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Bilayer crystals, built from monolayers of two-dimensional (2D) crystals with different lattice orientations, generate interlayer potentials leading to unique excitonic properties. However, the ability to tune the interlayer potential is limited by the fixed covalent 2D lattice geometries. Synthetically substituting one of the layers with an atomically thin molecular crystal could substantially expand the design space for tuning the excitonic response, enabled by explicit control of chemical and electronic structures of the molecular building blocks. Here we report the large-scale synthesis of four-atom-thick hybrid bilayer crystals (HBCs), comprising perylene-based molecular and transition metal dichalcogenide (TMD) monolayer single crystals, which show precise tuning of the HBC lattices at the molecular level. We observe near-unity anisotropic photoluminescence, which is directly tuned by specific molecular geometry and HBC composition. Our ab initio GW and Bethe-Salpeter equation calculations show that the anisotropic emission originates from delocalized and anisotropic hybrid excitons. These excitons inherit characteristics from states associated with both the TMD and molecular layers, resulting from a hybridized bilayer band structure of the HBC. By introducing HBCs as a scalable solid-state platform, our work paves the way for tunable interlayer energy landscapes achievable through direct synthesis, opening up new frontiers in molecule-based quantum materials.

Understanding exciton thermalization is critical for optimizing optoelectronic and photocatalytic processes in many materials. However, it is hard to access the dynamics of such processes experimentally, especially on systems such as monolayer transition metal dichalcogenides, where various low-energy excitations pathways can compete for exciton thermalization. Here, we study exciton dynamics due to exciton-phonon scattering in monolayer MoS2 from a first-principles, interacting Green's function approach, to obtain the relaxation and thermalization of low-energy excitons following different initial excitations at different temperatures. We find that the thermalization occurs on a picosecond timescale at 300 K but can increase by an order of magnitude at 100 K. The long total thermalization time, owing to the nature of its excitonic band structure, is dominated by slow spin-flip scattering processes in monolayer MoS2. In contrast, thermalization of excitons in individual spin-aligned and spin-anti-aligned channels can be achieved within a few hundred fs when exciting higher-energy excitons. We further simulate the intensity spectrum of time-resolved angle-resolved photoemission spectroscopy (TR-ARPES) experiments and anticipate that such calculations may serve as a map to correlate spectroscopic signatures with microscopic exciton dynamics., Comment: 19 pages, 8 figures

Halide double perovskites are a chemically-diverse and growing class of compound semiconductors that are promising for optoelectronic applications. However, the prediction of their fundamental gaps and optical properties with density functional theory (DFT) and {\it ab initio} many-body perturbation theory has been a significant challenge. Recently, a nonempirical Wannier-localized optimally-tuned screened range-separated hybrid (WOT-SRSH) functional has been shown to accurately produce the fundamental band gaps of a wide set of semiconductors and insulators, including lead halide perovskites. Here we apply the WOT-SRSH functional to five halide double perovskites, and compare the results with those obtained from other known functionals and previous $GW$ calculations. We also use the approach as a starting point for $GW$ calculations and we compute the band structures and optical absorption spectrum for Cs\textsubscript{2}Ag{Bi}Br\textsubscript{6}, using both time-dependent DFT and the $GW$-Bethe-Salpeter equation approach. We show that the WOT-SRSH functional leads to accurate fundamental and optical band gaps, as well as optical absorption spectra, consistent with spectroscopic measurements, thereby establishing WOT-SRSH as a viable method for the accurate prediction of optoelectronic properties of halide double perovskites.

