Electron Spin-orbit Coupling Research Articles

Consistent Second-Order Treatment of Spin-Orbit Coupling and Dynamic Correlation in Quasidegenerate N-Electron Valence Perturbation Theory.

We present a formulation and implementation of second-order quasidegenerate N-electron valence perturbation theory (QDNEVPT2) that provides a balanced and accurate description of spin-orbit coupling and dynamic correlation effects in multiconfigurational electronic states. In our approach, the energies and wave functions of electronic states are computed by treating electron repulsion and spin-orbit coupling operators as equal perturbations to the nonrelativistic complete active-space wave functions, and their contributions are incorporated fully up to the second order. The spin-orbit effects are described using the Breit-Pauli (BP) or exact two-component Douglas-Kroll-Hess (DKH) Hamiltonians within spin-orbit mean-field approximation. The resulting second-order methods (BP2- and DKH2-QDNEVPT2) are capable of treating spin-orbit coupling effects in nearly degenerate electronic states by diagonalizing an effective Hamiltonian expanded in a compact non-relativistic basis. For a variety of atoms and small molecules across the entire periodic table, we demonstrate that DKH2-QDNEVPT2 is competitive in accuracy with variational two-component relativistic theories. BP2-QDNEVPT2 shows high accuracy for the second- and third-period elements, but its performance deteriorates for heavier atoms and molecules. We also consider the first-order spin-orbit QDNEVPT2 approximations (BP1- and DKH1-QDNEVPT2), among which DKH1-QDNEVPT2 is reliable but less accurate than DKH2-QDNEVPT2. Both DKH1- and DKH2-QDNEVPT2 hold promise as efficient and accurate electronic structure methods for treating electron correlation and spin-orbit coupling in a variety of applications.

Intercalation in 2D materials and in situ studies.

Intercalation of atoms, ions and molecules is a powerful tool for altering or tuning the properties - interlayer interactions, in-plane bonding configurations, Fermi-level energies, electronic band structures and spin-orbit coupling - of 2D materials. Intercalation can induce property changes in materials related to photonics, electronics, optoelectronics, thermoelectricity, magnetism, catalysis and energy storage, unlocking or improving the potential of 2D materials in present and future applications. In situ imaging and spectroscopy technologies are used to visualize and trace intercalation processes. These techniques provide the opportunity for deciphering important and often elusive intercalation dynamics, chemomechanics and mechanisms, such as the intercalation pathways, reversibility, uniformity and speed. In this Review, we discuss intercalation in 2D materials, beginning with a brief introduction of the intercalation strategies, then we look into the atomic and intrinsic effects of intercalation, followed by an overview of their in situ studies, and finally provide our outlook.

Spin-orbit coupling of electrons on separate lanthanide atoms of Pr2O2 and its singly charged cation.

Although it plays a critical role in the photophysics and catalysis of lanthanides, spin-orbit coupling of electrons on individual lanthanide atoms in small clusters is not well understood. The major objective of this work is to probe such coupling of the praseodymium (Pr) 4f and 6s electrons in Pr2O2 and Pr2O2+. The approach combines mass-analyzed threshold ionization spectroscopy and spin-orbit multiconfiguration second-order quasi-degenerate perturbation theory. The energies of six ionization transitions are precisely measured; the adiabatic ionization energy of the neutral cluster is 38 045 (5) cm-1. Most of the electronic states involved in these transitions are identified as spin-orbit coupled states consisting of two or more electron spins. The electron configurations of these states are 4f46s2 for the neutral cluster and 4f46s for the singly charged cation, both in planar rhombus-type structures. The spin-orbit splitting due to the coupling of the electrons on the separate Pratoms is on the order of hundreds of wavenumbers.

Intersystem crossing as vibronically induced phonon emission and absorption processes: a unified view of nonradiative transitions in a molecule

Abstract An analytical expression for the nonradiative rate constant is derived based on Fermi's golden rule within the mixed-spin crude adiabatic (CA) approximation. The mixed-spin CA basis is defined by a set of eigenstates for the electronic Hamiltonian that comprises the nonrelativistic electronic Hamiltonian and spin-orbit coupling clumped at the reference nuclear configuration. The mixed-spin basis differs from the pure-spin basis defined by a set of eigenstates for the nonrelativistic electronic Hamiltonian. The mixed-spin CA representation provides a unified view of the nonradiative transitions; both internal conversion and intersystem crossing (ISC) are regarded as vibronically induced phonon emission and absorption processes. The analytical expression enables us to determine important vibrational modes that are responsible for phonon emission/absorption (promoting modes) and accepting excitation energy (accepting modes) according to the selection rule of vibronic coupling. An advantage of the CA representation is that the spatial distribution of vibronic coupling is elucidated based on its density form, i.e. vibronic coupling density, which can be applied to theoretical molecular designs with controlled nonradiative processes. The calculated ISC rate constant for tetracene reproduces the experimental result well.

