDs). We use this technique to study the lattice response to strain via polarized Raman spectroscopy in monolayer WSe2 and WS2. The application of strain causes mode-dependent redshifts, with larger shift rates observed for in-plane modes. We observe a splitting of the degeneracy of the in-plane E' modes in both materials and measure the Gruneisen parameters. At large strain, we observe that the reduction of crystal symmetry c…
Employing ab initio electronic calculations, we propose a new type of two-dimensional (2D) topological insulator (TI), monolayer (ML) low buckled (LB) mercury telluride (HgTe) and mercury selenide (HgSe), with tunable band gaps. Monolayer LB HgTe undergoes a transition to a topological nontrivial phase under the appropriate in-plane tensile strain (ε > 2.6%) due to the combination effects of strain and spin orbital coupling (SOC). Under the 2.6%< ε <4.2% tensile strain, the band inversion and topological nontrivial gap are induced by the SOC. For ε >4.2%, the band inversion is already realized…
We report the strong dependence of resistance on uniaxial strain in monolayer WSe2 at various temperatures, where the gauge factor can reach as large as 2400. The observation of strain-dependent resistance and giant gauge factor is attributed to the emergence of nonzero Berry curvature dipole. Upon increasing strain, Berry curvature dipole can generate net orbital magnetization, which would introduce additional magnetic scattering, decreasing the mobility and thus conductivity. Our work demonstrates the strain engineering of Berry curvature and thus the transport properties, making monolayer W…
Atomic monolayers of transition metal dichalcogenides represent an emerging material platform for the implementation of ultra compact quantum light emitters via strain engineering. In this framework, we discuss experimental results on creation of strain induced single photon sources using a WSe2 monolayer on a silver substrate, coated with a very thin dielectric layer. We identify quantum emitters which are formed at various locations in the sample. The emission is highly linearly polarized, stable in linewidth and decay times down to 300 ps are observed. We provide numerical calculations of o…
The Berry curvature dipole is a physical quantity that is expected to allow various quantum geometrical phenomena in a range of solid-state systems. Monolayer transition metal dichalcogenides provide an exceptional platform to modulate and investigate the Berry curvature dipole through strain. Here we theoretically demonstrate and experimentally verify for monolayer MoS$_\rm{2}$ the generation of valley orbital magnetization as a response to an in-plane electric field due to the Berry curvature dipole. The measured valley orbital magnetization shows excellent agreement with the calculated Berr…
In this work, the electrical properties of monolayer InSb in the presence of biaxial strain using density functional theory are investigated. Here, we first explore the band structure of InSb with and without spin-orbit coupling (SOC) consideration. The electron and hole effective mass modify with SOC consideration. The electron and hole effective masses lowered two and ten times, respectively. The location of valleys in conduction and valence band for various strains are explored, and the corresponding effective masses are reported. A lower effective mass is obtained for both electron and hol…
We present ab initio calculations which show that the direct-band-gap, effective masses and Fermi velocities of charge carriers in ZnO monolayer (ML-ZnO) in graphene-like honeycomb structure are all tunable by application of in-plane homogeneous biaxial strain. Within our simulated strain limit of $\pm 10$%, the band gap remains direct and shows a strong non-linear variation with strain. Moreover, the average Fermi velocity of electrons in unstrained ML-ZnO is of the same order of magnitude as that in graphene. The results promise potential applications of ML-ZnO in mechatronics/straintronics …
Strain engineering is an important method for tuning the properties of semiconductors and has been used to improve the mobility of silicon transistors for several decades. Recently, theoretical studies have predicted that strain can also improve the mobility of two-dimensional (2D) semiconductors, e.g. by reducing intervalley scattering or lowering effective masses. Here, we experimentally show strain-enhanced electron mobility in monolayer MoS2 transistors with uniaxial tensile strain, on flexible substrates. The on-state current and mobility are nearly doubled with tensile strain up to 0.7%,…
Graphene monolayers supported on oxide substrates have been demonstrated with superior charge mobility and thermal transport for potential device applications. Morphological corrugation can strongly influence the transport properties of the supported graphene. In this paper, we theoretically analyze the morphological stability of a graphene monolayer on an oxide substrate, subject to van der Waals interactions and in-plane mismatch strains. First, we define the equilibrium separation and the interfacial adhesion energy as the two key parameters that characterize the van der Waals interaction b…
Strain presents a straightforward tool to tune electronic properties of atomically thin nanomaterials that are highly sensitive to lattice deformations. While the influence of strain on the electronic band structure has been intensively studied, there are only few works on its impact on optical properties of monolayer transition metal dichalcogenides (TMDs). Combining microscopic theory based on Wannier and Bloch equations with nearestneighbor tight-binding approximation, we present an analytical view on how uni- and biaxial strain influences the optical fingerprint of TMDs including their exc…
We develop two types of graphene devices based on nanoelectromechanical systems (NEMS), that allows transport measurement in the presence of in situ strain modulation. Different mobility and conductance responses to strain were observed for single layer and bilayer samples. These types of devices can be extended to other 2D membranes such as MoS2, providing transport, optical or other measurements with in situ strain.
