We report local probe $\left(\mu \mathrm{SR}\right)$ measurements on the recently discovered tetragonal FeS superconductor which has been predicted to be electronically very similar to superconducting FeSe. Most remarkably, we find that low-moment $\left({10}^{-2}{10}^{-3}{\mu }_{\mathrm{B}}\right)$ disordered magnetism with a transition temperature of $T_{\mathrm{N}}\approx 20$ K microscopically coexists with bulk superconductivity below $T_{\mathrm{c}}=4.3\left(1\right)$ K. From transverse field $\mu \mathrm{SR}$ we obtain an in-plane penetration depth ${\lambda }_{\mathrm{ab}}\left(0\right)=223\left(2\right)$ nm for FeS. The temperature dependence of the corresponding superfluid density ${\lambda }_{\mathrm{ab}}^{-2}\left(T\right)$ indicates a fully gapped superconducting state and is consistent with a two gap $s$-wave model. Additionally, we find that the superconducting $T_{\mathrm{c}}$ of FeS continuously decreases for hydrostatic pressures up to 2.2 GPa.

Knowledge of exact properties of the exchange-correlation (xc) functional is important for improving the approximations made within density functional theory. Features such as steps in the exact xc potential are known to be necessary for yielding accurate densities, yet little is understood regarding their shape, magnitude, and location. We use systems of a few electrons, where the exact electron density is known, to demonstrate general properties of steps. We find that steps occur at points in the electron density where there is a change in the ‘local effective ionization energy’ of the electrons. We provide practical arguments, based on the electron density, for determining the position, shape, and height of steps for ground-state systems, and extend the concepts to time-dependent systems. These arguments are intended to inform the development of approximate functionals, such as the mixed localization potential (MLP), which already demonstrate their capability to produce steps in the Kohn-Sham potential.

Point-defect formation energies calculated within the framework of density functional theory often depend on the choice of the exchange and correlation (xc) functional. We show that variations between the local density approximation (LDA), generalized gradient approximation (GGA), and hybrid functionals mainly arise from differences in the position of the bulk valence-band maximum, as well as in the reference energies for the chemical potential obtained with distinct xc functionals. We demonstrate for point defects relevant for $p$-type GaN that these differences can be accounted for by corrections, reducing the maximum disagreement between the different functionals from more than 2 eV to below 0.2 eV. Our correction scheme should be useful for performing high-throughput calculations in cases where full hybrid functional calculations are prohibitively expensive.

The recently discovered $C_4$ tetragonal magnetic phase in hole-doped members of the iron-based superconductors provides insights into the origin of unconventional superconductivity. Previously observed in ${\mathrm{Ba}}_{\text{1-}x}{\mathrm{Na}}_x{\mathrm{Fe}}_{\text{2}}{\mathrm{As}}_{\text{2}}$ (with $A$ = K, Na), the $C_4$ magnetic phase exists within the well-studied $C_2$ spin-density-wave dome, arising just before the complete suppression of antiferromagnetic order but after the onset of superconductivity. Here, we present detailed x-ray and neutron diffraction studies of ${\mathrm{Sr}}_{\text{1-}x}{\mathrm{Na}}_x{\mathrm{Fe}}_{\text{2}}{\mathrm{As}}_{\text{2}}$ $\left(0.10\le x\le 0.60\right)$ to determine their structural evolution and the extent of the $C_4$ phase. Spanning $\mathrm{\Delta }x\sim 0.14$ in composition, the $C_4$ phase is found to extend over a larger range of compositions, and to exhibit a significantly higher transition temperature, $T_r\sim 65$ K, than in either of the other systems in which it has been observed. The onset of this phase is seen near a composition $\left(x\sim 0.30\right)$ where the bonding angles of the ${\mathrm{Fe}}_{\text{2}}{\mathrm{As}}_{\text{2}}$ layers approach the perfect $109.{46}^{\circ }$ tetrahedral angle. We discuss the possible role of this return to a higher symmetry environment for the magnetic iron site in triggering the magnetic reorientation and the coupled reentrance to the tetragonal structure. Finally, we present a phase diagram, complete with the $C_4$ phase, and use its observation in a third hole-doped 122 system to suggest the universality of this phase.

