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At least 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Topological Doping and Superconductivity in Cuprates: An Experimental Perspective

Hole doping into a correlated antiferromagnet leads to topological stripe correlations, involving charge stripes that separate antiferromagnetic spin stripes of opposite phases. The topological spin stripe order causes the spin degrees of freedom within the charge stripes to feel a geometric frustration with their environment. In the case of cuprates, where the charge stripes have the character of a hole-doped two-leg spin ladder, with corresponding pairing correlations, anti-phase Josephson coupling across the spin stripes can lead to a pair-density-wave order in which the broken translation symmetry of the superconducting wave function is accommodated by pairs with finite momentum. This scenario is now experimentally verified by recently reported measurements on La2−xBaxCuO4 with x=1/8. While pair-density-wave order is not common as a cuprate ground state, it provides a basis for understanding the uniform d-wave order that is more typical in superconducting cuprates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Magnon gap tuning in lithium-doped MnTe

Manganese telluride (MnTe) is a prospective platform for ultrafast carrier dynamics, spin-based thermoelectrics, and magnon-drag transport due to its unique electronic and magnetic properties. We use inelastic neutron scattering to study both pure and lithium-doped MnTe, focusing on the influence of doping in opening a magnon gap. We use neutron powder diffraction to determine critical exponents for the phase transition in both pure and Li-doped MnTe and complement this information with muon spin rotation/relaxation. In conclusion, the opening of the magnon gap and spin reorientation in Li-doped MnTe is mainly due to increased magnetic anisotropy along the [001] axis, a feature not present in pure MnTe.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Spin pumping from antiferromagnetic insulator spin-orbit-proximitized by adjacent heavy metal: a first-principles Floquet-nonequilibrium Green function study

Motivated by the recent experiment on spin pumping from sub-THz radiation-driven uniaxial antiferromagnetic insulator (AFI) MnF 2 into heavy metal (HM) Pt hosting strong spin-orbit (SO) coupling, we compute and compare pumped spin currents in Cu/MnF 2 /Cu and Pt/MnF 2 /Cu heterostructures. Recent theories of spin pumping by AFI have relied on simplistic Hamiltonians (such as tight-binding) and the scattering approach to quantum transport yielding the so-called interfacial spin mixing conductance (SMC), but the concept of SMC ceases to be applicable when SO coupling is present directly at the interface. In contrast, we use a more general first-principles quantum transport approach which combines noncollinear density functional theory with Floquet-nonequilibrium Green's functions in order to take into account: SO-proximitized AFI as a new type of quantum material, different from isolated AFI and brought about by AFI hybridization with adjacent HM layer; strong SO coupling at the interface; and evanescent wavefunctions penetrating from Pt or Cu into AFI layer to make its interfacial region conducting rather than insulating as in the isolated AFI. The DC component of pumped spin current $I_\mathrm{DC}^{S_z}$ vs. precession cone angle $\theta_{\boldsymbol{l}}$ of the Néel vector l of AFI does not follow putative $I^{S_z}_\mathrm{DC} \propto \sin^2 \theta_{\boldsymbol{l}}$, except for very small angles $\theta_{\boldsymbol{l}} \lesssim 10^\circ$ for which we define an effective SMC from the prefactor and find that it doubles from MnF2/Cu to MnF2/Pt interface. In addition, the angular dependence $I^{S_z}_\mathrm{DC}(\theta_{\boldsymbol{l}})$ differs for opposite directions of precession of the Néel vector, leading to twice as large SMC for the right-handed than for the left-handed chirality of the precession mode.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Direct Observation of Modulated Radical Spin States in Metal–Organic Frameworks by Controlled Flexibility