Atomically thin semiconductors, encompassing both 2D materials and quantum wells, exhibit a pronounced enhancement of excitonic effects due to geometric confinement. Consequently, these materials have become foundational platforms for the exploration and utilization of excitons. Recent ab initio studies have demonstrated that phonons can substantially screen electron-hole interactions in bulk semiconductors and strongly modify the properties of excitons. While excitonic properties of atomically thin semiconductors have been the subject of extensive theoretical investigations, the role of phonon screening on excitons in atomically thin structures remains unexplored. In this work, we demonstrate via ab initio GW-Bethe-Salpeter equation calculations that phonon screening can have a significant impact on optical excitations in atomically thin semiconductors. We further show that the degree of phonon screening can be tuned by structural engineering. We focus on atomically thin GaN quantum wells embedded in AlN and identify specific phonons in the surrounding material, AlN, that dramatically alter the lowest-lying exciton in monolayer GaN via screening. Our studies provide new intuition beyond standard models into the interplay among structural properties, phonon characteristics, and exciton properties in atomically thin semiconductors, and have implications for future experiments.

Understanding the processes governing the dissociation of excitons to free charge carriers in semiconductors and insulators is of central importance for photovoltaic applications. Dyson's $\mathcal{S}$-matrix formalism provides a framework for computing scattering rates between quasiparticle states derived from the same underlying Hamiltonian, often reducing to familiar Fermi's golden rule like expressions at first order. By presenting a rigorous formalism for multi-channel scattering, we extend this approach to describe scattering between composite quasiparticles and in particular, the process of exciton dissociation mediated by the electron-phonon interaction. Subsequently, we derive rigorous expressions for the exciton dissociation rate, a key quantity of interest in optoelectronic materials, which enforce correct energy conservation and may be readily used in ab initio calculations. We apply our formalism to a three-dimensional model system to compare temperature-dependent exciton rates obtained for different scattering channels.

Materials that transition between metal and insulator, the two opposing states that distinguish all solids, are fascinating because they underlie many mysteries in the physics of the solid state. In 1T-TaS$_{2}$, the metal-insulator transition is linked to a series of metastable states of a chiral charge density wave whose basic nature is still an open question. In this work, we show that pulses of current through these materials create current-carrying boundary channels that distinguish the metallic and insulating states. We demonstrate electrical control of these channels' properties, suggesting their formation could be due to the complex interplay of the formation of domain walls and the viscous flow of electrons. Our findings show that physical boundaries play a key role in the properties of the metastable states of the metal-insulator transition, highlighting new possibilities for in-situ electrical design and active manipulation of electrical components.

Accurate prediction of electronic and optical excitations in van der Waals (vdW) materials is a long-standing challenge for density functional theory. The recently proposed Wannier-localized optimally-tuned screened range-separated hybrid (WOT-SRSH) functional has proven successful in non-empirical determination of electronic band gaps and optical absorption spectra for various covalent and ionic crystals. However, for vdW materials the tuning of the material- and structure-dependent functional parameters has, until now, only been attained semi-empirically. Here, we present a non-empirical WOT-SRSH approach applicable to vdW materials, with the optimal functional parameters transferable between monolayer and bulk. We apply this methodology to prototypical vdW materials: black phosphorus, molybdenum disulfide, and hexagonal boron nitride (in the latter case including zero-point renormalization). We show that the WOT-SRSH approach consistently achieves accuracy levels comparable to experiments and ab initio many-body perturbation theory (MBPT) calculations for band structures and optical absorption spectra, both on its own and as an optimal starting point for MBPT calculations., Comment: 11 pages + 4 figures; Supporting Information (15 pages + 2 figures)

The ionization potential of molecular chains is well-known to be a tunable nano-scale property that exhibits clear quantum confinement effects. State-of-the-art methods can accurately predict the ionization potential in the small molecule limit and in the solid-state limit, but for intermediate, nano-sized systems prediction of the evolution of the electronic structure between the two limits is more difficult. Recently, optimal tuning of range-separated hybrid functionals has emerged as a highly accurate method for predicting ionization potentials. This was first achieved for molecules using the ionization potential theorem (IPT) and more recently extended to solid-state systems, based on an \textit{ansatz} that generalizes the IPT to the removal of charge from a localized Wannier function. Here, we study one-dimensional molecular chains of increasing size, from the monomer limit to the infinite polymer limit using this approach. By comparing our results with other localization-based methods and where available with experiment, we demonstrate that Wannier-localization-based optimal tuning is highly accurate in predicting ionization potentials for any chain length, including the nano-scale regime.