SOiCISCF: Combining SOiCI and iCISCF for Variational Treatment of Spin-Orbit Coupling.

It has recently been shown that the SOiCI approach [Zhang, N.; J. Phys.: Condens. Matter 2022, 34, 224007], in conjunction with the spin-separated exact two-component relativistic Hamiltonian, can provide very accurate fine structures of systems containing heavy elements by treating electron correlation and spin-orbit coupling (SOC) on an equal footing. Nonetheless, orbital relaxations/polarizations induced by SOC are not yet fully accounted for due to the use of scalar relativistic orbitals. This issue can be resolved by further optimizing the still real-valued orbitals self-consistently in the presence of SOC, as done in the spin-orbit coupled CASSCF approach [Ganyushin, D.; et al. J. Chem. Phys. 2013, 138, 104113] but with the iCISCF algorithm [Guo, Y.; J. Chem. Theory Comput. 2021, 17, 7545-7561] for large active spaces. The resulting SOiCISCF employs both double group and time reversal symmetries for computational efficiency and the assignment of target states. The fine structures of p-block elements are taken as showcases to reveal the efficacy of SOiCISCF.

On the electronic structure and spin-orbit coupling of BiB from photoelectron imaging of cryogenically-cooled BiB- anion.

We report a study on the electronic structure and chemical bonding of the BiB molecule using high-resolution photoelectron imaging of cryogenically cooled BiB- anion. By eliminating all the vibrational hot bands, we can resolve the complicated detachment transitions due to the open-shell nature of BiB and the strong spin-orbit coupling. The electron affinity of BiB is measured to be 2.010(1) eV. The ground state of BiB- is determined to be 2Π(3/2) with a σ2π3 valence electron configuration, while the ground state of BiB is found to be 3Σ-(0+) with a σ2π2 electron configuration. Eight low-lying spin-orbit excited states [3Σ-(1), 1Δ(2), 1Σ+(0+), 3Π(2), 3Π(1), 1Π(1)], including two forbidden transitions, [3Π(0-) and 3Π(0+)], are observed for BiB as a result of electron detachment from the σ and π orbitals of BiB-. The angular distribution information from the photoelectron imaging is found to be critical to distinguish detachment transitions from the σ or π orbital for the spectral assignment. This study provides a wealth of information about the low-lying electronic states and spin-orbit coupling of BiB, demonstrating the importance of cryogenic cooling for obtaining well-resolved photoelectron spectra for size-selected clusters produced from a laser vaporization cluster source.

Temperature and density dependence of line profiles of sodium perturbed by helium

Context. Ultracool stellar atmospheres and hot exoplanets show absorption by alkali resonance lines severely broadened by collisions with neutral perturbers. In the coolest and densest atmospheres, such as those of T dwarfs, Na I and K I broadened by molecular hydrogen and helium can come to dominate the entire optical spectrum. The effects of Na–He collision broadening are also central to understanding the opacity of cool DZ white dwarf stars. Aims. In order to be able to construct synthetic spectra of brown dwarfs and cool DZ white dwarfs, where helium density can reach several 1021 cm−3, Na–He line profiles of the resonance lines have been computed over a wide range of densities and temperatures. Methods. Unified line profiles that are valid from the core to the far wings at high densities are calculated in the semiclassical approach using up-to-date molecular data including electronic spin-orbit coupling from the sodium atom. Far wings are extended to more than 4000 cm−1 from the line center when the helium density can reach 1021 cm−3 at 5000 K. Results. We present a comprehensive study of Na–He collisional profiles at high density, and temperatures from 5000 K, which is the temperature prevailing in the atmosphere of ultra-cool DZ white dwarf stars, down to 1 K, which is the temperature in liquid helium clusters. Collision broadening and shift parameters within the impact approximation obtained in the semiclassical and quantum theory using our new accurate molecular data are presented.

Excited states of polonium(IV): electron correlation and spin-orbit coupling in the Po4+ free ion and in the bare and solvated [PoCl5]- and [PoCl6]2- complexes.

