Grain boundaries (GBs) have been studied for decades, but it remains a challenging task to describe characteristic GB properties by simple structural descriptors, especially at the local atomic level. In this paper, we use the atomic descriptor based on the smooth overlap of atomic positions (SOAP) to study the atomic energy at GBs by using machine learning and propose a route to simplify it. It is found that, compared with conventional local atomic descriptors such as the Voronoi index, excess volume, centrosymmetry, or local entropy, the SOAP vector shows excellent predictive performance for the atomic energy among the 172 Al and 388 Ni coincidence site lattice (CSL) GBs as well as general GBs in the nanocrystalline model. Additionally, we successfully used the datasets of GBs and amorphous models to predict the atomic energy of one another, which proves the similarity between the local atomic environments (LAEs) in GBs and the amorphous state. Furthermore, the distribution of local distortion factors based on the SOAP vector shows the transition in atomic pack ordering from special CSL GBs to general GBs and the amorphous structures. The simplified descriptor we propose can reduce the original SOAP vector from >1000 features to only a few yet still shows the superior predictive performance of the atomic energy at GBs in all cases than the conventional descriptors combined. It is expected that the simplification process can be adapted to study more complex GB behaviors. A simple and efficient descriptor of the LAEs should allow us to have a clearer picture of the structure-property correlation in GBs, which is essential for GB engineering.

When suppressing the itinerant antiferromagnetism in chromium by doping with the isostructural itinerant ferromagnet iron, a dome of spin-glass behavior emerges around a putative quantum critical point at an iron concentration $x\approx 0.15$. Here, we report a comprehensive investigation of polycrystalline samples of ${\mathrm{Fe}}_x{\mathrm{Cr}}_{1-x}$ in the range $0.05\le x\le 0.30$ using x-ray powder diffraction, magnetization, ac susceptibility, and neutron depolarization measurements, complemented by specific heat and electrical resistivity data for $x=0.15$. Besides antiferromagnetic $(x<0.15)$ and ferromagnetic regimes $(x\ge 0.15)$, we identify a dome of spin-glass behavior at low temperatures for $0.10\le x\le 0.25$. Neutron depolarization measurements indicate an increase of the size of ferromagnetic clusters with increasing $x$ and the Mydosh parameter $\varphi$, inferred from the ac susceptibility, implies a crossover from cluster-glass to superparamagnetic behavior. Taken together, these findings consistently identify ${\mathrm{Fe}}_x{\mathrm{Cr}}_{1-x}$ as an itinerant-electron system that permits to study the evolution of spin-glass behavior of gradually varying character in an unchanged crystalline environment.

Free-standing layers of nanoscale thickness are essential in numerous applications but challenging to fabricate for all but a small selection of materials. We report a versatile, chemical-free pathway of exfoliating centimeter-sized free-standing nanolayers from Si(100) with native oxide based on the spontaneous delamination of thin Ru and Ru-based films upon annealing at temperatures as low as 400 °C. Combining results from x-ray photoelectron spectroscopy (XPS), and transmission and scanning electron microscopy (TEM, SEM), we identify that the element Ru, a thin ${\mathrm{SiO}}_2$ layer, and the Si(100) substrate are essential ingredients for the delamination and propose a stress-based mechanism to explain the effect. The diffusion of Si into the layer upon annealing leads to the formation of a Ru-Si compound at the thin-film side of the Ru/Si(100) interface and pyramidal cavities in the Si(100) substrate. Moreover, the uptake of Si results in an increase in layer thickness and the buildup of in-plane compressive stress, which is reduced by local buckling and finally by the separation of the full layer from the substrate at the ${\mathrm{SiO}}_2$-Si(100) interface. The use of a thin Ru-buffer layer allows us to apply this delamination process to produce free-standing nanolayers of Mo and HfMoNbTiZr in this simple, chemical-free, and vacuum-compatible manner. These results indicate the potential of the reported effect for the fabrication of free-standing layers using a wide range of compositions, deposition techniques, and growth conditions below the onset temperature of delamination.

