The heterointerface between topological insulators (TIs) and magnetic materials provides a crucial platform for investigating exotic electronic and magnetic phases, with implications for both fundamental studies and potential applications. A key challenge is determining the spatial extent of the magnetic perturbation across the interface. In this study we grew $\mathrm{B}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_3$ films with mixed thicknesses of five and six quintuple layers (QLs) on a thick ferromagnetic $\mathrm{C}{\mathrm{r}}_2\mathrm{T}{\mathrm{e}}_3$ film. Chemical analysis indicates gradual Cr diffusion across the interface into $\mathrm{B}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_3$, reaching up to the fourth QL, while the fifth and sixth QLs remain free of Cr. Despite the absence of direct Cr incorporation, quasiparticle interference imaging using spectroscopic scanning tunneling microscopy reveals strong backscattering on the fifth QL surface. This suggests an intrinsic magnetic proximity effect, which breaks time-reversal symmetry without magnetic doping, extending into the fifth QL. Although variations may exist across different systems, the large magnetic perturbation length scale observed here is a valuable guiding principle for engineering exotic electronic and magnetic states at heterointerfaces between TIs and magnetic materials.

A systematic study of atomic dynamics and thermal properties of the family of layered chalcogenide compounds $M\mathrm{Cr}{X}_2$ $(M=\mathrm{Ag},\mathrm{Cu};X=\mathrm{S},\mathrm{Se})$ was performed, including neutron and x-ray scattering, thermal characterization, and first-principles simulations. In all compounds, we observe a breakdown of specific phonon modes across the superionic phase transition, for phonons whose eigenvectors exhibit large contributions of mobile ions. In particular, the nondispersive portions of transverse acoustic (TA) branches at short-wavelengths and the low-energy optical phonons with large contributions from ${\mathrm{Ag}}^{+}$ or ${\mathrm{Cu}}^{+}$ become severely damped in the superionic phase. However, well-defined quasiparticles persist in the superionic state for long-wavelength TA phonons. In the case of ${\mathrm{AgCrS}}_2$, the coupling of lattice dynamics with its antiferromagnetic transition was also investigated. The magnetic ordering couples with the monoclinic–rhombohedral structural transition, and the ${\mathrm{Cr}}^{3+}$ spin arrangement strongly affects the phonon dispersions. We qualitatively reproduce the magnetic and nuclear components of the INS measurement for antiferromagnetic ${\mathrm{AgCrS}}_2$ by combining models of spin-waves and spin-polarized first-principles phonon simulations. Quasielastic magnetic fluctuations persist in the paramagnetic phase up to high temperature, but are clearly distinguished from the nuclear component through their momentum dependence. Finally, we report measurements of the thermal properties of the selenide compounds and find good agreement with our DFT simulations.

We investigate and compare the electronic structure of ${\mathrm{OsO}}_2$ with the extensively studied ${\mathrm{RuO}}_2$. Calculations show that ${\mathrm{OsO}}_2$ exhibits antiferromagnetism and spin splitting driven by crystal symmetry, a characteristic of altermagnetism and similar to ${\mathrm{RuO}}_2$. Examination of the Fermi surface, with and without spin-orbit coupling, reveals that ${\mathrm{OsO}}_2$ has lower Fermi group velocities compared to ${\mathrm{RuO}}_2$, suggesting limited charge carrier mobility in ${\mathrm{OsO}}_2$. While this characteristic may constrain its performance in high-speed electronic transport applications, it may also enhance stability for spin-based information storage in spintronics. Additionally, comparison of the vibrational properties of these rutile oxide systems demonstrates dynamical stability, typical mass dependent behaviors, and favorable agreement with measured Raman data. The calculated phonon density of states for ${\mathrm{RuO}}_2$ also agrees with our neutron scattering data. These observations substantiate the implications of the electronic and vibrational behaviors in ${\mathrm{OsO}}_2$ and ${\mathrm{RuO}}_2$, encouraging further investigation of their potential for emerging technological applications.