Three-dimensional topological insulators (TIs) are characterized by spin-polarized Dirac-cone surface states that are protected from backscattering by time-reversal symmetry. Control of the spin polarization of topological surface states (TSSs) using femtosecond light pulses opens novel perspectives for the generation and manipulation of dissipationless surface spin currents on ultrafast time scales. Using time-, spin-, and angle-resolved spectroscopy, we directly monitor the ultrafast response of the spin polarization of photoexcited TSSs to circularly polarized femtosecond pulses of infrared light. We achieve all-optical switching of the transient out-of-plane spin polarization, which relaxes in about 1.2 ps. Our observations establish the feasibility of ultrafast optical control of spin-polarized Dirac fermions in TIs and pave the way for optospintronic applications at ultimate speeds.

We have performed high-resolution angle-resolved photoemission spectroscopy (ARPES) on noncentrosymmetric Weyl semimetal candidate NbP, and determined the electronic states of both Nb- and P-terminated surfaces. We revealed a drastic difference in the Fermi-surface topology between two types of surfaces, whereas the Fermi arcs on both surfaces are likely terminated at the surface projection of the same bulk Weyl nodes. A comparison of the ARPES data with our first-principles band calculations suggests a notable difference in the electronic structure at the Nb-terminated surface between theory and experiment. The present result opens a platform for realizing exotic quantum phenomena arising from the unusual surface properties of Weyl semimetals.

We investigate the thermodynamics and transient dynamics of the (unbiased) Ohmic two-state system by exploiting the equivalence of this model to the interacting resonant level model. For the thermodynamics, we show, by using the numerical renormalization group (NRG) method, how the universal specific heat and susceptibility curves evolve with increasing dissipation strength $\alpha$ from those of an isolated two-level system at vanishingly small dissipation strength, with the characteristic activatedlike behavior in this limit, to those of the isotropic Kondo model in the limit $\alpha \to 1^{-}$. At any finite $\alpha >0$, and for sufficiently low temperature, the behavior of the thermodynamics is that of a gapless renormalized Fermi liquid. Our results compare well with available Bethe ansatz calculations at rational values of $\alpha$, but go beyond these, since our NRG calculations, via the interacting resonant level model, can be carried out efficiently and accurately for arbitrary dissipation strengths $0\le \alpha <1^{-}$. We verify the dramatic renormalization of the low-energy thermodynamic scale $T_0$ with increasing $\alpha$, finding excellent agreement between NRG and density matrix renormalization group (DMRG) approaches. For the zero-temperature transient dynamics of the two-level system, $P\left(t\right)=\langle {\sigma }_z\left(t\right)\rangle$, with initial-state preparation $P(t\le 0)=+1$, we apply the time-dependent extension of the NRG (TDNRG) to the interacting resonant level model, and compare the results obtained with those from the noninteracting-blip approximation (NIBA), the functional renormalization group (FRG), and the time-dependent density matrix renormalization group (TD-DMRG). We demonstrate excellent agreement on short to intermediate time scales between TDNRG and TD-DMRG for $0\lesssim \alpha \lesssim 0.9$ for $P\left(t\right)$, and between TDNRG and FRG in the vicinity of $\alpha =\frac{1}{2}$. Furthermore, we quantify the error in the NIBA for a range of $\alpha$, finding significant errors in the latter even for $0.1\le \alpha \le 0.4$. We also briefly discuss why the long-time errors in the present formulation of the TDNRG prevent an investigation of the crossover between coherent and incoherent dynamics. Our results for $P\left(t\right)$ at short to intermediate times could act as useful benchmarks for the development of new techniques to simulate the transient dynamics of spin-boson problems.

Phase separation, i.e., the coexistence of two different phases, is observed in many systems away from the coexistence curve of a first-order transition, leading to a stable heterogeneous phase or region. Examples include various quantum ferromagnets, heavy-fermion systems, rare-earth nickelates, and others. These observations seem to violate basic notions of equilibrium thermodynamics, which state that phase separation can occur only on the coexistence curve. We show theoretically that quenched disorder allows for phase separation away from the coexistence curve even in equilibrium due to the existence of stable minority-phase droplets within the majority phase. Our scenario also answers a related question: How can a first-order transition remain sharp in the presence of quenched disorder without violating the rigorous lower bound $\nu \ge 2/d$ for the correlation-length exponent? We discuss this scenario in the context of experimental results for a large variety of systems.

