We present a deep-learning approach for modeling the atomic structure of amorphous silicon ($a$-Si). While accurate models of disordered systems require an ab initio description of the energy landscape which severely limits the attainable system size, large-scale models rely on empirical potentials, at the price of reduced reliability and a computational load that is still restricting for many purposes. In this paper, we explore an approach based on deep learning, particularly generative modeling that could reconcile both requirements of accuracy and efficiency by learning structural features from data. When trained on a set of observations, such models can generate new structures very efficiently with the desired level of accuracy, as determined by the data set. We first validate our approach by training a convolutional neural network to approximate the potential-energy surface of $a$-Si, as given by the Stillinger-Weber potential, which results in a root-mean-square error of 5.05 meV per atom—about $0.16\%$ of the atomic energy. We then train a deep generative model, the Wasserstein autoencoder, for the generation of $a$-Si configurations. Our approach leads to models which exhibit some of the essential features of $a$-Si while possessing too much structural disorder, thus suggesting that the method is viable; we indicate avenues for improving it towards the generation of state-of-the-art structures.

A detailed account of the local atomic structure and disorder at 5 K across the phase diagram of the high-temperature superconductor ${\mathrm{K}}_x{\mathrm{Fe}}_{2-y}{\mathrm{Se}}_{2-z}{\mathrm{S}}_z$ $(0\le z\le 2)$ is obtained from neutron total scattering and associated atomic pair distribution function (PDF) approaches. Various model-independent and model-dependent aspects of the analysis reveal a high level of structural complexity on the nanometer length scale. Evidence is found for considerable disorder in the $c$-axis stacking of the ${\mathrm{FeSe}}_{1-x}{\mathrm{S}}_x$ slabs without observable signs of turbostratic character of the disorder. In contrast to the related FeCh (Ch = S, Se)-type superconductors, substantial Fe-vacancies are present in ${\mathrm{K}}_x{\mathrm{Fe}}_{2-y}{\mathrm{Se}}_{2-z}{\mathrm{S}}_z$, deemed detrimental for superconductivity when ordered. Our study suggests that the distribution of vacancies significantly modifies the iron-chalcogen bond-length distribution, in agreement with observed evolution of the PDF signal. A crossoverlike transition is observed at a composition of $z\approx 1$, from a correlated disorder state at the selenium end to a more vacancy-ordered (VO) state closer to the sulfur end of the phase diagram. The S-content-dependent measures of the local structure are found to exhibit distinct behavior on either side of this crossover, correlating well with the evolution of the superconducting state to that of a magnetic semiconductor toward the $z\approx 2$ end. The behavior reinforces the idea of the intimate relationship of correlated Fe-vacancy order in the local structure and the emergent electronic properties.

Anderson localization on treelike graphs such as the Bethe lattice, Cayley tree, or random regular graphs has attracted attention due to its apparent mathematical tractability, hypothesized connections to many-body localization, and the possibility of nonergodic extended regimes. This behavior has been conjectured to also appear in many-body localization as a “bad metal” phase, and constitutes an intermediate possibility between the extremes of ergodic quantum chaos and integrable localization. Despite decades of research, a complete consensus understanding of this model remains elusive. Here we use cages, maximally treelike structures from extremal graph theory; and numerical continuous unitary Wegner flows of the Anderson Hamiltonian to develop an intuitive picture which, after extrapolating to the infinite Bethe lattice, appears to capture ergodic, nonergodic extended, and fully localized behavior.