An intrinsic feature of disordered and out-of-equilibrium materials, such as glasses, is the dependence of their properties on their history. An important example is rheological memory, in which disordered solids obtain properties based on their deformation history. Here, we employ x-ray photon correlation spectroscopy with in situ rheometry to characterize memory formation in a nanocolloidal soft glass due to cyclic shear. During a cycle, particles undergo irreversible displacements composed of a combination of shear-induced diffusion and heterogeneous, residual strain fields. At lower shear amplitudes, the displacements resemble a random walk in which the directions in each cycle are independent of those in preceding cycles, while at high amplitude, the irreversible displacements in consecutive cycles become correlated. The magnitudes of the displacements decrease with each cycle before reaching a steady state where the microstructure has been trained to achieve enhanced reversibility even at shear amplitudes well above yielding and despite the presence of thermal fluctuations. At amplitudes below and near yielding, these decreases are monotonic, while well above yielding, they are nonmonotonic, suggesting evidence of shear banding. Accompanying this microstructural training are corresponding decreases in the dissipation during each cycle and the magnitude of the residual stress toward steady-state values. Memory of the training is revealed by measurements in which the amplitude of the shear is changed after steady state is reached. The magnitude of the particle displacements, as well as the dissipation and the change in residual stress, vary nonmonotonically with the new shear amplitude, having minima near the training amplitude, thereby revealing correlated microscopic and macroscopic signatures of memory.

Resolving the local structure motifs that characterize phase evolution as a function of composition is a key challenge in structure characterization of complex materials. In this study, we combine first-principles simulations and x-ray absorption near-edge structures (XANES) analysis to gain insights into the structure evolution revealed by measurements across a combinatorial zinc titanate thin film, which was grown with smoothly varying composition over a wide range of the Ti:Zn ratio. Specifically, we propose a cluster blind-signal-separation (cBSS) method for XANES spectral analysis based on a library of the structures and spectra of representative local motifs. In addition to motifs from zinc titanate crystals, two types of Ti-defect models constructed in this study are key to the understanding of the structure characteristics in the Zn-rich region. The cBSS method makes use of both spectral clustering of the simulated site-XANES spectra library and the BSS procedure to construct high-fidelity spectral basis functions from an experimental spectral sequence. The method provides a rigorous measure of the spectral sensitivity and basis completeness. The results of the XANES analysis are corroborated with other experimental modalities, including x-ray diffraction and spectroscopic ellipsometry, to validate the cBSS method. The calculated motif weights resulting from fitting the XANES spectra with the cBSS basis probe the atomic structure characteristics of both crystalline and amorphous phases as a function of the Ti/Zn composition. The insights of the local structure motif evolution are pivotal to the understanding of the nonmonotonic trend in the optical gap, which may lead to potential applications through tuning the optical properties of zinc titanate. The workflow of the XANES spectral analysis developed in this work can be generalized to construct the structure-property relationship in a broad material space.

The physical properties of single-crystalline ${\mathrm{Eu}}_2{\mathrm{CuZn}}_2{\mathrm{P}}_3$ were inspected via thermodynamic, transport, and neutron diffraction measurements. ${\mathrm{Eu}}_2{\mathrm{CuZn}}_2{\mathrm{P}}_3$ is composed of EuCuP and ${\mathrm{EuZn}}_2{\mathrm{P}}_2$ motifs stacked in a one-to-one ratio. The magnetic response of ${\mathrm{Eu}}_2{\mathrm{CuZn}}_2{\mathrm{P}}_3$ is similar to that of ${\mathrm{EuZn}}_2{\mathrm{P}}_2$ in its A-type antiferromagnetic (semiconducting) state. A Néel temperature of $T_N=40.3\mathrm{K}$ is obtained from the specific heat capacity. Single-crystal neutron diffraction reveals a (001) magnetic propagation vector, with primarily in-plane moments coupled along [001] in an up-up-down-down pattern. This spin structure retains the ferromagnetic EuCuP motifs and antiferromagnetic coupling across the ${\mathrm{EuZn}}_2{\mathrm{P}}_2$ motifs. The electrical resistivity is characterized by metallic behavior above 100 K, an increase in $\rho$ upon cooling below $\approx 75\mathrm{K}$, and a large negative magnetoresistance below $T_{\mathrm{N}}$. First principles calculations evidence a narrow band gap for antiferromagnetic ordering and semimetallic behavior for the ferromagnetic state. This is consistent with the observed effect of magnetic field on the electrical resistivity. Hall effect measurements reveal a field-induced, negative anomalous Hall effect that increases on cooling down to 2 K. Also, an unconventional contribution to the Hall effect dominates the low-field Hall signal, particularly near $T_{\mathrm{N}}$, and is similar in appearance to a topological Hall effect. However, further work is necessary to understand if any of the transport properties have topological origins or if magnetism-induced modifications to the Fermi surface induce these unusual Hall effect signals in this and related materials.