During the growth of ultrathin Bi films, Bi(110) islands with a black phosphorus (BP)-like structure nucleate initially. These Bi(110) islands reorganize to Bi(111) islands with a rhombohedral structure at a certain critical thickness ${\theta }_c$. This transition has been theoretically explained by the balance between the surface and bulk energies of the Bi islands with the two structures. However, we found that ${\theta }_c$ decreases with increasing growth rate on both Si(111)$\sqrt{3}\times \sqrt{3}$-B and $7\times 7$ substrates according to the results of scanning tunneling microscopy observations. Monte Carlo simulations revealed that the edges of the Bi(110) islands become rough at higher growth rates. These rough edges effectively capture migrating atoms injected at the gaps and tops of the preexisting Bi(110) islands, thereby suppressing further Bi nucleation on the Bi(110) islands and promoting the lateral expansion of the islands while maintaining the original height. However, the strain cannot be relaxed effectively by edges in the laterally extended Bi(110) islands. Thus ${\theta }_c$ is considered to decrease in growth at larger rates.

A novel computational strategy is presented to calculate from first principles the coefficient of thermal expansion and the elastic constants of a material over meaningful intervals of temperature and pressure. This strategy combines a novel implementation of the quasiharmonic approximation to calculate the isothermal-isochoric linear and nonlinear elastic constants of a material, with elementary equations of nonlinear continuum mechanics. Our implementation of the quasiharmonic approximation relies on finite deformations, the use of nonprimitive supercells to describe a material, a recently proposed technique to calculate generalized mode Grüneisen parameters, and the numerical differentiation of the stress tensor to calculate both second- and third-order elastic constants. The combination of this method with nonlinear continuum mechanics is shown to yield accurate predictions of lattice parameters and linear elastic constants of a material over finite intervals of temperature and pressure, at the cost of calculating isothermal second- and third-order elastic constants for a single reference state. Here, the validity and limits of our novel methods are assessed by carrying out calculations of MgO based on classical interatomic potentials. To demonstrate potential, our methods are then used in conjunction with a density functional theory approach to calculate thermal expansion and elastic properties of silicon, lithium hydrate, and graphite.

Rare-earth doped GaN is of interest for optoelectronics and spintronics and potentially for quantum applications. A fundamental understanding of the interaction between RE dopants and the semiconductor host is key to realizing the material's full potential. This paper reports an investigation of lanthanide ($Ln$) defects in GaN using hybrid density-functional defect calculations. We find that all the $Ln$ dopants incorporated at the Ga lattice site, $L{n}_{\mathrm{Ga}}$ ($Ln$ = La–Lu), are stable as trivalent ions, but Eu and Yb can also be stabilized as divalent and Ce, Pr, and Tb as tetravalent. The location of $Ln$-related defect levels and the $Ln$ $4f$ states in the energy spectrum of the host material is determined from first principles. We elucidate the interplay between defect formation and electronic structure, including the $Ln$–N interaction, and the effect of doping on the local lattice environment. Optical properties are investigated by considering possible defect-to-band and band-to-defect transitions involving $L{n}_{\mathrm{Ga}}$ defects with in-gap energy levels, including broad charge-transfer transitions. These defects can also act as carrier traps and mediate energy transfer from the host into the $4f$-electron core of the $Ln$ ion which leads to sharp intra-$f$ luminescence.

Grain boundaries determine physical properties of bulk materials including ductility, diffusivity, and electrical conductivity. However, the role of grain boundaries in nanostructures and nanoparticles is much less understood, despite the wide application of nanoparticles in nanophotonics, nanoelectronics, and heterogeneous catalysis. Here, we investigate the role of high-angle grain boundaries in the oxidation of Cu nanoparticles, using a combination of in situ single particle plasmonic nanoimaging and $postmortem$ transmission electron microscopy image analysis, together with ab initio and classical electromagnetic calculations. We find an initial growth of a 5-nm-thick ${\mathrm{Cu}}_2\mathrm{O}$ shell on all nanoparticles, irrespective of different grain morphologies. This insensitivity of the ${\mathrm{Cu}}_2\mathrm{O}$ shell on the grain morphology is rationalized by extraction of Cu atoms from the metal lattice being the rate limiting step, as proposed by density functional theory calculations. Furthermore, we find that the change in optical scattering intensity measured from the individual particles can be deconvoluted into one contribution from the oxide layer growth and one contribution that is directly proportional to the grain boundary density. The latter contribution signals accumulation of Cu vacancies at the grain boundaries, which, as corroborated by calculations of the optical scattering, leads to increased absorption losses and thus a decrease of the scattering, thereby manifesting the role of grain boundaries as vacancy sinks and nuclei for Kirkendall void formation at a later stage of the oxidation process.