Electron-phonon interactions are of great importance to a variety of physical phenomena, and their accurate description is an important goal for first-principles calculations. Isolated examples of materials and molecular systems have emerged where electron-phonon coupling is enhanced over density functional theory (DFT) when using the Green's-function-based ab initio GW method, which provides a more accurate description of electronic correlations. It is however unclear how general this enhancement is, and how employing high-end quantum chemistry methods, which further improve the description of electronic correlations, might further alter electron-phonon interactions over GW or DFT. Here, we address these questions by computing the renormalization of the highest occupied molecular orbital energies of Thiel's set of organic molecules by harmonic vibrations using DFT, GW and equation-of-motion coupled-cluster calculations. We find that GW can increase the magnitude of the electron-phonon coupling across this set of molecules by an average factor of 1.1-1.8 compared to DFT, while equation-of-motion coupled-cluster leads to an increase of 1.4-2. The electron-phonon coupling predicted with the ab initio GW method is generally in much closer agreement to coupled cluster values compared to DFT, establishing GW as an accurate way of computing electron-phonon phenomena in molecules and beyond at a much lower computational cost than higher-end quantum chemistry techniques.

Despite the weak, van-der-Waals interlayer coupling, photoinduced charge transfer vertically across atomically thin interfaces can occur within surprisingly fast, sub-50fs timescales. Early theoretical understanding of the charge transfer is based on a noninteracting picture, neglecting excitonic effects that dominate the optical properties of such materials. Here, we employ an ab initio many-body perturbation theory approach which explicitly accounts for the excitons and phonons in the heterostructure. Our large-scale first-principles calculations directly probe the role of exciton-phonon coupling in the charge dynamics of the WS$_2$/MoS$_2$ heterobilayer. We find that the exciton-phonon interaction induced relaxation time of photo-excited excitons at the $K$ valley of MoS$_2$ and WS$_2$ is 67 fs and 15 fs at 300 K, respectively, which sets a lower bound to the intralayer-to-interlayer exciton transfer time and is consistent with experiment reports. We further show that electron-hole correlations facilitate novel transfer pathways which are otherwise inaccessible to non-interacting electrons and holes., Comment: 15 pages, 4 figures

The properties of excitons, or correlated electron-hole pairs, are of paramount importance to optoelectronic applications of materials. A central component of exciton physics is the electron-hole interaction, which is commonly treated as screened solely by electrons within a material. However, nuclear motion can screen this Coulomb interaction as well, with several recent studies developing model approaches for approximating the phonon screening to the properties of excitons. While these model approaches tend to improve agreement with experiment for exciton properties, they rely on several approximations that restrict their applicability to a wide range of materials, and thus far they have neglected the effect of finite temperatures. Here, we develop a fully first-principles, parameter-free approach to compute the temperature-dependent effects of phonon screening within the ab initio GW-Bethe Salpeter equation framework. We recover previously proposed models of phonon screening as well-defined limits of our general framework, and discuss their validity by comparing them against our first-principles results. We develop an efficient computational workflow and apply it to a diverse set of semiconductors, specifically AlN, CdS, GaN, MgO and SrTiO3. We demonstrate under different physical scenarios how excitons may be screened by multiple polar optical or acoustic phonons, how their binding energies can exhibit strong temperature dependence, and the ultrafast timescales on which they dissociate into free electron-hole pairs.

Using both time-dependent density functional theory (TDDFT) and the ``single-shot" $GW$ plus Bethe-Salpeter equation ($GW$-BSE) approach, we compute optical band gaps and optical absorption spectra from first principles for eight common binary and ternary closed-shell metal oxides (MgO, Al$_2$O$_3$, CaO, TiO$_2$, Cu$_2$O, ZnO, BaSnO$_3$, and BiVO$_4$), based on the non-empirical Wannier-localized optimally-tuned screened range-separated hybrid functional. Overall, we find excellent agreement between our TDDFT and $GW$-BSE results and experiment, with a mean absolute error less than 0.4 eV, including for Cu$_2$O and ZnO, traditionally considered to be challenging for both methods.