Owing to their switchable spin states and dynamic electronic character, organic-based radical species have been invoked in phenomena unique to a variety of fields. When incorporated in solid state materials, generation of organic radicals proves challenging due to aggregation. Metal–organic frameworks (MOFs) are promising candidates for immobilization and stabilization of organic radicals because of the tunable spatial arrangement of organic linkers and metal nodes, which sequesters the reactive species. Herein, a flexible, redox-active tetracarboxylic acid linker bearing two imidazole units was chosen to construct a new Zr 6 -MOF, NU-910, with scu topology. By exploiting the structural flexibility of NU-910, we successfully modulate the dynamics between an isolated organic radical species and an organic radical π-dimer species in the MOF system. Single-crystal X-ray diffraction analysis reveals that through solvent exchange from N,N-diethylformamide to acetone, NU-910 undergoes a structural contraction with interlinker distances decreasing from 8.32 Å to 3.20 Å at 100 K. Organic radical species on the bridging linkers are generated via UV light irradiation. Direct observation of temperature-induced spin switches from an isolated radical species to a magnetically silent radical π-dimer in NU-910 after irradiation in the solid state was achieved via variable-temperature single-crystal X-ray diffraction and variable-temperature electron paramagnetic resonance spectroscopy. Ultraviolet–visible–near infrared spectroscopy and density functional theory calculations further substantiated the formation of a radical cation π-dimer upon irradiation. As a result, this work demonstrates the potential of using flexible MOFs as a platform to modulate radical spin states in the solid phase.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Electric and magnetic dipole strength in 112,114,116,118,120,124 Sn

Background: There is renewed interest in electric dipole strength distributions for a variety of reasons including the extraction of the dipole polarizability related to properties of the symmetry energy and a measure for the neutron skin thickness, understanding the structure of low-energy $\textit{E}$1 strength in nuclei with neutron excess, and establishing the systematics of the isovector giant dipole resonance (IVGDR). Inelastic proton scattering at energies of a few hundred MeV and very forward angles including 0° has been established as a tool for the study of electric and magnetic dipole strength distributions in nuclei. Purpose: The present work aims at a systematic investigation of the electric and magnetic dipole strength distributions in the chain of stable even-mass tin isotopes. Methods: Inelastic proton scattering experiments were performed at the Research Center for Nuclear Physics, Osaka, with a 295-MeV beam covering laboratory angles 0°–6° and excitation energies 6–22 MeV. Cross sections due to $\textit{E}$1 and $\textit{M}$1 excitations were extracted with a multipole decomposition analysis (MDA) and then converted to reduced transition probabilities with the “virtual photon method” for $\textit{E}$1 and the “unit cross section method” for $\textit{M}$1 excitations, respectively. Including a theory-aided correction for the high-excitation-energy region not covered experimentally, the electric dipole polarizability was determined from the $\textit{E}$1 strength distributions. Results: In this work, total photoabsorption cross sections derived from the $\textit{E}$1 and $\textit{M}$1 strength distributions show significant differences compared to those from previous ($\textit{γ, xn}$) experiments in the energy region of the IVGDR. The widths of the IVGDR deduced from the present data with a Lorentz parametrization show an approximately constant value of about 4.5 MeV in contrast to the large variations between isotopes observed in previous work. The IVGDR centroid energies are in good correspondence to expectations from empirical systematics of their mass dependence. Furthermore, a study of the dependence of the IVGDR energies on bulk matter properties is presented. The $\textit{E}$1 strengths below neutron threshold show fair agreement in this work with results from ($\textit{γ, γ'}$) experiments on 112,116,120,124 Sn in the energy region between 6 and 7 MeV, where also isoscalar $\textit{E}$1 strength was found for 124 Sn. At higher excitation energies, large differences are observed, pointing to a different nature of the excited states with small ground-state branching ratios. The isovector spin-$\textit{M}$1 strengths exhibit a broad distribution between 6 and 12 MeV in all studied nuclei. Conclusions: The present results contribute to the solution of a variety of nuclear structure problems including the systematics of the energy and width of the IVGDR, the structure of low-energy $\textit{E}$1 strength in nuclei, new constraints to energy density functionals (EDFs) aiming at a systematic description of the dipole polarizability across the nuclear chart, from which properties of the symmetry energy can be derived, and the systematics of the isovector spin-$\textit{M}$1 strength in heavy nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Quasi-Two-Dimensional Antiferromagnetic Spin Fluctuations in the Spin-Triplet Superconductor Candidate CeRh 2 As 2