When considering transition-metal dichalcogenides (TMDCs) in van der Waals (vdW) heterostructures for periodic ab-initio calculations, usually, lattice mismatch is present, and the TMDC needs to be strained. In this study we provide a systematic assessment of biaxial strain effects on the orbital, spin-orbit, and optical properties of the monolayer TMDCs using ab-initio calculations. We complement our analysis with a minimal tight-binding Hamiltonian that captures the low-energy bands of the TMDCs around K and K' valleys. We find characteristic trends of the orbital and spin-orbit parameters a…
We present a computational study on the impact of tensile/compressive uniaxial ($\varepsilon_{xx}$) and biaxial ($\varepsilon_{xx}=\varepsilon_{yy}$) strain on monolayer MoS$_{2}$ NMOS and PMOS FETs. The material properties like band structure, carrier effective mass and the multi-band Hamiltonian of the channel, are evaluated using the Density Functional Theory (DFT). Using these parameters, self-consistent Poisson-Schrödinger solution under the Non-Equilibrium Green's Function (NEGF) formalism is carried out to simulate the MOS device characteristics. 1.75$%$ uniaxial tensile strain is found…
Electrical control of the orbital degrees of freedom is an important area of research in the emerging field of "orbitronics." Orbital {\it gyrotropic} magneto-electric effect (OGME) is the generation of an orbital magnetization in a nonmagnetic metal by an applied electric field. Here, we show that strain induces a large GME in the monolayer Nb$X_2$ ($X =$ S, Se) normal to the plane, primarily driven by the orbital moments of the Bloch bands as opposed to the conventional spin magnetization, without any need for spin-orbit coupling. The key physics is captured within an effective two-band vall…
Recent experimental studies of out-of-plane straining geometries of transition metal dichalchogenide (TMD) monolayers have demonstrated sufficient band gap renormalisation for device application such as single photon emitters. Here, a simple continuum-mechanical plate-theory approach is used to estimate the topography of TMD monolayers layered atop nanopillar arrays. From such geometries, the induced conduction band potential and band gap renormalisation is given, demonstrating a curvature of the potential that is independent of the height of the deforming nanopillar. Additionally, with a semi…
By using first-principles calculations, we investigated the monolayer $ReS_2$ with vacancies under strain engineering, specifically focusing on its energy of formation, band gap, electron density of states, effective mass and optical properties. The calculated results disclose that S4 defect is more likely to form than other kinds of vacancies. Asymmetric deformation induced by strain makes its band structure transformation from direct band gap to indirect band gap. The analysis of the partial density of states indicates that the Re-d, Re-p and S-d orbitals are the major components of the defe…
We use micro-Raman and photoluminescence (PL) spectroscopy at 300K to investigate the influence of uniaxial tensile strain on the vibrational and optoelectronic properties of monolayer and bilayer MoS2 on a flexible substrate. The initially degenerate E^1_{2g} Raman mode is split into a doublet as a direct consequence of the strain applied to MoS2 through Van der Waals coupling at the sample-substrate interface. We observe a strong shift of the direct band gap of 48meV/(% of strain) for the monolayer and 46meV/% for the bilayer, whose indirect gap shifts by 86meV/%. We find a strong decrease o…
Strain engineering is one of the most promising and effective routes toward continuously tuning the electronic and optic properties of materials, while thermal properties are generally believed to be insensitive to mechanical strain. In this paper, the strain-dependent thermal conductivity of monolayer silicene under uniform bi-axial tension is computed by solving the phonon Boltzmann transport equation with force constants extracted from first-principles calculations. Unlike the commonly believed understanding that thermal conductivity only slightly decreases with increased tensile strain for…
In monolayer transition metal dichalcogenides, quantum emitters are associated with localized strain that can be deterministically applied to create designer nano-arrays of single photon sources. Despite an overwhelming empirical correlation with local strain, the nanoscale interplay between strain, excitons, defects and local crystalline structure that gives rise to these quantum emitters is poorly understood. Here, we combine room-temperature nano-optical imaging and spectroscopy of excitons in nanobubbles of localized strain in monolayer WSe2 with atomistic structural models to elucidate ho…
We study theoretically effects of an anisotropic elastic strain on the exciton energy spectrum fine structure and optical selection rules in atom-thin crystals based on transition-metal dichalcogenides. The presence of strain breaks the chiral selection rules at the $\bm K$-points of the Brillouin zone and makes optical transitions linearly polarized. The orientation of the induced linear polarization is related to the main axes of the strain tensor. Elastic strain provides an additive contribution to the exciton fine structure splitting in agreement with experimental evidence obtained from un…