The microscopic nature of an insulating state in the vicinity of a superconducting state in the presence of disorder is a hotly debated question. While the simplest scenario proposes that Coulomb interactions destroy the Cooper pairs at the transition, leading to localization of single electrons, an alternate possibility supported by experimental observations suggests that Cooper pairs instead directly localize. The question of the homogeneity, granularity, or possibly glassiness of the material on the verge of this transition is intimately related to this fundamental issue. Here, by combining macroscopic and nanoscale studies of superconducting ultrathin NbN films, we reveal nanoscopic inhomogeneities that emerge when the film thickness is reduced. For the thinnest films, scanning tunneling spectroscopy at low temperature unveils inhomogeneities in the superconducting properties, of typical size $L_i$, that are not correlated to any structural inhomogeneity and that are found to persist above the critical temperature in the form of a pseudogap. Remarkably enough, while the thickest films display a purely two-dimensional behavior in the superconducting fluctuations above the critical temperature, paraconductivity in the pseudogap regime of the thinnest samples demonstrates fluctuations of the amplitude of the order parameter, corresponding to zero-dimensional fluctuating regions of size precisely $L_i$. We propose that an anomalous diffusion slowing-down process is at play at long wave vectors, leading to some “confinement” of the superconducting fluctuations, which allows us to explain the simultaneous paradoxical presence of a pseudogap and zero-dimensional amplitude fluctuations of the order parameter. These findings call for further theoretical investigation to understand this intermediate state where Cooper pairs continuously evolve from a bound state of fermionic objects into localized bosonic entities.

This work investigated the electric polarization of $M{\mathrm{Mn}}_7{\mathrm{O}}_{12}$ ($M=\mathrm{Ca}$, Sr, Cd, Pb) by means of both the conventional pyroelectric current (PC) method and the bias electric field (BE) method. All samples generated intense, broad peaks below the highest magnetic ordering temperature $\left(T_{\mathrm{N}1}\right)$ during PC measurements. In contrast, these peaks were not observed in the BE data, indicating that they are not intrinsically generated through ferroelectricity but rather are thermally stimulated current (TSC) in origin. In addition to the TSC peaks, we observed anomalous small, sharp peaks in both the PC and BE data at $T_{\mathrm{N}2}$, leading to a very small relative polarization value of $\mathrm{\Delta }P\sim 0.2 \mu \mathrm{C}/{\mathrm{m}}^2$ at 46 K in the case of ${\mathrm{CaMn}}_7{\mathrm{O}}_{12}$ and values of $\mathrm{\Delta }P\sim 0.2 \mu \mathrm{C}/{\mathrm{m}}^2$ at 33 K for ${\mathrm{CdMn}}_7{\mathrm{O}}_{12}$ and $\mathrm{\Delta }P\sim 4.0\mu \mathrm{C}/{\mathrm{m}}^2$ at 77 K for ${\mathrm{PbMn}}_7{\mathrm{O}}_{12}$, while ${\mathrm{SrMn}}_7{\mathrm{O}}_{12}$ showed no measurable polarization. In the case of ${\mathrm{CaMn}}_7{\mathrm{O}}_{12}$, large ferroelectric polarization values below $T_{\mathrm{N}1}$ have been reported: $440 \mu \mathrm{C}/{\mathrm{m}}^2$ for a polycrystalline sample and $2870 \mu \mathrm{C}/{\mathrm{m}}^2$ for a single crystal. Nevertheless, we conclude from the present results that these reported large polarization values are not associated with intrinsic ferroelectricity in ${\mathrm{CaMn}}_7{\mathrm{O}}_{12}$.

We present a combined study of Ni $K$-edge resonant x-ray scattering and density functional calculations to probe and distinguish electronically driven ordering and lattice distortions in nickelate heterostructures. We demonstrate that due to the low crystal symmetry, contributions from structural distortions can contribute significantly to the energy-dependent Bragg peak intensities of a bond-ordered ${\mathrm{NdNiO}}_3$ reference film. For a ${\mathrm{LaNiO}}_3\text{−}{\mathrm{LaAlO}}_3$ superlattice that exhibits magnetic order, we establish a rigorous upper bound on the bond-order parameter. We thus conclusively confirm predictions of a dominant spin density wave order parameter in metallic nickelates with a quasi-two-dimensional electronic structure.

We demonstrate that in-plane charge current can effectively control the spin precession resonance in an $\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3/\mathrm{CoFeB}/\mathrm{Ta}$ heterostructure. Brillouin light scattering was used to detect the ferromagnetic resonance field under microwave excitation of spin waves at fixed frequencies. The current control of spin precession resonance originates from modification of the in-plane uniaxial magnetic anisotropy field $H_{\mathrm{k}}$, which changes symmetrically with respect to the current direction. Numerical simulation suggests that the anisotropic stress introduced by joule heating plays an important role in controlling $H_{\mathrm{k}}$. These results provide new insight into current manipulation of magnetic properties and have broad implications for spintronic devices.