We introduce a maximally-localized Wannier function representation of Bloch excitons, two-particle correlated electron-hole excitations, in crystalline solids, where the excitons are maximally-localized with respect to an average electron-hole coordinate in real space. As a proof-of-concept, we illustrate this representation in the case of low-energy spin-singlet and triplet excitons in LiF, computed using the ab initio Bethe-Salpeter equation approach. We visualize the resulting maximally-localized exciton Wannier functions (MLXWFs) in real space, detail the convergence of the exciton Wannier spreads, and demonstrate how Wannier-Fourier interpolation can be leveraged to obtain exciton energies and states at arbitrary exciton crystal momenta in the Brillouin zone. We further introduce an approach to treat the long-range dipolar coupling between singlet MLXWFs and discuss it in depth. The MLXWF representation sheds light on the fundamental nature of excitons and paves the way towards Wannier-based post-processing of excitonic properties, enabling the construction of ab initio exciton tight-binding models, efficient interpolation of the exciton-phonon vertex, the computation of Berry curvature associated with exciton bands, and beyond.

The accurate description of electronic properties and optical absorption spectra is a long-standing challenge for density functional theory. Recently, the introduction of screened range-separated hybrid (SRSH) functionals for solid-state materials has allowed for the calculation of fundamental band gaps and optical absorption spectra that are in very good agreement with many-body perturbation theory. However, since solid-state SRSH functionals are typically tuned to reproduce the properties of bulk phases, their transferability to low-dimensional structures, which experience substantially different screening than in the bulk, remains an open question. In this work, we explore the transferability of SRSH functionals to several prototypical van der Waals materials, including transition-metal sulfides and selenides, indium selenide, black phosphorus, and hexagonal boron nitride. Considering the bulk and a monolayer of these materials as limiting cases, we show that the parameters of the SRSH functional can be determined systematically, using only the band-edge quasiparticle energies of these extremal structural phases as fitting targets. The resulting SRSH functionals can describe both electronic bandstructures and optical absorption spectra with accuracy comparable to more demanding ab initio many-body perturbation theory (GW and Bethe-Salpeter equation) approaches. Selected examples also demonstrate that the SRSH parameters, obtained from the bulk and monolayer reference structures, display good accuracy for bandstructures and optical spectra of bilayers, indicating a degree of transferability that is independent of the fitting procedure., Comment: 14 pages + 8 figures; Supporting Information (21 pages + 18 figures)

Non-radiative exciton relaxation processes are critical for energy transduction efficiencies in optoelectronic materials, but how these processes are connected to the underlying crystal structure and its associated electron, exciton, and phonon band structures is poorly understood. Here, we present a first-principles approach to explore exciton relaxation pathways in pentacene, a paradigmatic molecular crystal and optoelectronic semiconductor. We compute the momentum- and band-resolved exciton-phonon interactions, and use them to analyse key scattering channels. We find that exciton intraband transitions on femtosecond timescales leading to dark-state occupation is a dominant nonradiative relaxation channel in pentacene. We further show how the nature of real-time propagation of the exciton wavepacket is connected with the longitudinal-transverse exciton splitting, stemming from crystal anisotropy, and concomitant anisotropic exciton and phonon dispersions. Our results provide a framework for understanding time-resolved exciton propagation and energy transfer in molecular crystals and beyond.