In this work, the electrical and spin properties of monolayer MoSi2X4 (X= N, P, As, and Sb) under vertical strain are investigated. The band structures state that MoSi2N4 is an indirect semiconductor, whereas other compounds are direct semiconductors. The vertical strain has been selected to modify the electrical properties. The bandgap shows a maximum and decreases for both tensile and compressive strains. The valence band at K-point displays a large spin-splitting, whereas the conduction band has a negligible splitting. On the other hand, the second conduction band has a large spin-splitting…
The strain effects on the spin-orbit induced splitting of the valence band maximum and conduction band minimum in monolayer MoS2 and the gap in graphene are calculated using first-principles calculations. The dependence of these splittings on the various symmetry types of strain is described by means of an effective Hamiltonian based on the method of invariants and the parameters in the model are extracted by fitting to the theory. These splittings are related to acoustic phonon deformation potentials, or electron-phonon coupling matrix elements which enter the spin-dependent scattering theory…
The electronic, phonon, and thermoelectric properties of a two-dimensional HfS2 monolayer are investigated by using the first-principles calculations combined with the Boltzmann transport theory. The band valleys of the HfS2 monolayer can be effectively tuned by the applied biaxial strain. The Seebeck coefficient and therefore the peak value of the power factor (with the relaxation time inserted) increase when the degeneracy of the band valleys is increased by the strain. When no strain is applied, the HfS2 monolayer is an excellent n-type thermoelectric material, while the thermoelectric perf…
Nanoscale Mapping of Strain-engineered Excitons in Monolayer WSe$_2$
University of Arizona（亚利桑那大学）；Wyant College of Optical Sciences, University of Arizona（亚利桑那大学怀特光学学院）；United States Naval Research Laboratory（美国海军研究实验室）；Laboratory for Physical Sciences（物理科学实验室）；National Institute for Materials Science（物质材料研究机构）
We study the effects of an applied in-plane uniaxial strain on the plasmon dispersions of monolayer, bilayer and double-layer phosphorene structures in the long-wavelength limit within the linear elasticity theory. In the low energy limit, these effects can be modeled through the change in the curvature of the anisotropic energy band along the armchair and zigzag directions. We derive analytical relations for the plasmon modes under uniaxial strain and show that the direction of the applied strain is important. Moreover, we observe that along the armchair direction, the changes of the plasmon …
Our First-principles Full-Potential Density Functional Theory (DFT) calculations show that a monolayer of ZnS (ML-ZnS), which is predicted to adopt a graphene-like planar honeycomb structure with a direct band gap, undergoes strain-induced modifications in its structure and band gap when subjected to in-plane homogeneous biaxial strain ($δ$). ML-ZnS gets buckled for compressive strain greater than 0.92%; the buckling parameter $Δ$ (= 0.00 Å\, for planar ML-ZnS) linearly increases with increasing compressive strain ($Δ= 0.435$ Å\,at $δ= - 5.25$%). A tensile strain of 2.91% turns the direct band…
Regulation of electronic structure and mobility cut-on rate in two-dimensional transition metal dichalcogenides (TMDs) has attracted much attention because of its potential in electronic device design. The anisotropic Raman scattering and mobility cut-on rate of monolayer unique distorted-1T(1Td) ReS2 with external strain are determined theoretically based on the density function theory. The angle-dependent Raman spectrum of Ag-like, Eg-like and Cp models are used to discriminate and analysis structural anisotropy; the strain is exploited to adjust the structural symmetry and electronic struct…
Recent observation of intrinsic ferromagnetism in two-dimensional (2D) CrI$_3$ is associated with the large magnetic anisotropy due to strong spin-orbit coupling (SOC) of I. Magnetic anisotropy energy (MAE) defines the stability of magnetization in a specific direction with respect to the crystal lattice and is an important parameter for nanoscale applications. In this work we apply the density functional theory to study the strain dependence of MAE in 2D monolayer chromium trihalides CrX$_3$ (with X = Cl, Br, and I). Detailed calculations of their energetics, atomic structures and electronic …
We investigate the transport of excitons and trions in monolayer semiconductor WS$_2$ subjected to controlled non-uniform mechanical strain. We actively control and tune the strain profiles with an AFM-based setup in which the monolayer is indented by an AFM tip. Optical spectroscopy is used to reveal the dynamics of the excited carriers. The non-uniform strain configuration locally changes the valence and conduction bands of WS$_2$, giving rise to effective forces attracting excitons and trions towards the point of maximum strain underneath the AFM tip. We observe large changes in the photolu…