Inversion symmetry-breaking-driven charge generation in ferroelectrics upon visible light absorption has become a focal point for light-harvesting applications. Although several light-induced phenomena have been proposed to explain photovoltaic effects in many ferroelectric thin-film systems, photovoltaic mechanisms in ${\mathrm{Bi}}_2{\mathrm{FeCrO}}_6$ (BFCO) films remain elusive. Here, by combining advanced scanning probe techniques capable of locally assessing light-induced charge generation with macroscopic photovoltaic and spectroscopic experiments, we reveal that the photovoltaic effect in this system is strongly influenced by abrupt discontinuities in electronic band structure at the BFCO/substrate interface. In particular, BFCO/Nb-doped ${\mathrm{SrTiO}}_3$ is found to exhibit an interfacial built-in electric field that promotes a dominant p-n junction-like photovoltaic effect, whereas $\mathrm{BFCO}/{\mathrm{La}}_{2/3}{\mathrm{Sr}}_{1/3}{\mathrm{MnO}}_3$ shows no interfacial built-in field, demonstrating instead a bulk photovoltaic effect. These findings suggest that an interfacial electric field can significantly reduce bulk photovoltaic effects. In addition, strong sensitivity to ferroelectric polarization direction is observed, offering a promising approach to controlling photoelectric responses. This study provides clearer insights into the photovoltaic properties of BFCO thin films, suggesting potential applications not only in solar energy harvesting but also in switch-type optoelectronic devices.

Topology and superconductivity, two distinct phenomena, offer unique insight into quantum properties and their applications in quantum technologies, spintronics, and sustainable energy technologies. Tin (Sn) plays a pivotal role here as an element because of its two structural phases, α-Sn exhibiting topological characteristics and β-Sn showing superconductivity. Here, we demonstrate precise control of these phases in Sn thin films using molecular beam epitaxy with systematically varied lattice parameters of the buffer layer. The Sn films exhibit either β-Sn or α-Sn phases as the buffer layer's lattice constant varies from $6.10\AA$ to $6.48\AA$, spanning the range from GaSb (like InAs) to InSb. The crystal structures of α- and β-Sn films are characterized by x-ray diffraction and confirmed by Raman spectroscopy and scanning transmission electron microscopy. Atomic force microscopy validates the smooth, continuous surface morphology. Electrical transport measurements further verify the phases: resistance drop near 3.7 K for β-Sn superconductivity and Shubnikov-de Haas oscillations for α-Sn topological characteristics. Density functional theory shows that α-Sn is stable under tensile strain and β-Sn under compressive strain, aligning well with experimental findings. Hence, this study introduces a platform controlling Sn phases through lattice engineering, enabling innovative applications in quantum technologies and beyond.

Aluminum oxide (alumina, ${\mathrm{Al}}_2{\mathrm{O}}_3$) exists in various structures and has broad industrial applications. While the crystal structure of $\alpha \text{−}{\mathrm{Al}}_2{\mathrm{O}}_3$ is well-established, those of transitional aluminas remain highly debated. In this study, we propose a universal machine learning interatomic potential (MLIP) for aluminas, trained using the neuroevolution potential (NEP) approach. The dataset is constructed through iterative training and farthest point sampling, ensuring the generation of the most representative configurations for an exhaustive sampling of the potential energy surface. The accuracy and generality of the potential are validated through simulations under a wide range of conditions, including high temperatures and pressures. A phase diagram is presented that includes both transitional aluminas and $\alpha \text{−}{\mathrm{Al}}_2{\mathrm{O}}_3$ based on the NEP. We also successfully extrapolate the phase diagram of aluminas under extreme conditions ([0, 4000] K and [0, 200] GPa ranges of temperature and pressure, respectively), while maintaining high accuracy in describing their properties under more moderate conditions. Furthermore, combined with our developed structure search workflow, the NEP provides an evaluation of existing $\gamma \text{−}{\mathrm{Al}}_2{\mathrm{O}}_3$ structure models. The NEP developed in this work enables highly accurate dynamic simulations of various aluminas on larger scales and longer timescales, while also offering new insights into the study of transitional aluminas structures.