Polonium (Po, Z = 84) is a main-block element with poorly known physico-chemical properties. Not much information has been firmly acquired since its discovery by Marie and Pierre Curie in 1898, especially regarding its speciation in aqueous solution and spectroscopy. In this work, we revisit the absorption properties of two complexes, [PoCl5]- and [PoCl6]2-, using quantum mechanical calculations. These complexes have the potential to exhibit a maximum absorption at 418 nm in HCl medium (for concentrations of 0.5 mol L-1 and above). Initially, we examine the electronic spectra of the Po4+ free ion and of its isoelectronic analogue, Bi3+, in the spin-orbit configuration interaction (SOCI) framework. Our findings demonstrate that the SOCI matrix should be dressed with correlated electronic energies and that the quality of the spectra is largely improved by decontracting the reference states at the complete active space plus singles (CAS + S) level. Subsequently, we investigate the absorption properties of the [PoCl5]- and [PoCl6]2- complexes in two stages. Firstly, we perform methodological tests at the MP2/def2-TZVP gas phase geometries, indicating that the decontraction of the reference states can be skipped without compromising the accuracy significantly. Secondly, we study the solution absorption properties by means of single-point calculations performed at the solvated geometries, obtained by an implicit solvation treatment or a combination of implicit and explicit solvation. Our results highlight the importance of saturating the first coordination sphere of the PoIV ion to obtain a qualitatively correct picture. Finally, we conclude that the known-for-decades 418 nm peak could be attributed to a mixture of both the [PoCl5(H2O)]- and [PoCl6]2- complexes. This finding not only aligns with the behaviour of the analogous BiIII ion under similar conditions but also potentially provides an explanation for previous discrepancies in the literature.

Ferrocene/ferrocenium, cobaltocene/cobaltocenium and nickelocene/nickelocenium: from gas phase ionization energy to one-electron reduction potential in solvated medium.

We propose a theoretical procedure for accurate determination of reduction potentials for three metallocene couples, Cp2M+/Cp2M, where M = Fe, Co and Ni. This procedure first computes the gas phase ionization energy (IE) using the explicitly correlated CCSD(T)-F12 method and includes the zero-point energy correction, core-valence electronic correlation, and relativistic and spin-orbit coupling effects. By means of Born-Haber thermochemical cycle, the one-electron reduction potential is obtained as the sum of the gas phase IE and the corresponding Gibbs free energies of solvation (ΔGsolv) for both the neutral and cationic species. Among the three solvent models (PCM, SMD and uESE) investigated here, it turns out that only the SMD model (computed at the DFT level) gives the best estimation of the value for "ΔGsolv(cation) - ΔGsolv(neutral)" and thus, combining with the accurate IE values, the theoretical protocol is capable of yielding reliable values (in V) for , and . These predictions compare favorably with the available experimental data (in V): , , and . We show that our theoretical procedure is reliable for accurate reduction potential predictions of Cp2Fe+/Cp2Fe, Cp2Co+/Cp2Co and Cp2Ni+/Cp2Ni redox couples in aqueous and non-aqueous media; the maximum absolute deviation is as small as ≈120 mV, which outperforms those of the existing theoretical methods.

Global dynamical analysis of an electronic spin–orbit coupling system

By means of a canonical generalized momentum and a canonical conjugate spin variable, a complete canonical Hamiltonian formalism is designed to describe a coulomb field with electronic spin–orbit coupling in a semi-classical and non-relativistic way. After this operation, unlike the existing Lagrange formulation, the concepts of hidden momentum, hidden angular momentum and spin kinetic energy are not used in the canonical formalism. Besides, it is easy to find that there are four first integrals involving the conserved total energy and the conserved total angular momentum vector in an 8-dimensional phase space of the system. In this sense, the global dynamics is typically integrable, regular and non-chaotic, and each orbit in the phase space is a quasi-periodic 4-dimensional Kolmogorov-Arnold-Moser(KAM) torus.

Vacancy localization effects on MX2 transition-metal dichalcogenides: A systematic ab initio study

Two-dimensional transition-metal dichalcogenide (${\mathrm{MX}}_{2}$) vacancy formation energetics are extensively investigated. Within an ab initio approach, we study the ${\mathrm{MX}}_{2}$ systems, with M = Mo, W, Ni, Pd, and Pt, and X = S, Se, and Te. Here we classify that chalcogen vacancies are always energetically favorable over the transition-metal ones. However, for late transition metals Pd $4d$, and Pt $5d$ the metal vacancies are experimentally achievable, bringing up localized magnetic moments within the semiconducting matrix. By quantifying the localization of the chalcogen vacancy states we show that it rules the intra- and intervacancy interactions that establish both the number of vacancy states neatly lying within the semiconducting gap, as well as its electronic dispersion and spin-orbit coupling splitting. Combining different vacancies and phase variability $1T$ and $1H$ of the explored systems allows us to construct a guiding picture of the vacancy state localization.