In this work, we present a computational study on the possibility of strain engineering in monolayer Black Phosphorus (black P) and Blue Phosphorus (blue P) based MOSFETs. The material properties like band structure, carrier effective masses, carrier densities at band extrema are evaluated using Generalized Gradient Approximation (GGA) in Density Functional Theory (DFT).Thereafter self-consistent Non-Equilibrium Greens Function (NEGF) simulations are carried out to study the device performance metrics (such as output characteristics, ON currents, transconductance etc.) of such strained black P…
Monolayers of transition metal dichalcogenides (TMDs) have recently emerged as a promising optoelectronic platform. To leverage their full potential, however, it is important to understand and engineer the properties of the different exciton species that exist in these monolayers, as well as to control their transport through the material. A promising approach relies on engineering strain landscapes in atomically thin semiconductors that excitons navigate. In WSe$_2$ monolayers, for example, localized strain has been used to control the emission wavelength of excitons, induce exciton funneling…
The influence of triaxial in-plane strain on the electronic properties of a hexagonal boron-nitride sheet is investigated using density functional theory. Different from graphene, the triaxial strain localizes the molecular orbitals of the boron-nitride flake in its center depending on the direction of the applied strain. The proposed technique for localizing the molecular orbitals that are close to the Fermi level in the center of boron nitride flakes can be used to actualize engineered nanosensors, for instance, to selectively detect gas molecules. We show that the central part of the strain…
Many classes of two-dimensional (2D) materials have emerged as potential platforms for novel electronic and optical devices. However, the physical properties are strongly influenced by nanoscale heterogeneities in the form of edges, grain boundaries, and nucleation sites. Using combined tip-enhanced Raman scattering (TERS) and photoluminescence (TEPL) nano-spectroscopy and -imaging, we study the associated effects on the excitonic properties in monolayer WSe2 grown by physical vapor deposition (PVD). With <15 nm spatial resolution we resolve nonlocal nanoscale correlations of PL spectral inten…
The interplay between topology and valley degree of freedom has attracted much interest because it can realize new phenomena and applications. Here, based on first-principles calculations, we demonstrate intrinsically valley-polarized quantum anomalous Hall effect in monolayer ferrovalley material: Janus VSiGeN4, of which the edge states are chiral-spin-valley locking. Besides, a small tensile or compressive strain can drive phase transition in the material from valley-polarized quantum anomalous Hall state to half-valley-metal state. With the increase of the strain, the material turns into fe…
The electronic properties of a graphene monolayer in a magnetic and a strain-induced pseudo-magnetic field are studied in the presence of spin-orbit interactions (SOI) that are artificially enhanced, e.g., by suitable adatom deposition. For the homogeneous case, we provide analytical results for the Landau level eigenstates for arbitrary intrinsic and Rashba SOI, including also the Zeeman field. The edge states in a semi-infinite geometry are studied in the absence of the Rashba term. For a critical value of the magnetic field, we find a quantum phase transition separating two phases with spin…
Due to their great potential in electronics, optoelectronics and piezoelectronics, Janus transition metal dichalcogenide (TMD) monolayers have attracted increasing research interest, the MoSSe of which with sandwiched S-Mo-Se structure has been synthesized experimentally. In this work, the biaxial strain dependence of electronic structures and transport properties of Janus PtSSe monolayer is systematically investigated by using generalized gradient approximation (GGA) plus spin-orbit coupling (SOC). Calculated results show that SOC has a detrimental effect on power factor of PtSSe monolayer, w…
Strain-Induced Tuning of Third-Harmonic Generation in Monolayer Black Phosphorene
University of Science and Technology Beijing（北京科技大学）；Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences（中国科学院长春光学精密机械与物理研究所）；Zhengzhou University（郑州大学）
In this paper, spin properties of monolayer MX (M=Ga, In and X=S, Se, Te) in the presence of strain are studied. Density functional theory is used to investigate spin properties. The strain changes modification of bandgap due to spin-orbit coupling, the results indicate the spin-orbit coupling has a higher effect in the compressive regime. Also, spin splitting in the conduction and valence bands respect to strain are compared for six materials. The location of conduction band minimum (CBM) imposed a type of spin properties. These materials with mirror symmetry can display the Rashba effect whi…
We investigate the impact of mechanical strains and a perpendicular electric field on the electronic and magnetic ground-state properties of two-dimensional monolayer CrI$_3$ using density functional theory. We propose a minimal spin model Hamiltonian, consisting of symmetric isotropic exchange interactions, magnetic anisotropy energy, and Dzyaloshinskii-Moriya (DM) interactions, to capture most pertinent magnetic properties of the system. We compute the mechanical strain and electric field dependence of various spin-spin interactions. Our results show that both the amplitudes and signs of the…