The tetragonal heavy-fermion superconductor CeRh 2 ⁢As 2 (T c = 0.3 K) exhibits an exceptionally high critical field of 14 T for B ∥ c. It undergoes a field-driven first-order phase transition between superconducting states, potentially transitioning from spin-singlet to spin-triplet superconductivity. To further understand these superconducting states and the role of magnetism, we probe spin fluctuations in CeRh 2 ⁢As 2 using neutron scattering. Here, we find dynamic (π, π) antiferromagnetic (AFM) spin correlations with an anisotropic quasi-two-dimensional correlation volume. Our data place an upper limit of 0.31 μ B on the staggered magnetization of corresponding Néel orders at T = 0.08 K. Density functional theory calculations, treating Ce 4⁢ƒ electrons as core states, show that the AFM wave vector connects significant areas of the Fermi surface. Our findings indicate that the dominant excitations in CeRh 2 ⁢As 2 for ℏω⁢ < 1.2 meV are magnetic and suggest that superconductivity in CeRh 2⁢ As 2 is mediated by AFM spin fluctuations associated with a proximate quantum critical point.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Anisotropy, frustration, and saddle point in the twisted kagome compound ErPdPb

The kagome lattice, with its inherent geometric frustration, provides a rich platform for exploring intriguing magnetic phenomena and topological electronic structures. In reduced-symmetry structures, such as twisted kagome systems involving rare earth elements, additional anisotropy can arise, enabling intriguing properties including spin-ice states, magnetocaloric effects, noncollinear magnetic ordering, and the anomalous Hall effect. Here, we report the synthesis of single crystals of ErPdPb, which features a twisted kagome lattice net of Er atoms within the hexagonal ZrNiAl-type structure, and we investigate its magnetic, electronic, and thermal properties. The material exhibits a highly anisotropic, correlated magnetic state below 2.7 K, as evidenced by magnetic, transport, and heat capacity measurements. Density functional theory (DFT) calculations indicate strong easy-axis anisotropy, consistent with experiment and crystal-field expectations, as well as quasi-one-dimensional bands and a spin-split saddle point at the zone center. Here, the coexistence of competing magnetic interactions along different crystallographic directions suggests an inherent degree of frustration. ErPdPb thus provides a promising platform for exploring the interplay of frustration, anisotropy, and electronic structure in a twisted kagome lattice.

Antiferromagnets↗
DOE OSTI2022

Weak magnetic field-dependent photoluminescence properties of lead bromide perovskites

The strong spin–orbit coupling (SOC) in lead halide perovskites, when inversion symmetry is lifted, has provided opportunities for investigating the Rashba effect in these systems. Moreover, the strong orbital moment, which, in turn, impacts the spin-pair in singlet and triplet electronic states, plays a significant role in enhancing the optoelectronic properties in the presence of external magnetic fields in lead halide perovskites. Here, we investigate the effect of weak magnetic fields (<1 T) on the photoluminescence (PL) properties of CsPbBr 3 nanocrystals with and without Ruddlesden–Popper (RP) faults and single crystals of CH 3 NH 3 PbBr 3 . Along with an enhancement in the PL intensity as a function of an external magnetic field, which is observed in both lead bromide perovskites, the PL emission red-shifts in CsPbBr 3 nanocrystals. Density-functional theory calculations of the electronic band-edge in CsPbBr 3 show almost no change in the energy gap as a function of the external magnetic field. The experimental results, thus, suggest the role of mixing of the triplet and singlet excitonic states under weak magnetic fields. This is further deduced from an enhancement in PL lifetimes as a function of the field in CsPbBr 3 ⁠. In CH 3 NH 3 PbBr 3⁠ , an increase in PL intensity is observed under weak magnetic fields; however, no changes in the peak energy or PL lifetimes are observed. The internal magnetic fields due to SOC are characterized for all three samples and found to be the highest for CsPbBr 3 nanocrystals with RP faults.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Effects of spin-orbit coupling and very large supercells on the description of acceptors in CdTe

Predicting accurate shallow donor and acceptor levels in semiconductors has been quite challenging using periodic boundary conditions as implemented in current density functional theory codes. The reason is that the wave functions associated with the shallow centers are quite extended and are not fully contained in the supercell (typically with a few hundred atoms) so impurities in the periodically repeated image cells interact with each other. Errors of ~0.1 eV are expected, and these are of the same order of magnitude as the ionization energies themselves. In the case of acceptors in CdTe, this problem is exacerbated by the strong spin-orbit coupling that split the Te-related states at the top of the valence band, making the calculations at least 8 times more expensive. CdTe is an important solar-cell material with record high efficiency of 22%. One of the main limiting factors to increasing the efficiency towards the theoretical limit of ~30% is the often reported very low hole concentration. Pushing to the limit of computational capability by using very large supercells with spin-orbit coupling we report the results of hybrid functional calculations of group-V acceptors in CdTe. We show that extrapolation to the dilute limit leads to an interpretation of the experimental data that is qualitatively different from previous DFT and hybrid functional calculation reports. We find that the group-V impurities indeed behave as shallow acceptors and that the corresponding compensating AX-centers are unstable and do not limit p-type doping. We address the differences between our results and previous theoretical predictions and show that our calculated ionization energies predict hole concentrations that are in excellent agreement with recent temperature-dependent Hall measurements on high-quality single-crystal samples.