Charge ordering in Ir dimers in the ground state of Ba5AlIr2O11

It has been well established experimentally that the interplay of electronic correlations and spin-orbit interactions in ${\mathrm{Ir}}^{4+}$ and ${\mathrm{Ir}}^{5+}$ oxides results in insulating ${J}_{\mathrm{eff}}=1/2$ and ${J}_{\mathrm{eff}}=0$ ground states, respectively. However, in compounds where the structural dimerization of iridium ions is favorable, the direct Ir $d\text{\ensuremath{-}}d$ hybridization can be significant and takes a key role. Here, we investigate the effects of direct Ir $d\text{\ensuremath{-}}d$ hybridization in comparison with electronic correlations and spin-orbit coupling in ${\mathrm{Ba}}_{5}{\mathrm{AlIr}}_{2}{\mathrm{O}}_{11}$, a compound with Ir dimers. Using a combination of ab initio many-body wave-function quantum chemistry calculations and resonant inelastic x-ray scattering experiments, we elucidate the electronic structure of ${\mathrm{Ba}}_{5}{\mathrm{AlIr}}_{2}{\mathrm{O}}_{11}$. We find excellent agreement between the calculated and the measured spin-orbit excitations. Contrary to expectations, the analysis of the many-body wave function shows that the two Ir (${\mathrm{Ir}}^{4+}$ and ${\mathrm{Ir}}^{5+}$) ions in the ${\mathrm{Ir}}_{2}{\mathrm{O}}_{9}$ dimer unit in this compound preserve their local ${J}_{\mathrm{eff}}$ character close to 1/2 and 0, respectively. The local point group symmetry at each of the Ir ions plays an important role, significantly limiting the direct $d\text{\ensuremath{-}}d$ hybridization. Our results emphasize that minute details in the local crystal field environment can lead to dramatic differences in the electronic states in iridates and $5d$ oxides in general.

Spin-orbit-driven ferromagnetism at half moiré filling in magic-angle twisted bilayer graphene.

Strong electron correlation and spin-orbit coupling (SOC) can have a profound influence on the electronic properties of materials. We examine their combined influence on a 2-dimensional electronic system at the atomic interface between magic-angle twisted bilayer graphene and a tungsten diselenide crystal. Strong electron correlation within the moiré flatband stabilizes correlated insulating states at both quarter and half filling, and SOC transforms these Mott-like insulators into ferromagnets, evidenced by robust anomalous Hall effect with hysteretic switching behavior. The coupling between spin and valley degrees of freedom is demonstrated through the control of the magnetic order with an in-plane magnetic field, or a perpendicular electric field. Our findings establish an experimental knob to engineer topological properties of moiré bands in twisted bilayer graphene and related systems.

Prediction of two-dimensional monolayer C2O2Fe with chiral magnetic and ferroelectric orders.

Low-dimensional multiferroics are highly desired for applications and contain exotic physical properties. Here we predict a two-dimensional material, C2O2Fe monolayer, through Fe intercalation in the graphene oxide monolayer. The crystal stable texture, chiral spin order, and ferroelectric polarization of the C2O2Fe monolayer are theoretically studied by considering the electron on-site Coulomb interaction and spin orbit coupling, which also manifests the ferroelectric polarization and reversal barrier at 30% biaxial tensile strain comparable with the other two-dimensional ferroelectric materials, such as GeS and GeSe. Moreover, first-principles calculations show that the polarization flipping is accompanied by spin orientation reversal, when the ferroelectric polarization is upward to the plane, a clockwise chiral antiferromagnetic ground state is obtained, while when the polarization is downward, the monolayer shows the anticlockwise chiral antiferromagnetic structure. In this sense, a strong electrically controlled magnetism exists in the designed C2O2Fe monolayer film.