Traditionally, materials discovery has been guided by basic physical rules, and such rules embody the basic understanding of the physical characteristics of interest of the material. However, the discovery of physical rules remains a challenging task due to the inherent difficulty in recognizing patterns in the high-dimensional and highly nonuniform distributed materials space. The standard data analytics approach using machine learning (ML) may fall short in producing meaningful results due to fundamental differences between the underlying assumptions and goals of ML vs materials discovery. ML is mainly focused on estimating complex black-box predictive models (that are nonlinear and multivariate), whereas in materials discovery, the goal is to come up with interpretable data-driven physical rules. Here, we attempt to tackle this problem by proposing a robust data analytics framework that allows us to derive basic physical rules from data. We introduce the concept of global and local modeling, utilizing both supervised and unsupervised learning, for highly nonuniformly distributed materials data. To enhance the model interpretation, we also introduce a model-independent interpretation technique to assist human experts in extracting useful physical rules. The proposed framework for extracting data-derived physical rules at the global and local level is illustrated using two case studies: (1) classification of van der Waals (vdW) and non-vdW (nvdW) materials and (2) classification of wide bandgap and non-wide bandgap vdW materials.

Establishing the structure-property relationship for grain boundaries (GBs) is critical for developing next-generation functional materials but has been severely hampered due to its extremely large configurational space. Atomistic simulations with low computational cost and high predictive power are strongly desirable, but the conventional simulations using empirical interatomic potentials and density functional theory suffer from the lack of predictive power and high computational cost, respectively. A machine learning interatomic potential (MLIP) recently emerged but often requires extensive size of the training dataset, making it a less feasible approach. Here, we demonstrate that an MLIP trained with a rationally designed small training dataset can predict thermal transport across GBs in graphene with ab initio accuracy at an affordable computational cost. We employed a rational approach based on the structural unit model to find a small set of GBs that can represent the entire configurational space and thus can serve as a cost-effective training dataset for the MLIP. Only 5 GBs were found to be enough to represent the entire configurational space of graphene GBs. Using the atomistic Green's function approach and the MLIP, we revealed that the structure-thermal resistance relation in graphene does not follow the common understanding that large dislocation density causes larger thermal resistance. In fact, thermal resistance is nearly independent of dislocation density at room temperature and is higher when the dislocation density is small at sub-room temperature. We explain this intriguing behavior with the buckling near a GB causing a strong scattering of flexural phonon modes. In this paper, we show that a machine learning technique combined with conventional wisdom (e.g., structural unit model) can extend the recent success of ab initio thermal transport simulation, which has been mostly limited to single crystals, to complex yet practically important polycrystals with GBs.

La-doped intermetallic single crystals of ${{\mathrm{Ce}}_1}_{-x}{\mathrm{La}}_x{\mathrm{In}}_3$ were synthesized via an In self-flux method throughout the entire range $\left(x=0–1\right)$. The prototypical heavy-fermion compound ${\mathrm{CeIn}}_3$ shows an antiferromagnetic phase transition at 10.1 K and becomes superconducting near a critical pressure where $T_N$ is completely suppressed. As the La concentration increases, Ce moments are diluted, and the lattice constant increases linearly, satisfying Vegard's law. The electrical resistivity of the high-quality single crystals of ${{\mathrm{Ce}}_1}_{-x}{\mathrm{La}}_x{\mathrm{In}}_3$ shows a gradual suppression of $T_N$ to 0 K at approximately $x_c=0.65$. The sign of the slope of the low-temperature resistivity vs temperature changes from positive to negative in the vicinity of the critical concentration $x_c$, indicating a change in the Kondo ground states from the Kondo lattice to the Kondo impurity state. In the Kondo lattice state $\left(x<x_c\right)$, the coherence temperature $(=50\mathrm{K})$ assigned as the peak in the resistivity is almost independent of the La concentration. In the Kondo impurity state $\left(x>x_c\right)$, on the other hand, a kinklike feature in the resistivity appears at $\sim 50\mathrm{K}$ and persists up to $x=0.97$, indicating a change of the Kondo scattering owing to the crystalline electric field effects. These results suggest that the critical concentration is closely connected to the emergence of the Kondo coherence state.