14 SOLAR ENERGY↗
DOE OSTI2021

57Fe Mössbauer isomer shift of pure iron and iron oxides at high pressure—An experimental and theoretical study

The 57Fe isomer shift (IS) of pure iron has been measured up to 100 GPa using synchrotron Mössbauer spectroscopy in the time domain. Apart from the expected discontinuity due to the α→ε structural and spin transitions, the IS decreases monotonically with increasing pressure. The absolute shifts were reproduced without semi-empirical calibrations by periodic density functional calculations employing extensive localized basis sets with several common density functionals. However, the best numerical agreement is obtained with the B1WC hybrid functional. Extension of the calculations to 350 GPa, a pressure corresponding to the Earth’s inner core, predicted the IS range of 0.00 to -0.85 mm/s, covering the span from Fe(0) to Fe(VI) compounds measured at ambient pressure. The calculations also reproduced the pressure trend from polymorphs of prototypical iron oxide minerals, FeO and Fe2O3. Analysis of the electronic structure shows a strong donation of electrons from oxygen to iron at high pressure. The assignment of formal oxidation to the Fe atom becomes ambiguous under this condition.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Band-mixing effects in one-dimensional charge transfer insulators

The low-energy properties of transition metal oxides (TMOs) are governed by the electrons occupying strongly correlated $d$-orbitals that are hybridized with surrounding ligand oxygen $p$ orbitals to varying degrees. Their physics is thus established by a complex interplay between the transition-metal (TM)-ligand hopping $t$, charge transfer energy $\Delta_\mathrm{CT}$, and on-site TM Hubbard repulsion $U$. Here, we study the spectral properties of a one-dimensional (1D) analog of such a $pd$ system, with alternating TM $d$ and ligand anion $p$ orbitals situated along a chain. Using the density matrix renormalization group method, we study the model's single-particle spectral function, x-ray absorption spectrum, and dynamical spin structure factor as a function of $\Delta_\mathrm{CT}$ and $U$. In particular, we present results spanning from the Mott insulating ($\Delta_\mathrm{CT} > U$) to negative charge transfer regime $\Delta_\mathrm{CT} < 0$ to gain a better understanding of the ground and momentum-resolved excited state properties of these different regimes. Our results can guide new studies on TMOs that seek to situate them within the Mott-Hubbard/charge transfer insulator classification scheme.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Non-bonding interaction of dual atom catalysts for enhanced oxygen reduction reaction

Here, we demonstrate the design of graphene-supported dual atom catalysts (DACs) for the four-electron oxygen reduction reaction (ORR), by utilizing the non-bonding interaction of counterpart metals (M) that synergistically tune the electronic properties and catalytic activity of the Fe active site in FeMN 6 -DAC and FeMN 8 -DAC systems, where M stands for Fe, Co, Ni, Cu, and Zn. More specifically, for Fe-M distances below 15Å, the non-bonding interaction is significant, making the system act as the DAC. We predicted that FeNiN 6 -DAC and FeNiN 8 -DAC exhibit a low ORR overpotential (η ORR ) of 0.28 V and 0.47 V, respectively, which are at the summits of volcano plots. This low η ORR originates from the high Bader charge transfer coupled with high spin density at the Fe site in both the FeNiN 6 -DAC and FeNiN 8 -DAC systems, which weakens the adsorption of OH* intermediate while enhancing its desorption to H 2 O. Guided by these density functional theory (DFT) computational results, we synthesized FeCoN 8 -DAC and FeNiN 8 -DAC along with N-doped graphene and confirmed their structures with scanning transmission electron microscopy (STEM), X-ray photoelectron spectroscopy (XPS), X-ray absorption near-edge structure (XANES), extended X-ray absorption fine structure (EXAFS), and electron spin resonance (ESR). We verify experimentally the catalytic activities and find that FeNiN 8 -DAC has the low experimental overpotential of 0.39 V with a Tafel slope of 47 mVdec -1 . Based on these results, we propose a DFT-guided strategy to tune the charge transfer and spin population of the active site toward designing DACs for electrochemical ORR.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Elucidation of complex triplet excited state dynamics in Pd(ii) biladiene tetrapyrroles