Electronic Structure of Pyrochlore Iridate Pr2Ir2O7: Interplay Between Spin-Orbit Coupling and Hubbard Potential

We have investigated the electronic structure of pyrochlore iridate Pr2Ir2O7 compound with Fd-3m space group using first-principle density functional theory calculations. [Formula: see text] calculations show that the PrAFM–IrNM state in Pr2Ir2O7 compound is energetically more favorable than the other phases. Combining of the interaction of electronic correlation (U) and spin-orbit coupling (SO) leads to three different phases for this material. (1) An anti-ferromagnetic metal is found by the [Formula: see text] ([Formula: see text][Formula: see text]eV) approximation without taking into account the spin orbit interaction. (2) A metal-semimetal transition appears, when the spin-orbit coupling is applied. (3) A semi-conductor characteristic with a narrow gap increases slightly by varying the Hubbard potential of nonmagnetic Ir atoms from 0.5[Formula: see text]eV to 1.5[Formula: see text]eV. The effect of the spin orbit (SO) coupling and the interaction (U) clearly influences the Fermi region of the calculated band structures and densities of states of this system. The hydrostatic pressure effect on the energy gap has shown a further advantage in predicting the desired gap value for this kind of materials. The optical properties, including the dielectric function, refractive index, reflectivity and real part of optical conductivity, are calculated for radiation up to 8[Formula: see text]eV. Overall, however, for both [Formula: see text] values of Pr2Ir2O7, the compound shows similar optical characteristics.

Comparing the effective enhancement of local and nonlocal spin-orbit couplings on honeycomb lattices due to strong electronic correlations

We investigate the interplay of electronic correlations and spin-orbit coupling (SOC) for a one-band and a two-band honeycomb lattice model. The main difference between the two models concerning SOC is that in the one-band case the SOC is a purely non-local term in the basis of the $p_z$ orbitals, whereas in the two-band case with $p_x$ and $p_y$ as basis functions it is purely local. In order to grasp the correlation effects on non-local spin-orbit coupling, we apply the TRILEX approach that allows to calculate non-local contributions to the self-energy approximatively. For the two-band case we apply dynamical mean-field theory. In agreement with previous studies, we find that for all parameter values in our study, the effect of correlations on the spin-orbit coupling strength is that the bare effective SOC parameter is increased. However, this increase is much weaker in the non-local than in the local SOC case. Concerning the TRILEX method, we introduce the necessary formulas for calculations with broken SU(2) symmetry.

Interplay of spin magnetism, orbital magnetism, and atomic structure in layered van der Waals ferromagnet VI3

Recently discovered ferromagnetism of the layered van der Waals material ${\mathrm{VI}}_{3}$ attracts much research attention. Despite substantial progress, in the following important aspects no consensus has been reached: (i) a possible deviation of the easy axis from the normal to the ${\mathrm{VI}}_{3}$ layers, (ii) a possible inequivalence of the V atoms, (iii) the value of the V magnetic moments. The theoretical works differ in the conclusions on the conduction nature of the system, the value, and the role of the V orbital moments. To the best of our knowledge there are no theoretical works addressing issues (i) and (ii) and only one work dealing with the reduced value of the V moment. By combining the symmetry arguments with density functional theory (DFT) and $\mathrm{DFT}+U$ calculations we have shown that the antidimerization distortion of the crystal structure reported by Son et al. [Phys. Rev. B 99, 041402(R) (2019)] must lead to the deviation of the easy axis from the normal to the ${\mathrm{VI}}_{3}$ layers in close correlation with the experimental results. The antidimerization accompanied by breaking the inversion symmetry leads to the inequivalence of the V atoms. Our $\mathrm{DFT}+U$ calculations result in large value $\ensuremath{\sim}0.8\phantom{\rule{4pt}{0ex}}{\ensuremath{\mu}}_{B}$ of the V orbital moments of the V atoms leading to reduced total V moment in agreement with a number of experimental results and with the physical picture suggested by Yang et al. [Phys. Rev. B 101, 100402(R) (2020)]. We obtained large intra-atomic noncollinearity of the V spin and orbital moments revealing strong competition between effects coursed by the onsite electron correlation, spin-orbit coupling, and interatomic hybridization since pure intra-atomic effects lead to collinear spin and orbital moments. Our calculations confirm the experimental results of strong magnetoelastic coupling revealing itself in the strong dependence of the magnetic properties on the distortion of the atomic structure.