Continuous strain glass transition (STGT) in shape memory alloys (SMAs) has attracted much attention and shows potential applications in biomedical, robotics, and micro-electromechanical systems due to its quasilinear superelasticity (SE). However, the reported strain glass system in NiTi alloys through doping antisite point defects can only produce local $R$-phase martensitic domains and show small recoverable strain ($\sim 1\%$), which limits its wide applications. Here, we propose a method to design B19′ strain glass with large recoverable strain in NiTi binary alloys by introducing interstitial atoms and vacancies through low-energy irradiation by integrating molecular dynamics and phase field modeling. The interstitial atoms play the most important role to transform the normal martensitic transformation (MT) to STGT. A complete phase diagram is established to describe the relationship between MT/STGT and irradiation energy. The system after large irradiation energy $\left(\sim 5.3\times {10}^{12}\mathrm{keV}/\mathrm{c}{\mathrm{m}}^2\right)$ has shown obvious frequency dependence of storage modulus, continuous volume fraction change, and B19′ martensitic nanodomains, which confirm the existence of B19′ STGT. This B19′ strain glass has shown large recoverable strain $(\sim 5.8\%)$ over a wide temperature range (from 100 to 300 K), which can be attributed to the continuous nucleation and growth of martensitic nanodomains in this temperature range. Our calculations theoretically proposed a method to design strain glass systems with giant quasilinear SE by interstitial defects and may stimulate the application of SMAs.

Colloidal gels respond as soft solids at rest, whereas they flow as liquids under external shear. Starting from a fluidized state under an applied shear rate ${\dot{\gamma }}_p$, abrupt flow cessation triggers a liquid-to-solid transition during which the stress relaxes towards a so-called residual stress ${\sigma }_{\mathrm{res}}$ that tallies a macroscopic signature of previous shear history. Here, we report on the liquid-to-solid transition in gels of boehmite, an aluminum oxide, that shows a remarkable nonmonotonic stress relaxation towards a residual stress ${\sigma }_{\mathrm{res}}\left({\dot{\gamma }}_p\right)$ characterized by a dual behavior relative to a critical value ${\dot{\gamma }}_c$ of the shear rate ${\dot{\gamma }}_p$. Following shear at ${\dot{\gamma }}_p>{\dot{\gamma }}_c$, the gel obtained upon flow cessation is insensitive to shear history, and the residual stress is negligible. However, for ${\dot{\gamma }}_p<{\dot{\gamma }}_c$, the gel encodes some memory of the shear history, and ${\sigma }_{\mathrm{res}}$ increases for decreasing shear rate, directly contributing to reinforcing the gel viscoelastic properties. Moreover, we show that both ${\sigma }_{\mathrm{res}}$ and the gel viscoelastic properties increase logarithmically with the strain accumulated during the shear period preceding flow cessation. Such a shear-induced “overaging” phenomenon bears great potential for tuning the rheological properties of colloidal gels.