Pd(II) biladienes have been developed over the last five years as non-aromatic oligotetrapyrrole complexes that support a rich triplet photochemistry. In this work, we have undertaken the first detailed photophysical interrogation of three homologous Pd(II) biladienes bearing different combinations of methyl- and phenyl-substituents on the frameworks’ sp 3 -hybridized meso-carbon (i.e., the 10-position of the biladiene framework). These experiments have revealed unexpected excited-state dynamics that are dependent on the wavelength of light used to excite the biladiene. More specifically, transient absorption spectroscopy revealed that higher-energy excitation (λ exc ~ 350–500 nm) led to an additional lifetime (i.e., an extra photophysical process) compared to experiments carried out following excitation into the lowest-energy excited states (λ exc = 550 nm). Each Pd(II) biladiene complex displayed an intersystem crossing lifetime on the order of tens of ps and a triplet lifetime of ~20 μs, regardless of the excitation wavelength. However, when higher-energy light is used to excite the complexes, a new lifetime on the order of hundreds of ps is observed. The origin of the ‘extra’ lifetime observed upon higher energy excitation was revealed using density functional theory (DFT) and time-dependent DFT (TDDFT). These efforts demonstrated that excitation into higher-energy metal-mixed-charge-transfer excited states with high spin–orbit coupling to higher energy metal-mixed-charge-transfer triplet states leads to the additional excitation deactivation pathway. Furthermore, the results of this work demonstrate that Pd(II) biladienes support a unique triplet photochemistry that may be exploited for development of new photochemical schemes and applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Adiabatic quantum decoherence in many non-interacting subsystems induced by the coupling with a common boson bath

Highlights: • System–environment quantum correlation: a main solid state NMR decoherence channel. • Non-separable system–environment model yields realistic spin decoherence rates. • New open quantum system approach explains irreversible decay of refocused NMR echoes. • Adiabatic quantum decoherence is inherently irreversible and eigen-selective. This work addresses adiabatic quantum decoherence of many-body spin systems coupled with a boson field in the framework of open quantum systems theory. We generalize the traditional spin-boson model by considering a system–environment interaction Hamiltonian that represents a partition of non-interacting subsystems and highlights the collective correlation that appears exclusively due to the coupling with a common environment. Remarkably, this simple, exactly solvable model encompasses relevant aspects of a many-body open quantum system and features the subtle quantum effects that arise when the size scales up to a macroscopic level. We derive an analytical expression for the time dependence of the density matrix elements (in the preferred basis) without assuming coarse-graining. The resulting decoherence function is eigen-selective and is a complex exponential whose exponent has a real part that introduces a decay similar to that in the spin-boson model. On the contrary, the imaginary part depends on the quantum numbers and geometry of the whole partition and does not reflect the system temperature. Motivated by decoherence in solid-state NMR, and in search of realistic numerical estimations, we apply the theoretical results to a partition of dipole-coupled spin pairs in contact with a common phonon bath, using typical parameters of hydrated salts. The proposal allows estimating the decoherence time scale in terms of the system physical constants: sound velocity and eigenvalue distribution width. As a significant novelty, the decoherence function phase depends on the eigenvalue distribution throughout the sample. It plays the leading role, overshadowing the mechanism associated with the bath thermal state. Finally, we apply the formalism to describe decoherence in the “magic echo” NMR reversal experiment. We find that the system–environment correlation explains the origin of irreversibility, and both the decoherence rate value and its dependence on the dipolar frequency, are remarkably similar to the experiment.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Exploring the Limits of Dative Boratrane Bonding: Iron as a Strong Lewis Base in Low-Valent Non-Heme Iron-Nitrosyl Complexes