The intrinsic weak and highly non-local dielectric screening of two-dimensional materials is well known to lead to high sensitivity of their optoelectronic properties to environment. Less studied theoretically is the role of free carriers on those properties. Here, we use ab initio GW and Bethe-Salpeter equation calculations, with a rigorous treatment of dynamical screening and local-field effects, to study the doping-dependence of the quasiparticle and optical properties of a monolayer transition metal dichalcogenide, 2H MoTe$_2$. We predict a quasiparticle band gap renormalization of several hundreds meV for experimentally-achievable carrier densities, and a similarly sizable decrease in the exciton binding energy. This results in an almost constant excitation energy for the lowest-energy exciton resonance with increasing doping density. Using a newly-developed and generally-applicable quasi-2D plasmon-pole model and a self-consistent solution of the Bethe-Salpeter equation, we reveal the importance of accurately capturing both dynamical and local-field effects to understand detailed photoluminescence measurements., Comment: 22 pages, 5 figures, under review in Nano Letters

Monolayer transition metal dichalcogenide (TMDC) semiconductors exhibit strong excitonic optical resonances which serve as a microscopic, non-invasive probe into their fundamental properties. Like the hydrogen atom, such excitons can exhibit an entire Rydberg series of resonances. Excitons have been extensively studied in most TMDCs (MoS$_2$, MoSe$_2$, WS$_2$ and WSe$_2$), but detailed exploration of excitonic phenomena has been lacking in the important TMDC material molybdenum ditelluride (MoTe$_2$). Here, we report an experimental investigation of excitonic luminescence properties of monolayer MoTe$_2$ to understand the excitonic Rydberg series, up to 3s. We report significant modification of emission energies with temperature (4K to 300K), quantifying the exciton-phonon coupling. Furthermore, we observe a strongly gate-tunable exciton-trion interplay for all the Rydberg states governed mainly by free-carrier screening, Pauli blocking, and band-gap renormalization in agreement with the results of first-principles GW plus Bethe-Salpeter equation approach calculations. Our results help bring monolayer MoTe$_2$ closer to its potential applications in near-infrared optoelectronics and photonic devices., Comment: 5 figures (main text)

The spatial extent of excitons in molecular systems underpins their photophysics and utility for optoelectronic applications. Phonons are reported to lead to both exciton localization and delocalization. However, a microscopic understanding of phonon-induced (de)localization is lacking, in particular how localized states form, the role of specific vibrations, and the relative importance of quantum and thermal nuclear fluctuations. Here we present a first-principles study of these phenomena in solid pentacene, a prototypical molecular crystal, capturing the formation of bound excitons, exciton-phonon coupling to all orders, and phonon anharmonicity, using density functional theory, the \emph{ab initio} $GW$-Bethe-Salpeter equation approach, finite difference, and path integral techniques. We find that for pentacene zero-point nuclear motion causes uniformly strong localization, with thermal motion providing additional localization only for Wannier-Mott-like excitons. Anharmonic effects drive temperature-dependent localization, and while such effects prevent the emergence of highly delocalized excitons, we explore the conditions under which these might be realized.

Tomonaga-Luttinger liquid (TLL) behavior in one-dimensional systems has been predicted and shown to occur at semiconductor-to-metal transitions within two-dimensional materials. Reports of mirror twin boundaries (MTBs) hosting a Fermi liquid or a TLL have suggested a dependence on the underlying substrate, however, unveiling the physical details of electronic contributions from the substrate require cross-correlative investigation. Here, we study TLL formation in MTBs within defectively engineered WS$_2$ atop graphene, where band structure and the atomic environment is visualized with nano angle-resolved photoelectron spectroscopy, scanning tunneling microscopy and scanning tunneling spectroscopy, and non-contact atomic force microscopy. Correlations between the local density of states and electronic band dispersion elucidated the electron transfer from graphene into a TLL hosted by MTB defects. We find that MTB defects can be substantially charged at a local level, which drives a band gap shift by $\sim$0.5 eV., Comment: Main text is 13 pages, 4 figures; Supplementary text is 14 pages, 11 figures