With advanced synthetic techniques, a wide variety of well-defined graphene nanoribbons (GNRs) can be produced with atomic precision. Hence, finding the relation between their structures and properties becomes important for the rational design of GNRs. In this work, we explore the complete chemical space of gulf-edged zigzag graphene nanoribbons (ZGNR-Gs), a subclass of zigzag GNRs in which the zigzag edges miss carbon atoms in a regular sequence. We demonstrate that the electronic properties of ZGNR-Gs depend on four structural parameters: ribbon width, gulf edge size, unit length, and gulf offset. Using tight-binding calculations and the Hubbard model, we find that all ZGNR-Gs are semiconductors with varying band gaps; there are no metals in this class of materials. Notably, when spin polarization is considered, most ZGNR-Gs exhibit antiferromagnetic behavior, with the spin moments and spin-induced band gap opening being stabilized by longer zigzag segments at the edges. Furthermore, we provide simple empirical rules that describe the ${\mathbb{Z}}_2$ topological invariant based on the aforementioned structural parameters. By analyzing the full chemical space of ZGNR-Gs, we offer insights into the design of GNRs with desired electronic, magnetic, and topological properties for nanoelectronic applications.

The electronic density of states (DOS) provides information regarding the distribution of electronic energy levels in a material, and can be used to approximate its optical and electronic properties and therefore guide computational materials design. Given its usefulness and relative simplicity, it has been one of the first electronic properties used as a target for machine-learning approaches going beyond interatomic potentials. A subtle but important point, well appreciated in the condensed matter community but usually overlooked in the construction of data-driven models, is that for bulk configurations the absolute energy reference of single-particle energy levels is ill-defined. Only energy differences matter, and quantities derived from the DOS are typically independent of the absolute alignment. We introduce an adaptive scheme that optimizes the energy reference of each structure as part of the training process and show that it consistently improves the quality of machine-learning models compared to traditional choices of energy reference for different classes of materials and different model architectures. On a practical level, we trace the improved performance to the ability of this self-aligning scheme to match the most prominent features in the DOS. More broadly, we believe that this paper highlights the importance of incorporating insights on the nature of the physical target into the definition of the architecture and of the appropriate figures of merit for machine-learning models, translating into better transferability and overall performance.

We explore the optical dipole orientation of single photon emitters in monolayer $\mathrm{Mo}{\mathrm{S}}_2$ as produced by a focused helium ion beam. The single photon emitters can be understood as single-sulfur vacancies. The corresponding far-field luminescence spectra reveal several photoluminescence lines below the dominating luminescence of the exciton in $\mathrm{Mo}{\mathrm{S}}_2$. These sub-bandgap emission lines were predicted by ab initio theory, but they have never been resolved in luminescence experiments because of their small amplitude. We reveal the lines by their dependence as a function of the photon energy and momentum as measured in the back focal plane of the optical circuitry. The agreement between theory and experiment suggests that the defect states interact strongly within the Brillouin zone.

Antiferromagnets with exotic spin textures promise low-power spintronic devices with extremely high operating frequencies and resistance to external perturbations. In particular, the combination of highly tunable correlated electron physics, as in complex oxides, with metallicity and antiferromagnetism is desirable but exceedingly rare. ${\mathrm{LaNiO}}_3$, the lone example of a perovskite nickelate which is metallic across all temperatures, has long been a promising candidate, but the antiferromagnetic metallic state has remained elusive. We demonstrate the emergence of this state in ultrathin films of (111)-oriented ${\mathrm{LaNiO}}_3$ using a combination of polarized neutron reflectometry, low-energy muon spectroscopy and anomalous Hall effect measurements, and density functional theory calculations with a Hubbard U term. Further, we find a highly strained symmetry-breaking interfacial region which may support canting of the AFM moments leading to a vanishingly small net magnetization at the film-substrate interface, providing a convenient route toward control of the Néel order. Evidence of antiferromagnetic metallic behavior in (111)LNO films highlights the role of crystal symmetry in tuning the novel quantum states in complex oxides.