Two-dimensional ferromagnetic Chern insulator: WSe2 monolayer

Quantum anomalous Hall (QAH) effect presents a promising platform for next generation nano-electronics due to its dissipationless edge states. Unfortunately, until now, QAH materials suitable for practical applications are rare. Based on the first-principles calculations, we found a novel two-dimensional (2D) QAH insulator: WSe2 monolayer. Both the spin-polarized electronic structure and spin-orbit coupling (SOC) of WSe2 contribute to the QAH effect. When SOC is ignored, the WSe2 monolayer is a spin-polarized Dirac half-metal (DHM). Taking SOC into account, a global band gap about 30 meV is opened and the system behaves as an intrinsic Chern insulator with a Curie temperature of 160 K. The non-trivial properties are proved by the nonzero Chern number, quantized anomalous Hall conductivity, and gapless chiral edge states. We expect the material will become a promising candidate for realizing the QAH effect with higher experimental temperature.

Effect of spin–orbit coupling on strong field ionization simulated with time-dependent configuration interaction

Time-dependent configuration interaction with a complex absorbing potential has been used to simulate strong field ionization by intense laser fields. Because spin-orbit coupling changes the energies of the ground and excited states, it can affect the strong field ionization rate for molecules containing heavy atoms. Configuration interaction with single excitations (CIS) has been employed for strong field ionization of closed shell systems. Single and double excitation configuration interaction with ionization (CISD-IP) has been used to treat ionization of degenerate states of cations on an equal footing. The CISD-IP wavefunction consists of ionizing single (one hole) and double (two hole/one particle) excitations from the neutral atom. Spin-orbit coupling has been implemented using an effective one electron spin-orbit coupling operator. The effective nuclear charge in the spin-orbit coupling operator has been optimized for Ar+, Kr+, Xe+, HX+ (X = Cl, Br, and I). Spin-orbit effects on angular dependence of the strong field ionization have been studied for HX and HX+. The effects of spin-orbit coupling are largest for ionization from the π orbitals of HX+. In a static field, oscillations are seen between the 2Π3/2 and 2Π1/2 states of HX+. For ionization of HX+ by a two cycle circularly polarized pulse, a single peak is seen when the maximum in the carrier envelope is perpendicular to the molecular axis and two peaks are seen when it is parallel to the axis. This is the result of the greater ionization rate for the π orbitals than for the σ orbitals.

Structure, magnetism, and electronic properties in 3d−5d based double perovskite ( Sr1−xCax)2FeIrO6 ( 0≤x≤1 )

The $3d\text{\ensuremath{-}}5d$ based double perovskites offer an ideal playground to study the interplay between electron correlation ($U$) and spin-orbit coupling (SOC) effect, showing exotic physics. The ${\mathrm{Sr}}_{2}{\mathrm{FeIrO}}_{6}$ is an interesting member in this family with ionic distribution of ${\mathrm{Fe}}^{3+}$ ($3{d}^{5}$) and ${\mathrm{Ir}}^{5+}$ ($5{d}^{4}$) where the later is believed to be nonmagnetic under the picture of strong SOC. Here we report a detailed investigation of structural, magnetic, and electronic transport properties along with electronic structure calculations in ${({\mathrm{Sr}}_{1\ensuremath{-}x}{\mathrm{Ca}}_{x})}_{2}{\mathrm{FeIrO}}_{6}$ series with $x$ from 0 to 1. While the basic interactions such as $U$ and SOC are unlikely to be modified, a structural modification is expected due to ionic size difference between ${\mathrm{Sr}}^{2+}$ and ${\mathrm{Ca}}^{2+}$ which would influence other properties such as crystal field effect and bandwidths. While nonmonotonic changes in lattice parameters are observed across the series, the spectroscopic investigations reveal that $3+/5+$ charge state of Fe/Ir continue till the end of the series. An analysis of magnetic data suggests similar nonmonotonic evolution of magnetic parameters with doping. Temperature dependent crystal structure as well as low temperature (5 K) magnetic structure have been determined from neutron powder diffraction measurements which further indicate site ordered moments for both Fe and Ir. The whole series shows insulating behavior with a nonmonotonic variation in resistivity where the charge transport follows the three-dimensional variable range hopping model. The electronic structure calculations show, SOC enhanced, a noncollinear antiferromagnetic and a Mott-type insulating state is the stable ground state for the present series with a substantial amount of orbital moment, but less than the spin magnetic moment, at the Ir site and the magnetocrystalline anisotropy. The calculations further show the evolution of the spin and orbital magnetic moment components across the series along with the magnetization density. The obtained results imply that the local structural modification with introduction of lower size ${\mathrm{Ca}}^{2+}$ has a large influence on the magnetic and transport properties, further showing a large agreement between experimental results as well as theoretical calculations.