We introduce a new, general-purpose, range-separated hybrid van der Waals density \ph{functional, termed vdW-DF-ahbr,} within the non-empirical vdW-DF method [JPCM 32, 393001 (2020)]. It combines correlation from vdW-DF2 with a screened Fock exchange that is fixed by \ph{a new model of exchange effects} in the density-explicit vdW-DF2-b86r functional [PRB 89, 121103(R) (2014)]. The new vdW-DF2-ahbr prevents spurious exchange binding and has a small-density-gradient form set from many-body perturbation analysis. It is accurate for \ph{bulk as well as layered materials} and it systematically and significantly improves the performance of present vdW-DFs for molecular problems. Importantly, vdW-DF2-ahbr also outperforms present-standard (dispersion-corrected) range-separated hybrids on a broad collection of noncovalent-interaction benchmark sets, while at the same time successfully mitigating the density-driven errors that often affect the description of molecular transition states and isomerization calculations. vdW-DF2-ahbr furthermore improves on state of the art density functional theory approaches by 1) correctly predicting both the substrate structure and the site preference for CO adsorption on Pt(111), 2) outperforming existing non-empirical vdW-DFs for the description of CO$_2$ adsorption in both a functionalized and in a simple metal-organic framework, and 3) being highly accurate \ph{for the} set of base-pair interactions in a model of DNA assembly., Comment: 54 pages and 14 figures

The dependence of ab initio many-body perturbation theory within the $GW$ approximation on the eigensystem used in calculating quasiparticle corrections limits this method's predictive power. Here, we investigate the accuracy of the recently developed Wannier-localized optimally tuned screened range-separated hybrid (WOT-SRSH) functional as a generalized Kohn-Sham starting point for single-shot $GW$ ($G_0W_0$) calculations for a range of semiconductors and insulators. Comparison to calculations based on well-established functionals, namely PBE, PBE0, and HSE, as well as to self-consistent $GW$ schemes and to experiment, shows that band gaps computed via $G_0W_0$@WOT-SRSH have a level of precision and accuracy that is comparable to that of more advanced methods such as quasiparticle self-consistent $GW$ (QS$GW$) and eigenvalue self-consistent $GW$ (ev$GW$). We also find that $G_0W_0$@WOT-SRSH improves the description of states deeper in the valence band manifold. Finally, we show that $G_0W_0$@WOT-SRSH significantly reduces the sensitivity of computed band gaps to ambiguities in the underlying WOT-SRSH tuning procedure.

Machine learning for materials discovery has largely focused on predicting an individual scalar rather than multiple related properties, where spectral properties are an important example. Fundamental spectral properties include the phonon density of states (phDOS) and the electronic density of states (eDOS), which individually or collectively are the origins of a breadth of materials observables and functions. Building upon the success of graph attention networks for encoding crystalline materials, we introduce a probabilistic embedding generator specifically tailored to the prediction of spectral properties. Coupled with supervised contrastive learning, our materials-to-spectrum (Mat2Spec) model outperforms state-of-the-art methods for predicting ab initio phDOS and eDOS for crystalline materials. We demonstrate Mat2Spec's ability to identify eDOS gaps below the Fermi energy, validating predictions with ab initio calculations and thereby discovering candidate thermoelectrics and transparent conductors. Mat2Spec is an exemplar framework for predicting spectral properties of materials via strategically incorporated machine learning techniques., Comment: 26 pages, 15 figures, Minor edits to match the proofs from Nat.Commun

One-dimensional electron systems (1DESs) exhibit properties that are fundamentally different from higher-dimensional systems. For example, electron-electron interactions in 1DESs have been predicted to induce Tomonaga-Luttinger liquid behavior. Naturally-occurring grain boundaries in single-layer semiconducting transition metal dichalcogenides provide 1D conducting channels that have been proposed to host Tomonaga-Luttinger liquids, but charge density wave physics has also been suggested to explain their behavior. Clear identification of the electronic ground state of this system has been hampered by an inability to electrostatically gate such boundaries and thereby tune their charge carrier concentration. Here we present a scanning tunneling microscopy/spectroscopy study of gate-tunable mirror twin boundaries (MTBs) in single-layer 1H-MoSe$_2$ devices. Gating here enables STM spectroscopy to be performed for different MTB electron densities, thus allowing precise characterization of electron-electron interaction effects. Visualization of MTB electronic structure under these conditions allows unambiguous identification of collective density wave excitations having two distinct velocities, in quantitative agreement with the spin-charge separation predicted by finite-length Tomonaga-Luttinger-liquid theory., Comment: 5 figures