Lead halide perovskites possess high photoluminescence (PL) efficiency and strong electron-phonon interactions, and therefore optical cooling using up-conversion PL has been expected. We investigate anti-Stokes PL from green-luminescent ${\mathrm{Cs}}_4{\mathrm{PbBr}}_6$, whose origin is attributable to ${\mathrm{CsPbBr}}_3$ nanostructures embedded in a ${\mathrm{Cs}}_4{\mathrm{PbBr}}_6$ crystal. Because of the high transparency, low refractive index, and high stability of ${\mathrm{Cs}}_4{\mathrm{PbBr}}_6$, the green PL displays high external quantum efficiency without photodegradation. Time-resolved PL spectroscopy reveals the excitonic behaviors in the recombination process. The shape of the PL spectrum is almost independent of excitation photon energy, which means that the spectral width is determined by homogeneous broadening. We demonstrate that the phonon-assisted process dominates the Urbach tail of optical absorption and anti-Stokes PL at room temperature. Anti-Stokes PL is observed down to 70 K. We determine the temperature dependence of the Urbach energy and estimate the strength of the electron-phonon coupling. Our spectroscopic data show that ${\mathrm{CsPbBr}}_3$ nanostructures have potentially useful features for optical cooling.

Single crystals of ${\mathrm{Ce}}_{3+x}{\mathrm{Ru}}_4{\mathrm{Sn}}_{13-x}$ $(0.05\le x\le 0.34)$, which adopt the cubic structure ($Pm\overline{3}n$, No. 223), have been grown with Sn flux. Thermodynamic and transport property measurements from single-crystal samples do not show any sign of magnetic ordering down to 1.8 K and indicate coexistence of the Kondo effect and crystalline electric field effect. The local minimum in the electrical resistivity and highly enhanced specific heat values at low temperatures characterize this family as a heavy fermion Kondo lattice system. A broad peak is observed at $\sim$3.5 K for $x=0.05$ in the specific heat and magnetic susceptibility, suggesting a significant Kondo contribution, and the peak disappears as $x$ increases. The evolution of physical properties of ${\mathrm{Ce}}_{3+x}{\mathrm{Ru}}_4{\mathrm{Sn}}_{13-x}$ compounds can be attributed to the nature of the individual Ce ions that occupy two inequivalent $2a$ and $6d$ crystallographic sites.

We report the synthesis of powder and single-crystal samples of cerium pyrohafnate and their characterization using neutron diffraction, thermogravimetry and x-ray absorption spectroscopy. We evaluate the amount of nonmagnetic ${\mathrm{Ce}}^{4+}$ defects and use this result to interpret the spectrum of crystal-electric field transitions observed using inelastic neutron scattering. The analysis of these single-ion transitions indicates the dipole-octupole nature of the ground-state doublet and a significant degree of spin-lattice coupling. The single-ion properties calculated from the crystal-electric field parameters obtained spectroscopically are in good agreement with bulk magnetic susceptibility data down to about 1 K. Below this temperature, the behavior of the magnetic susceptibility indicates a correlated regime without showing any sign of magnetic long-range order or freezing down to 0.08 K. We conclude that ${\mathrm{Ce}}_2{\mathrm{Hf}}_2{\mathrm{O}}_7$ is another candidate to investigate exotic correlated states of quantum matter, such as the octupolar quantum spin ice recently argued to exist in the isostructural compounds ${\mathrm{Ce}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$ and ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$.

Direct and inverse spin Hall effects lie at the heart of novel applications that utilize spins of electrons as information carriers, allowing the generation of spin currents and detecting them via the electric voltage. In the standard arrangement, an applied electric field induces transverse spin current with perpendicular spin polarization. Although conventional spin Hall effects are commonly used in spin-orbit torques or spin Hall magnetoresistance experiments, the possibilities to configure electronic devices according to specific needs are quite limited. Here, we investigate unconventional spin Hall effects that have the same origin as conventional ones, but manifest only in low-symmetry crystals where spin polarization, spin current, and charge current are not enforced to be orthogonal. Based on the symmetry analysis for all 230 space groups, we have identified crystal structures that could exhibit unusual configurations of charge-to-spin conversion. The most relevant geometries have been explored in more detail; in particular, we have analyzed the collinear components yielding transverse charge and spin current with spin polarization parallel to one of them, as well as the longitudinal ones, where charge and spin currents are parallel. In addition, we have demonstrated that an unconventional spin Hall effect can be induced by controllable breaking of the crystal symmetries by an external electric field, which opens a perspective for the external tuning of spin injection and detection by electric fields. The results have been confirmed by density functional theory calculations performed for various materials relevant for spintronics. We are convinced that our findings will stimulate further computational and experimental studies of unconventional spin Hall effects.