A typical nanotribology simulation setup is the semi-infinite substrate, featuring a sliding bead on top and with the lower substrate layers thermostatted to control temperature. A challenge is dealing with phonons that backreflect from the substrate lower boundary, as these will artificially reduce the friction $F_{\mathrm{fr}}$ acting on the sliding bead. One proposed solution is to use a Langevin thermostat, operating at temperature $T_{\mathrm{lan}}$, and with the corresponding damping parameter $\gamma$, optimally tuned such that $F_{\mathrm{fr}}$ is maximized [Benassi et al., Phys. Rev. B 82, 081401 (2010)]. In this paper, the method is revisited and related to the substrate phonon lifetime, the substrate temperature $T_{\mathrm{sub}}$, and the sliding speed. At low sliding speed, where the time between stick-slip events is large compared to the phonon lifetime, we do not observe much dependence of $F_{\mathrm{fr}}$ on $\gamma$, and here thermostat tuning is not required. At high sliding speed, upon varying $\gamma$, we confirm the aforementioned friction maximum but also observe a pronounced minimum in $T_{\mathrm{sub}}$, which here deviates from $T_{\mathrm{lan}}$. For substrate particle interactions that are strongly anharmonic, the variation of $F_{\mathrm{fr}}$ with $\gamma$ can be understood as a manifestation of thermolubricity, backreflections being essentially unimportant. In contrast, for harmonic interactions, where phonon lifetimes become very long, $F_{\mathrm{fr}}$ is strongly affected by backreflecting phonons, though not enough to overturn thermolubricity.

We theoretically investigate the transport properties of the two coupled antiferromagnon modes in a uniaxial antiferromagnetic insulator. The exchange-induced magnon-magnon scattering is found to give rise to strong mode splitting and confluence processes, which conserve the total angular momentum but change the magnon number. These processes can dramatically affect the antiferromagnon dynamics by driving the two oppositely polarized antiferromagnon species to opposite chemical potentials, resulting in a counterflow of the two species with the net magnon current being significantly suppressed. Our results suggest that the antiferromagnetic insulators could be a suitable platform for studying bosonic pure spin currents in insulators.

The generation of the spinmotive force (SMF) requires the temporal and spatial variations of the magnetic moments. We explore an approach to satisfy this requirement by creating asymmetry in a thin film structure along the out-of-plane direction, through the use of an exchange-coupled $L{1}_0-\mathrm{FePt}/{\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ bilayer element. As the spin wave is excited by a rf magnetic field, a continuous dc voltage signal in the out-of-plane direction of the bilayer element appears. The sign of the voltage signal and its microwave power dependency agree with the theoretical framework of the SMF. The corresponding spin wave modes are revealed by carrying out the micromagnetic simulation. Our results demonstrate the generation of the SMF using a vertically structured element in addition to previously reported in-plane structured devices.

8-nm $\epsilon -{\mathrm{Fe}}_2{\mathrm{O}}_3$ nanoparticles exhibit a spin reorientation transition that begins at 150 K which is a hallmark of this unique iron-oxide polymorph. We find that the change from the high- to low-temperature magnetic structures has been suppressed by $\sim 50$ K. At the spin reorientation temperature, a change of the field-dependent response of the tetrahedral sites in intermediate field strengths (0.25–1.5 T) indicates that a collective tetrahedral distortion occurs to which the octahedral sites adjust, altering the magnetic anisotropy. An abrupt step in the hyperfine parameters' temperature dependencies, especially at 125 K for the hyperfine field associated with the ${\mathrm{Fe}}_4$ tetrahedral sites, suggests strongly that a change in the superexchange pathways is responsible for the spin reorientation.

We investigate topological features of electronic structures which produce large anomalous Hall effect in the noncollinear antiferromagnetic metallic states of antiperovskite manganese nitrides by first-principles calculations. We first predict the stable magnetic structures of these compounds to be noncollinear antiferromagnetic structures characterized by either $T_{1g}$ or $T_{2g}$ irreducible representation by evaluating the total energy for all of the magnetic structures classified according to the symmetry and multipole moments. The topology analysis is next performed for the Wannier tight-binding models obtained from the first-principles band structures. Our results reveal the small Berry curvature induced through the coupling between occupied and unoccupied states with the spin-orbit coupling, which is widely spread around the Fermi surface in the Brillouin zone, dominantly contributes after the $\mathit{k}$-space integration to the anomalous Hall conductivity, while the local divergent Berry curvature around Weyl points has a rather small contribution to the anomalous Hall conductivity.