We previously reported the synthesis and preliminary characterization of a unique series of low-spin (ls) {FeNO} 8–10 complexes supported by an ambiphilic trisphosphineborane ligand, [Fe(TPB)(NO)] +/0/– . In this study, we use advanced spectroscopic techniques and density functional theory (DFT) calculations to extract detailed information as to how the bonding changes across the redox series. We find that, in spite of the highly reduced nature of these complexes, they feature an NO + ligand throughout with strong Fe–NO π-backbonding and essentially closed-shell electronic structures of their FeNO units. This is enabled by an Fe–B interaction that is present throughout the series. In particular, the most reduced [Fe(TPB)(NO)] – complex, an example of a ls-{FeNO} 10 species, features a true reverse dative Fe → B bond where the Fe center acts as a strong Lewis-base. Hence, this complex is in fact electronically similar to the ls-{FeNO} 8 system, with two additional electrons “stored” on site in an Fe–B single bond. The outlier in this series is the ls-{FeNO} 9 complex, due to spin polarization (quantified by pulse EPR spectroscopy), which weakens the Fe–NO bond. These data are further contextualized by comparison with a related N 2 complex, [Fe(TPB)(N 2 )] – , which is a key intermediate in Fe(TPB)-catalyzed N 2 fixation. Our present study finds that the Fe → B interaction is key for storing the electrons needed to achieve a highly reduced state in these systems, and highlights the pitfalls associated with using geometric parameters to try to evaluate reverse dative interactions, a finding with broader implications to the study of transition metal complexes with boratrane and related ligands.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Weyl nodal ring states and Landau quantization with very large magnetoresistance in square-net magnet EuGa 4

Magnetic topological semimetals allow for an effective control of the topological electronic states by tuning the spin configuration. Among them, Weyl nodal line semimetals are thought to have the greatest tunability, yet they are the least studied experimentally due to the scarcity of material candidates. Here, using a combination of angle-resolved photoemission spectroscopy and quantum oscillation measurements, together with density functional theory calculations, we identify the square-net compound EuGa 4 as a magnetic Weyl nodal ring semimetal, in which the line nodes form closed rings near the Fermi level. The Weyl nodal ring states show distinct Landau quantization with clear spin splitting upon application of a magnetic field. At 2 K in a field of 14 T, the transverse magnetoresistance of EuGa 4 exceeds 200,000%, which is more than two orders of magnitude larger than that of other known magnetic topological semimetals. Our theoretical model suggests that the non-saturating magnetoresistance up to 40 T arises as a consequence of the nodal ring state.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Trigonal symmetry breaking and its electronic effects in the two-dimensional dihalides MX 2 and trihalides MX 3

We study the consequences of the approximately trigonal (D 3d ) point symmetry of the transition metal (M) site in two-dimensional van der Waals MX 2 dihalides and MX 3 trihalides. The trigonal symmetry leads to a 2-2-1 orbital splitting of the transition metal d shell, which is best represented by d orbitals that describe the trigonal rather than Oh symmetry. The ligand-ligand bond length differences (rather than metal-ligand) take the role of a Jahn-Teller-like mode and in combination with interlayer distances and dimensionality effects tune the crystal field splittings and bandwidths. These effects, in turn, are amplified by electronic correlation effects—leading to crystal field splittings of the order of 0.1–1 eV between the singlet and the lowest orbital doublet—as opposed to the often assumed degenerate 3 t 2g states. Our calculations explain why most of the materials in this family are insulating, and why these considerations have to be taken into account in realistic models of them. Further, orbital order coupled to various lower symmetry lattice modes may lift the remaining orbital degeneracies, and we explain how these may support unique electronic states using ZrI 2 and CuCl 2 as examples, and offer a brief overview of possible electronic configurations in this class of materials. By building and analyzing Wannier models adapted to the appropriate symmetry we examine how the interplay among trigonal symmetry, electronic correlation effects, and – d orbital charge transfer leads to insulating, orbitally polarized magnetic and/or orbital-selective Mott states, and we provide a simple framework and numerical tool for others. Our paper establishes a rigorous framework to understand, control, and tune the electronic states in low-dimensional correlated halides. Furthermore, our analysis shows that trigonal symmetry and its breaking is a key feature of the two-dimensional halides that needs to be accounted for in search of novel electronic states in materials ranging from CrI 3 to α–RuCl 3 .

2-dimensional systems↗