The non-local spin valve (NLSV) is a useful device for studying spin transport at nanoscopic dimensions, with potential technological applications. Despite this appeal, background signals, unrelated to spin diffusion, often hinder the interpretation of spin signals in NLSVs and could compromise performance in future devices. In this paper, we comprehensively investigate these background signals in all-metallic NLSVs fabricated from a variety of ferromagnetic (FM; $\mathrm{N}{\mathrm{i}}_{80}\mathrm{F}{\mathrm{e}}_{20}$, Fe, Co) and nonmagnetic (NM; Al, Cu) metals. We demonstrate that a background signal emerges in AC measurements, with contributions from both current spreading and thermoelectric effects, with a complex dependence on both temperature and FM injector-detector separation. Despite the complexity of these dependencies, we demonstrate excellent agreement with three-dimensional finite-element modelling that accounts for current-spreading and thermoelectric effects, across a wide range of temperatures, FM separations, and FM/NM pairings. This approach additionally offers a means to estimate the Seebeck coefficients for the tested FM/NM pairings, providing further insight into the charge and heat flow in such nanoscopic spintronic devices.

Refractory high-entropy alloys show promising resistance to irradiation, yet little is known about the fundamental nature of radiation-induced defect formation. Here, we simulate threshold displacement energies in equiatomic MoNbTaVW using an accurate machine-learned interatomic potential, covering the full angular space of crystal directions. The effects of local chemical ordering are assessed by comparing results in random and short-range-ordered MoNbTaVW. The average threshold displacement energy in the random alloy is $44.3\pm 0.15\mathrm{eV}$, and slightly higher, $48.6\pm 0.15\mathrm{eV}$, in the short-range-ordered alloy. Both are significantly lower than in any of the constituent pure metals. We identify the mechanisms of defect creation and find they are mainly dependent on the masses of the recoiling and colliding elements. Low thresholds are generally found when heavy atoms (W, Ta) displace and replace the lightest atoms (V). The average threshold energies, when separated by recoiling element, are consequently ordered inversely according to their mass, opposite to the trend in the pure metals where W has by far the highest thresholds. However, the trend in the alloy is reversed when considering the cross sections for defect formation in electron irradiation, due to the mass-dependent recoil energies from the electrons.

${\mathrm{Li}}_6{\mathrm{PS}}_5\mathrm{Cl}$ is a promising candidate for the solid electrolyte in all-solid-state Li-ion batteries due to its high ionic conductivity. In applications, this material is in a polycrystalline state with grain boundaries (GBs) that can affect ionic conductivity. While atomistic modeling provides valuable information on the impact of GBs on Li diffusion, such studies face either high computational cost (when using ab initio methods) or accuracy limitations (when using classical potentials) as challenges. Here, we develop a quality-level-based active learning scheme for efficient and systematic development of ab initio–based machine-learning interatomic potentials, specifically moment tensor potentials (MTPs), for large-scale, long-time, and high-accuracy simulations of complex atomic structures and diffusion mechanisms as encountered in solid electrolytes. Based on this scheme, we obtain MTPs for ${\mathrm{Li}}_6{\mathrm{PS}}_5\mathrm{Cl}$ and investigate two tilt GBs, $\mathrm{\Sigma }3\left(1\overline{1}2\right)\left[110\right]$ and $\mathrm{\Sigma }3\left(\overline{1}11\right)\left[110\right]$, and one twist GB, $\mathrm{\Sigma }5\left(001\right)\left[001\right]$. All three GBs exhibit low formation energies of less than 20 meV$/{\AA }^2$, indicating their high stability in polycrystalline ${\mathrm{Li}}_6{\mathrm{PS}}_5\mathrm{Cl}$. Using the MTPs, diffusion coefficients of the anion-ordered and anion-disordered bulk, as well as the three GBs, are obtained from molecular dynamics simulations of atomistic models with more than $16000$ atoms for 5 ns. At 300 K, the GB diffusion coefficients fall between the ones of the anion-ordered bulk structure ($1.2\times {10}^{-9}{\mathrm{cm}}^2/\mathrm{s}$, corresponding to ionic conductivity about 0.2 mS/cm) and the anion-disordered bulk structure ($50\%$ Cl/S-anion disorder; $2.2\times {10}^{-7}{\mathrm{cm}}^2/\mathrm{s}$, about 29.8 mS/cm) of ${\mathrm{Li}}_6{\mathrm{PS}}_5\mathrm{Cl}$. Experimental data fall between the Arrhenius-extrapolated diffusion coefficients of the investigated atomic structures, supporting our quantitative in silico predictions.