We report the synthesis and characterization of a new quantum magnet [2-[Bis(2-hydroxybenzyl) aminomethyl]pyridine]Ni(II)-trimer (BHAP-${\mathrm{Ni}}_3$) in single-crystalline form. Our combined experimental and theoretical investigations reveal an exotic spin state that stabilizes a robust 2/3 magnetization plateau between 7 and 20 T in an external magnetic field. AC-susceptibility measurements show the absence of any magnetic order/glassy state down to 60 mK. The magnetic ground state is disordered and specific-heat measurements reveal the gapped nature of the spin excitations. Most interestingly, our theoretical modeling suggests that the 2/3 magnetization plateau emerges due to the interplay between antiferromagnetic Heisenberg and biquadratic exchange interactions within nearly isolated spin $S=1$ triangles.

The superconducting state of metals has long provided a classic example of particle-hole symmetry at low energy. Fermionic self-energy results based on first-principles theory for the electron-phonon coupling in ${\mathrm{H}}_3\mathrm{S}$ presented here illustrate strong particle-hole asymmetry in the dynamics arising from the underlying sharp structure in the fermionic density of states. Thus ${\mathrm{H}}_3\mathrm{S}$ not only is the superconductor with the highest critical temperature $T_c$ (through 2018), but its low-energy, low-temperature properties deviate strongly from textbook behavior. The minor momentum and band dependence of the fermionic self-energy allows evaluation of the momentum-resolved and zone-averaged spectral densities and interacting thermal distribution function, all of which clearly illustrate strong particle-hole asymmetry.

Spontaneous magnon decay is a generic feature of the magnetic excitations of anisotropic magnets and isotropic magnets with noncollinear order. In this Rapid Communication, we argue that the effect of interactions on one-magnon states can, under many circumstances, be treated in terms of an effective, energy-independent, non-Hermitian Hamiltonian for the magnons. In the vicinity of Dirac or Weyl touching points, we show that the spectral function has a characteristic anisotropy arising from topologically protected exceptional points or lines in the non-Hermitian spectrum. Such features can, in principle, be detected using inelastic neutron scattering or other spectroscopic probes. We illustrate this physics through a concrete example: a honeycomb ferromagnet with Dzyaloshinskii-Moriya exchange. We perform interacting spin-wave calculations of the structure factor and spectral function of this model, showing good agreement with results from a simple effective non-Hermitian model for the splitting of the Dirac point. Finally, we argue that the zoo of known topological protected magnon band structures may serve as a nearly ideal platform for realizing and exploring non-Hermitian physics in solid-state systems.

The interfacial Dzyaloshinskii-Moriya interaction (DMI) in multilayers of heavy metal and ferromagnetic metals enables the stabilization of novel chiral spin structures such as skyrmions. Magnetic insulators, on the other hand, can exhibit enhanced dynamics and properties such as lower magnetic damping and therefore it is of interest to combine the properties enabled by interfacial DMI with insulating systems. Here, we demonstrate the presence of interfacial DMI in heterostructures that include insulating magnetic layers. We use perpendicularly magnetized insulating thulium iron garnet (TmIG) films capped by the heavy metal platinum, grown on gadolinium gallium garnet (GGG) substrates, and find a surprisingly strong interfacial DMI that, combined with spin-orbit torque, results in efficient switching. The interfacial origin is confirmed through thickness-dependence measurements of the DMI, revealing the characteristic 1/thickness dependence. We combine chiral spin structures and spin-orbit torques for efficient switching and identify skyrmions that allow us to establish the GGG/TmIG interface as the possible origin of the DMI.