The ab initio Bethe-Salpeter equation (BSE) approach, an established method for the study of excitons in materials, is typically solved in a limit where only static screening from electrons is captured. Here, we generalize this framework to also include dynamical screening from phonons at lowest order in the electron-phonon interaction. We apply this generalized BSE approach to a series of inorganic lead halide perovskites, CsPbX3, with X = Cl, Br, and I. We find that inclusion of screening from phonons significantly reduces the computed exciton binding energies of these systems. By deriving a simple expression for phonon screening effects, we reveal general trends for the importance of phonon screening effects in semiconductors and insulators, based on a hydrogenic exciton model. We demonstrate that the magnitude of the phonon screening correction in isotropic materials can be reliably predicted using four material specific parameters: the reduced effective mass, the static and optical dielectric constants, and the phonon frequency of the most strongly coupled LO phonon mode. This framework helps to elucidate the importance of phonon screening and its relation to excitonic properties in a broad class of semiconductors.

Layered transition metal dichalcogenides (TMDCs) host a plethora of interesting physical phenomena ranging from charge order to superconductivity. By introducing magnetic ions into 2H-NbS$_2$, the material forms a family of magnetic intercalated TMDCs T$_x$NbS$_2$ (T = 3d transition metal). Recently, Fe$_{1/3+\delta}$NbS$_2$ has been found to possess intriguing resistance switching and magnetic memory effects coupled to the N\'{e}el temperature of T$_N \sim 45$ K [1,2]. We present comprehensive single crystal neutron diffraction measurements on under-intercalated ($\delta \sim -0.01$), stoichiometric, and over-intercalated ($\delta \sim 0.01$) samples. Magnetic defects are usually considered to suppress magnetic correlations and, concomitantly, transition temperatures. Instead, we observe highly tunable magnetic long-ranged states as the Fe concentration is varied from under-intercalated to over-intercalated, that is from Fe vacancies to Fe interstitials. The under- and over- intercalated samples reveal distinct antiferromagnetic stripe and zig-zag orders, associated with wave vectors $k_1$ = (0.5, 0, 0) and $k_2$ = (0.25, 0.5, 0), respectively. The stoichiometric sample shows two successive magnetic phase transitions for these two wave vectors with an unusual rise-and-fall feature in the intensities connected to $k_1$. We ascribe this sensitive tunability to the competing next nearest neighbor exchange interactions and the oscillatory nature of the Ruderman-Kittel-Kasuya-Yosida (RKKY) mechanism. We discuss experimental observations that relate to the observed intriguing switching resistance behaviors. Our discovery of a magnetic defect tuning of the magnetic structure in bulk crystals Fe$_{1/3+\delta}$NbS$_2$ provides a possible new avenue to implement controllable antiferromagnetic spintronic devices.

The advent of long-range magnetic order in non-centrosymmetric compounds has stimulated interest in the possibility of exotic spin transport phenomena and topologically protected spin textures for applications in next-generation spintronics. This work reports a novel wurtzite-structure polar magnetic metal, identified as AA'-stacked (Fe0.5Co0.5)5-xGeTe2, which exhibits a Neel-type skyrmion lattice as well as a Rashba-Edelstein effect at room temperature. Atomic resolution imaging of the structure reveals a structural transition as a function of Co-substitution, leading to the polar phase at 50% Co. This discovery reveals an unprecedented layered polar magnetic system for investigating intriguing spin topologies and ushers in a promising new framework for spintronics.