A detailed understanding of the irradiation-induced damage evolution is valuable when considering materials for extreme environments, such as in fusion applications. In this work, irradiation-induced pointlike defects and their recovery kinetics in vanadium are studied with positron annihilation spectroscopy. The defects were created with 10 MeV proton irradiation at cryogenic temperatures. Several distinct recovery stages are found, at 60 K, 100 K, 150 to 250 K, and 375 to 475 K. These are interpreted as the motion of self-interstitial atoms, monovacancies, clusters of vacancies and multivacancy-hydrogen complexes. These observations allow for estimating migration barriers for the elementary defects.

The thermodynamics of point defects is crucial for determining the functional properties of various materials. Typically, defect stability is assessed using grand-canonical defect formation energy, which requires deducing the equilibrium chemical potential or Fermi level that governs atom and electron exchange with the environment. This process is complicated by the interplay of chemical potential and Fermi level and their dependence on composition and temperature. Typically, the grand-canonical formation energy is incorporated as an additional term to the bulk Gibbs energy, creating a defect-centric framework where each new defect state necessitates a distinct Gibbs energy formulation. The calculation of phase diagrams (CALPHAD) method offers a more flexible alternative by integrating defect energies into the total Gibbs energy model, allowing for easier extrapolation to more complex compositions. Additionally, CALPHAD unifies the analysis of chemically and electronically driven defects using chemical composition as the primary variable. However, the compound energy formalism (CEF) used in CALPHAD has limitations, including a lack of clear connections between defect formation energies and Gibbs energy parameters and an exponential increase in complexity with added chemical or charge variations. We present the theoretical derivation of the defect energy formalism (DEF), which we have recently proposed. DEF overcomes the limitations of CEF by establishing explicit relationships between the absolute defect energies—independent of chemical potential or Fermi level—and the Gibbs energy parameters of defective compounds. This results in a first-principles model for dilute defects, eliminating the need for model fitting to experimental or simulation data. Additionally, DEF reduces the inherent complexity of CEF by applying the superposition of absolute defect energies, making it feasible for modeling multicomponent and chemically complex compounds. This paper presents a formal, general derivation of DEF and offers guidelines for its application, promising more accurate and efficient thermodynamic modeling of defective materials.

Fluctuations of quantum spins play a crucial role in the emergence of exotic magnetic phases and excitations. The lack of the charge degree of freedom in insulating quantum magnets, however, precludes such fluctuations from mediating electronic transport. Here, we show that the quantum fluctuations of a localized frustrated magnet induce strong proximitized charge transport of the conduction electrons in a synthetic heterostructure comprising an epitaxial ${\mathrm{Bi}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ ultrathin film on a single crystal of ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$. The proximity effects are evidenced by the scaling behavior of the ${\mathrm{Bi}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ resistance in correspondence with the dynamic scaling of the dynamic spin-correlation function of ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$, which is a result of quantum fluctuations near a multiphase quantum critical point. The proximitized transport in ${\mathrm{Bi}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ can be effectively tuned by a magnetic field through suppressing the quantum spin fluctuations (QSFs) as well as inducing transitions via magnetic anisotropy in ${\mathrm{Yb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$. In this paper, we establish a pathway for harnessing QSFs in magnetic insulators with electric transport, offering exciting prospects for potential applications in the realm of quantum spintronics.

Elastomeric materials display a complicated set of stretchability and fracture properties that strongly depend on the flaw size, which has long been of interest to engineers and material scientists. Here, we combine experiments and numerical simulations for a comprehensive understanding of the nonlocal, size-dependent features of fracture in elastomers. We quantitatively describe the size-dependent fracture behavior using a nonlocal continuum model. The key ingredient of the nonlocal model is the use of an intrinsic length scale associated with a finite fracture process zone, which is inferred from experiments. Of particular importance, our experimental and theoretical approach passes the critical set of capturing the key aspects of the size-dependent fracture in elastomers. Applications to a wide range of synthetic elastomers that exhibit moderate ($\sim 100\%$) to extreme stretchability ($\sim 1000\%$) are presented, which is also used to demonstrate the applicability of our approach in elastomeric specimens with complex geometries.