Motivated by recent experiments in the extremely hole doped iron pnictide compounds $A{\mathrm{Fe}}_2{\mathrm{As}}_2$ ($A=\mathrm{K}$, Rb, Cs), we consider spin-driven nematic order for incommensurate magnetic fluctuations. We classify the nematic order parameters by broken mirror symmetries of the tetragonal $D_{4h}$ point group, and use this scheme to construct a general Ginzburg-Landau theory that links the nematic order to spatial pattern of magnetic fluctuations. Our analysis points to incommensurate $(q,q)$ magnetic fluctuations as underlying a $B_{2g}$ nematic order in $A{\mathrm{Fe}}_2{\mathrm{As}}_2$. We substantiate this idea by microscopic calculations based on three-sublattice $(2\pi /3,2\pi /3)$ spin correlations in an extended bilinear-biquadratic Heisenberg model. Our classification scheme provides symmetry-based understanding for quasidegeneracy of several nematic channels. The proposed mechanism resolves recently emerged experimental puzzles. We suggest ways to further test it in future experiments and discuss the implications of our results for iron-based high temperature superconductivity.

We report a study of the atomic structure of the multiferroic material bismuth ferrite ${\mathrm{BiFeO}}_3$ using neutron total scattering measurements coupled with analysis using the Reverse Monte Carlo method. We have examined average neighboring interatomic distances and local coordination environments, together with their fluctuations, for temperatures between 16 and 800 K (the sample decomposed at higher temperatures). There is little change in the average structure as a function of temperature, but the results show unusually large thermal motion at higher temperatures. No anomalous behavior is seen within this range, suggesting that the anomalies reported to occur below room temperature most likely arise due to effects associated with surfaces and interfaces.

We study the magnetic behavior of a two-dimensional set of interacting magnetic nanoparticles. The single-domain nanoparticles exhibit competing cubic and uniaxial anisotropies, and they interact themselves through long-range dipolar interactions. We employ the stochastic Landau-Lifshitz-Gilbert equation to describe the time evolution of the magnetic moments of the system. We determine the magnetic relaxation of the system as a function of the ratio between cubic and uniaxial anisotropies, and from the strength of dipolar coupling. From the relaxation curves we calculate the effective energy barrier distribution by considering both situations where the uniaxial axes are completely aligned or randomly oriented relative to an external magnetic field. When the axes are randomly oriented, two peaks are observed in the distribution of energy barriers depending on the ratio of cubic and uniaxial anisotropies, as well as on the intensity of dipolar coupling. Through the zero-field-cooled curves we also determine the blocking temperature of the system and we show that it increases both with the ratio between the cubic and uniaxial anisotropies, as well as with the magnitude of dipolar interactions.

The atomic environments involved in the magnetostriction effect in $\mathrm{CoF}{\mathrm{e}}_2{\mathrm{O}}_4$ and $\mathrm{L}{\mathrm{a}}_{0.5}\mathrm{S}{\mathrm{r}}_{0.5}\mathrm{Co}{\mathrm{O}}_3$ polycrystalline samples have been identified by differential extended x-ray absorption fine structure (DiffEXAFS) spectroscopy. We demonstrate that cobalt atoms at octahedral sites are responsible for their magnetostriction. The analysis of DiffEXAFS data indicates that the local-site magnetostrictive strains of Co atoms are reversed in these two oxides, in agreement with the macroscopic magnetostriction. For the $\mathrm{CoF}{\mathrm{e}}_2{\mathrm{O}}_4$ spinel, a large negative strain along the (100) direction has been determined for the $\mathrm{Co}{\mathrm{O}}_6$ octahedron causing a tetragonal contraction in contrast with the $\mathrm{L}{\mathrm{a}}_{0.5}\mathrm{S}{\mathrm{r}}_{0.5}\mathrm{Co}{\mathrm{O}}_3$ perovskite, where a positive moderate strain along the (100) direction was found resulting in a tetragonal expansion. The different local-site magnetostriction is understood in terms of the different valence and spin state of the Co atoms for the two oxides. The macroscopic magnetostriction would be explained then by the relative change in volume, either contraction in $\mathrm{CoF}{\mathrm{e}}_2{\mathrm{O}}_4$ or expansion in $\mathrm{L}{\mathrm{a}}_{0.5}\mathrm{S}{\mathrm{r}}_{0.5}\mathrm{Co}{\mathrm{O}}_3$, when the tetragonal axis of the Co site is reoriented under an externally applied magnetic field.