GeTe is a material of intense topical interest due to its potential in the context of phase-change and nanowire memory devices, as a base for thermoelectric materials, and as a ferroelectric. The combination of a soft optic mode and a Peierls distortion contributes large strains at the cubic-rhombohedral phase transition near 625 K and the role of these has been investigated through their influence on elastic and anelastic properties by resonant ultrasound spectroscopy. The underlying physics is revealed by softening of the elastic constants by ∼30%–45%, due to strong coupling of shear and volume strains with the driving order parameter and consistent with an improper ferroelastic transition which is weakly first order. The magnitude of the softening is permissive of the transition mechanism involving a significant order/disorder component. A Debye loss peak in the vicinity of 180 K is attributed to freezing of the motion of ferroelastic twin walls and the activation energy of ∼0.07 eV is attributed to control by switching of the configuration of long and short Ge-Te bonds in the first coordination sphere around Ge. Precursor softening as the transition is approached from above can be described with a Vogel-Fulcher expression with a similar activation energy, which is attributed to coupling of acoustic modes with an unseen central mode that arises from dynamical clusters with local ordering of the Peierls distortion. The strain relaxation and ferroelastic behavior of GeTe depend on both displacive and order/disorder effects but the dynamics of switching will be determined by changes in the configuration of distorted $\mathrm{GeT}{\mathrm{e}}_6$ octahedra, with a rather small activation energy barrier.

We investigate the spin-$\frac{1}{2}$ Heisenberg model on the triangular lattice in the presence of nearest-neighbor $J_1$ and next-nearest-neighbor $J_2$ antiferromagnetic couplings. Motivated by recent findings from density-matrix renormalization group (DMRG) claiming the existence of a gapped spin liquid with signatures of spontaneously broken lattice point group symmetry [Zhu and White, Phys. Rev. B 92, 041105 (2015) and Hu, Gong, Zhu, and Sheng, Phys. Rev. B 92, 140403 (2015)], we employ the variational Monte Carlo (VMC) approach to analyze the model from an alternative perspective that considers both magnetically ordered and paramagnetic trial states. We find a quantum paramagnet in the regime $0.08\lesssim J_2/J_1\lesssim 0.16$, framed by ${120}^{\circ }$ coplanar (stripe collinear) antiferromagnetic order for smaller (larger) $J_2/J_1$. By considering the optimization of spin-liquid wave functions of a different gauge group and lattice point group content as derived from Abrikosov mean-field theory, we obtain the gapless $\text{U}\left(1\right)$ Dirac spin liquid as the energetically most preferable state in comparison to all symmetric or nematic gapped ${\mathbb{Z}}_2$ spin liquids so far advocated by DMRG. Moreover, by the application of few Lanczos iterations, we find the energy to be the same as the DMRG result within error bars. To further resolve the intriguing disagreement between VMC and DMRG, we complement our methodological approach by the pseudofermion functional renormalization group (PFFRG) to compare the spin structure factors for the paramagnetic regime calculated by VMC, DMRG, and PFFRG. This model promises to be an ideal test bed for future numerical refinements in tracking the long-range correlations in frustrated magnets.

We report that by measuring a current-induced hysteresis loop shift versus in-plane bias magnetic field, the spin-Hall effect (SHE) contribution of the current-induced effective field per current density ${\chi }_{\mathrm{SHE}}$ can be estimated for Pt- and Ta-based magnetic heterostructures with perpendicular magnetic anisotropy. We apply this technique to a Pt-based sample with its ferromagnetic (FM) layer being wedged deposited and discover an extra effective field contribution ${\chi }_{\mathrm{Wedged}}$ due to the asymmetric nature of the deposited FM layer. We confirm the correlation between ${\chi }_{\mathrm{Wedged}}$ and the asymmetric depinning process in FM layer during magnetization switching by magneto-optical Kerr microscopy. These results indicate the possibility of engineering deterministic spin-orbit torque switching by controlling the symmetry of domain expansion through the materials growth process.