Perpendicular magnetization is essential for high-density memory application using magnetic materials. High-spin polarization of conduction electrons is also required for realizing large electric signals from spin-dependent transport phenomena. The Heusler alloy is a well-known material class showing the half-metallic electronic structure. However, its cubic lattice nature favors in-plane magnetization and thus minimizes the perpendicular magnetic anisotropy (PMA), in general. This study focuses on an inverse-type Heusler alloy, ${\mathrm{Mn}}_{2-\delta }{\mathrm{CoGa}}_{1+\delta }$ (MCG), with a small off-stoichiometry ($\delta$), which is expected to be a half-metallic material. We observed a relatively large uniaxial magnetocrystalline anisotropy constant ($K_u$) of the order of ${10}^5$ J/${\mathrm{m}}^3$ at room temperature in MCG films with a small tetragonal distortion of a few percent. A positive correlation was confirmed between the $c/a$ ratio of lattice constants and $K_u$. Imaging of magnetic domains using Kerr microscopy clearly demonstrated a change in the domain patterns along with $K_u$. X-ray magnetic circular dichroism (XMCD) was employed using a synchrotron radiation soft x-ray beam to get insight into the origin of PMA. Negligible angular variation of orbital magnetic moment ($\mathrm{\Delta }{m}_{\mathrm{orb}}$) evaluated using the XMCD spectra suggested a minor role of the so-called Bruno's term to $K_u$. Our first-principles calculation reasonably explained the small $\mathrm{\Delta }{m}_{\mathrm{orb}}$ and the positive correlation between the $c/a$ ratio and $K_u$. The origin of the magnetocrystalline anisotropy was discussed based on the second-order perturbation theory in terms of the spin-orbit coupling, claiming that the mixing of the occupied $\uparrow$- and the unoccupied $\downarrow$-spin states is responsible for the PMA of the MCG films.

We perform first-principles density-functional theory calculations to determine the equilibrium defect structures, formation energies, charge transition levels, and electronic structures of Sn and S vacancies in monolayer SnS. Both Sn and S vacancies exhibit multiple charge transition levels and in-gap defect states, indicating that they may be stable in different charge states depending on the Fermi level in the system. Depending on the charge state of the vacancy, the easily distorted SnS lattice undergoes different relaxations, and in some cases, symmetry-breaking reconstructions, creating defect states within the gap that electrons can occupy at a lower energetic cost. Due to significant atomic relaxations between the equilibrium defect structures in different charge states, optical charge transitions involving both types of vacancies exhibit significant Stokes shifts of over 1 eV, which may provide opportunities for increased efficiency in light emission diode, solar cell, and solar concentrator applications.

Interfacial oxygen exchange at oxide interfaces bears huge potential in stabilizing metastable or novel phases of functional oxides down to the monolayer limit. By taking advantage of active oxygen supply of the substrate material, waiving any external oxygen dosage, high-quality, crystalline ultrathin films of the Heisenberg ferromagnet europium monoxide (EuO) were stabilized on YSZ (001). This so-called redox-assisted growth mode (or, vice versa, the extreme case of a distillation growth) was monitored end to end by in situ x-ray photoelectron emission spectroscopy and electron diffraction techniques. The evolution of Eu $3d$ core levels allows us to disentangle the processes of interfacial oxygen diffusion and vacancy formation in stabilizing the very first monolayers of EuO on YSZ (001). An expedient background correction analysis is presented, which allows us to quantify the critical ${\mathrm{Eu}}^{3+}/{\mathrm{Eu}}^{2+}$ ratio in the ultrathin film regime. We concluded on the key mechanisms of redox-assisted EuO/YSZ (001) thin film synthesis, which merge in a universal three-process growth model that may serve as guideline for redox-assisted synthesis of metastable low-dimensional oxides.