We show that the gauge-invariant kinetic equation of superconductivity provides an efficient approach to study the electromagnetic response of the gapless Nambu-Goldstone and gapful Higgs modes on an equal footing. We prove that the Fock energy in the kinetic equation is equivalent to the generalized Ward's identity. Hence, the gauge invariance directly leads to the charge conservation. Both linear and second-order optical responses are analytically investigated. The linear response of the Higgs mode vanishes in the long-wave limit, whereas the linear response of the Nambu-Goldstone mode interacts with the long-range Coulomb interaction, causing the original gapless energy spectrum effectively lifted up to the plasma frequency as a result of the Anderson-Higgs mechanism, consistent with previous work. The second-order response exhibits interesting physics. On the one hand, a finite second-order optical response of the Higgs mode is obtained in the long-wave limit. We reveal that this response, which has been experimentally observed, is attributed solely to the drive effect rather than the widely considered Anderson-pump effect. On the other hand, the second-order optical response of the Nambu-Goldstone mode, free from the influence of the long-range Coulomb interaction and hence the Anderson-Higgs mechanism, is predicted. We find that both Anderson-pump and drive effects play important role in this response. A tentative scheme to detect this second-order response is proposed.

It has been shown that singlet Cooper pairs can be converted into triplet ones and diffuse into a ferromagnet over a long distance in a phenomenon known as the long-range proximity effect (LRPE). This happens in materials with inhomogeneous magnetism or spin-orbit coupling (SOC). Most of the previous studies focus on the cases with small SOC and exchange field. However, the physics was not clear when SOC and exchange field strength are both much greater than the disorder strength. In this work, we consider a two-dimensional system with a large Rashba-type SOC and exchange field in the case where only one band is partially occupied. We develop a generalized quasiclassical theory by projecting the Green function onto the partially occupied band (POB). We find that when the SOC energy scale is comparable with the exchange field, there is no LRPE. The reason is that the nonmagnetic impurities together with the large SOC and exchange field can effectively generate spin-flip scattering, which suppresses the proximity effect. We also show that when increasing either SOC or exchange field, the decay length of superconducting correlations can be significantly increased due to an approximately restored time reversal symmetry or spin rotation symmetry around the $z$ (out-of-plane) axis.

The proximity effect in hybrid superconducting–normal-metal structures is shown to affect strongly the coherent oscillations of the superconducting order parameter $\mathrm{\Delta }$ known as the Higgs modes. The standard Higgs mode at frequency $2\mathrm{\Delta }$ is damped exponentially by the quasiparticle leakage from the primary superconductor. Two new Higgs modes with the frequencies depending on both the primary and induced gaps in the hybrid structure are shown to appear due to the coherent electron transfer between the superconductor and the normal metal. Altogether, these three modes determine the long-time asymptotic behavior of the superconducting order parameter disturbed either by the electromagnetic pulse or the quench of the system parameters and thus are of crucial importance for the dynamical properties and restrictions on the operating frequencies for superconducting devices based on the proximity effect used, e.g., in quantum computing, in particular, with topological low-energy excitations.

We report on an extensive experimental and numerical study of the low-energy electronic properties of superconducting FeSe single crystals, using point-contact Andreev reflection Spectroscopy (PCAR), specific heat, and London penetration depth measurements. Taking explicitly into account Fermi surface anisotropy and recently suggested orbital-selective quasiparticle spectral weights $Z_i$ ($i=d_{xy},d_{x^2-y^2},d_{xz},d_{yz},d_{z^2}$), our calculations quantitatively account for all our measurements as well as data from the literature, assuming that $Z_{yz}>Z_{xz}>Z_{xy}$. This study confirms the picture of a highly different quantum coherence of the Fe orbitals at the Fermi energy. In particular, the normal state properties (Sommerfeld coefficient and zero-temperature London penetration depth) strongly depend on the $Z_i$ values, which seem to be significantly sensitive to disorder.