The peculiar field-dependent magnetism of ${\mathrm{Na}}_{0.82}{\mathrm{CoO}}_2$ has been investigated through an analysis of its dc and ac spin susceptibilities. To account for the easily activated narrow $b_{2g}\text{−}{a}_{1g}$ gap of the crystal field for Co in the cobalt oxide layer, the spin-state transition of ${\mathrm{Co}}^{3+}$ ($3d^6$) between the low-spin (LS) state $b_{2g}^2{a}_{1g}^0$ of $S=0$ and the intermediate-spin (IS) state $b_{2g}^1{a}_{1g}^1$ of $S=1$ is thus seen as thermally activated and exhibits a Boltzmann distribution. The IS state of ${\mathrm{Co}}^{3+}$ within each $\sqrt{13}a$ hexagonal superlattice formed by the $S=1/2$ state of the ${\mathrm{Co}}^{4+}$ ions appears randomly within each supercell and shows significant temperature and field dependence. The magnetic field is found to assist in pinning down the thermally activated state of ${\mathrm{Co}}^{3+}$ and swings the Boltzmann distribution weight toward a higher fraction of the IS state. The field dependence of the in-plane magnetic moment from the added number of $S=1$ spins is used to explain the origin of $A$-type antiferromagnetic (AF) ordering, particularly that the ferromagnetic (FM)-like behavior below $T_N$ at low field is actually a ferrimagnetic IS spin ordering of ${\mathrm{Co}}^{3+}$.

The search for new ferroelectric (FE) materials holds promise for broadening our understanding of FE mechanisms and extending the range of application of FE materials. Here we investigate a class of $AB{\mathrm{O}}_3$ and $A_{2}B{B}^{\prime }{\mathrm{O}}_6$ materials that can be derived from the $X_2{\mathrm{O}}_3$ corundum structure by mixing two or three ordered cations on the $X$ site. Most such corundum derivatives have a polar structure, but it is unclear whether the polarization is reversible, which is a requirement for a FE material. In this paper, we propose a method to study the FE reversal path of materials in the corundum derivative family. We first categorize the corundum derivatives into four classes and show that only two of these allow for the possibility of FE reversal. We then calculate the energy profile and energy barrier of the FE reversal path using first-principles density functional methods with a structural constraint. Furthermore, we identify several empirical measures that can provide a rule of thumb for estimating the energy barriers. Finally, the conditions under which the magnetic ordering is compatible with ferroelectricity are determined. These results lead us to predict several potentially new FE materials.

We investigate the atomistic structure of ferroelastic-ferroelectric ${90}^{\circ }$ domain walls in ${\mathrm{PbTiO}}_3$ with first-principles calculations and high-resolution scanning transmission electron microscopy. We find sharp discontinuities in the variation of lattice parameters across the domain walls. Unexpectedly, the two neighboring domains become asymmetric across the boundary, giving rise to primitive unit cells with large tetragonality ratios ($c/a$) of the order of 1.11 close to the boundary. The variation of the domain wall structure with respect to strain is demonstrated. We show that oxygen vacancies are attracted to the plane adjacent to the ${90}^{\circ }$ domain wall. The mechanisms of domain wall pinning by oxygen vacancies is explained based on the energy landscape of the vacancies in the presence of the domain interface.

We study the intrinsic anisotropy of the superconducting state in ${\mathrm{KFe}}_2{\mathrm{As}}_2$ by using small-angle neutron scattering to image the vortex lattice as the applied magnetic field is rotated towards the FeAs crystalline planes. The anisotropy is found to be strongly field dependent, indicating multiband superconductivity. Furthermore, the high-field anisotropy significantly exceeds that of the upper critical field, providing further support for Pauli limiting in ${\mathrm{KFe}}_2{\mathrm{As}}_2$ for fields applied in the basal plane. The effect of Pauli paramagnetism on the unpaired quasiparticles in the vortex cores is directly evident from the ratio of scattered intensities due to the longitudinal and transverse vortex lattice field modulation.

The electronic structure of native defects and impurities in ${\mathrm{GdTiO}}_3$, a rare-earth titanate Mott insulator, is studied using density functional theory with a hybrid functional. Among native defects, the cation vacancies have the lowest formation energies in oxygen-rich conditions and oxygen vacancies have the lowest formation energy in oxygen-poor conditions. Among the impurities, ${\mathrm{Sr}}_{\mathrm{Gd}},{\mathrm{H}}_i$, and ${\mathrm{C}}_{\mathrm{O}}$ have low formation energies. A common feature of the native defects and impurities is that they lead to the formation of small hole polarons, which explains the frequent observation of $p$-type hopping conductivity in the rare-earth titanates. These small hole polarons also lead to optical absorption and act as electron traps in devices.