${\text{BaSi}}_2$-type disilicides and digermanides hold great promise for solar-cell applications, but their structural stability and phase transition mechanisms remain unresolved. Here we present ab initio calculations of pressure-induced structural phase transitions of ${\mathrm{BaSi}}_2,{\mathrm{BaGe}}_2$, and ${\mathrm{SrGe}}_2$ and show that Si tetrahedra in orthorhombic ${\mathrm{BaSi}}_2$ tend to convert to corrugated layers in the trigonal phase under high pressure with bond breaking along the $b$ axis, and a three-dimensional Si net in the cubic phase is stabilized energetically at low pressure. The orthorhombic semiconductor–to–trigonal metal conversion is also preferred for ${\mathrm{SrGe}}_2$ both energetically and kinetically. However, Ge tetrahedra in ${\mathrm{BaGe}}_2$ tend to convert to a ${\mathrm{ThSi}}_2$-type tetragonal net with bond breaking around the $c$ axis. The kinetic barriers are large for both the reaction ($\sim 0.43$ eV under compression) and the counter-reaction ($\sim 0.39$ eV under decompression) for ${\mathrm{BaSi}}_2$, which explains the stability of the trigonal and cubic phases at room temperature and the high-temperature requirement for the phase transitions.

On-the-fly kinetic Monte Carlo simulations are performed to investigate slow relaxation of nonequilibrium systems. Point defects induced by 25 keV cascades in $\alpha$-Fe are shown to lead to a characteristic time evolution, described by the replenish-and-relax mechanism. Then, we produce an atomistically based assessment of models proposed to explain the slow structural relaxation by focusing on the aggregation of 50 vacancies and 25 self-interstitial atoms in 10-lattice-parameter $\alpha$-Fe boxes, two processes that are closely related to cascade annealing and exhibit similar time signatures. Four atomistic effects explain the time scales involved in the evolution: defect concentration heterogeneities, concentration-enhanced mobility, cluster-size-dependent bonding energies, and defect-induced pressure. These findings suggest that the two main classes of models to explain slow structural relaxation, the Eyring model and the Gibbs model, both play a role in limiting the rate of relaxation of these simple point-defect systems.

A statistical mechanic study of the $XY$ model with nonlinear interaction is presented on bipartite sparse random graphs. The model properties are compared to those of the $p$-clock model, in which planar continuous spins are discretized into $p$ values. We test the goodness of the discrete approximation to $XY$ spins used in numerical computations and simulations and its limits of convergence in given, $p$-dependent temperature regimes. The models are applied to describe the mode-locking transition of the phases of light modes in lasers at the critical lasing threshold. A frequency is assigned to each variable node, and function nodes implement a frequency matching condition. A nontrivial unmagnetized phase-locking occurs at the phase transition, where the frequency dependence of the phases turns out to be linear over a broad range of frequencies, as in a standard mode-locking multimode laser at the optical power threshold.

Random dilution effects in the magnetic zigzag ladder ($J_1-J_2$ chain) $\beta \text{−}\mathrm{CaC}{\mathrm{r}}_{2-x}\mathrm{S}{\mathrm{c}}_x{\mathrm{O}}_4$ have been investigated combining magnetic susceptibility, specific heat measurements, and neutron scattering. The pseudogapped magnetic excitations observed above $T_{\mathrm{N}}$ in $\beta \text{−}\mathrm{CaC}{\mathrm{r}}_2{\mathrm{O}}_4 \left(x=0\right)$ persist up to $x=0.3$ with an increasing characteristic frequency $E_0$ but vanish for $x=0.5$ for which a quasielastic signal extending up to $8\mathrm{meV}$ becomes the characteristic feature of the magnetic spectrum. Magnetic ordering is seen up to $x=0.3$ with decreased ordering temperature $T_{\mathrm{N}}$ and correlation length. The results are interpreted in terms of the progressive confinement of one-dimensional excitations within shorter chains as $x$ increases and emphasize the crucial role of $J_2$ in propagating magnetic excitations. For an average chain length $l$ smaller than ∼16 magnetic atoms, the system breaks apart into a set of disconnected units with the dynamical properties of a spin glass.

We report structural and magnetic properties of the spin-$\frac{1}{2}$ quantum antiferromagnet $\mathrm{Cu[}{\mathrm{C}}_6{\mathrm{H}}_2{\left(\mathrm{COO}\right)}_4\mathrm{][}{\mathrm{C}}_2{\mathrm{H}}_5{\mathrm{NH}}_3\mathrm{]}{}_2$ by means of single-crystal x-ray diffraction, magnetization, heat capacity, and electron-spin-resonance (ESR) measurements on polycrystalline samples, as well as band-structure calculations. The triclinic crystal structure of this compound features ${\mathrm{CuO}}_4$ plaquette units connected into a two-dimensional framework through anions of the pyromellitic acid $\mathrm{[}{\mathrm{C}}_6{\mathrm{H}}_2{\left(\mathrm{COO}\right)}_4{\mathrm{]}}^{4-}$. The ethylamine cations $\mathrm{[}{\mathrm{C}}_2{\mathrm{H}}_5{\mathrm{NH}}_3{]}^{+}$ are located between the layers and act as spacers. Magnetic susceptibility and heat capacity measurements establish a quasi-two-dimensional, weakly anisotropic, and nonfrustrated spin-$\frac{1}{2}$ square lattice with the ratio of the couplings $J_a/J_c\simeq 0.7$ along the $a$ and $c$ directions, respectively. No clear signatures of the long-range magnetic order are seen in thermodynamic measurements down to 1.8 K. However, the gradual broadening of the ESR line suggests that magnetic ordering occurs at lower temperatures. Leading magnetic couplings are mediated by the organic anion of the pyromellitic acid and exhibit a nontrivial dependence on the Cu-Cu distance, with the stronger coupling between those Cu atoms that are farther apart.

Magnetic whirls in chiral magnets, so-called skyrmions, can be manipulated by ultrasmall current densities. Here we study both analytically and numerically the interactions of a single skyrmion in two dimensions with a small hole in the magnetic layer. Results from micromagnetic simulations are in good agreement with effective equations of motion obtained from a generalization of the Thiele approach. Skyrmion-defect interactions are described by an effective potential with both repulsive and attractive components. For small current densities a previously pinned skyrmion stays pinned whereas an unpinned skyrmion moves around the impurities and never gets captured. For higher current densities, $j_{c1}<j<j_{c2}$, however, single holes are able to capture moving skyrmions. The maximal cross section is proportional to the skyrmion radius and to $\sqrt{\alpha }$, where $\alpha$ is the Gilbert damping. For $j>j_{c2}$ all skyrmions are depinned. Small changes of the magnetic field strongly change the pinning properties; one can even reach a regime without pinning, $j_{c2}=0$. We also show that a small density of holes can effectively accelerate the motion of the skyrmion and introduce a Hall effect for the skyrmion.

By systematic real-space observations using Lorentz transmission electron microscopy, we report here various forms of skyrmions (and related spin textures) for a prototype of cubic helimagnet MnSi as well as their stability that depends on crystalline-orientation and crystal-plate thickness. Below a crossover thickness $(t_{\mathrm{c}}\sim 75\mathrm{nm})$ of a sample, the robust two-dimensional hexagonal skyrmion crystal (SkX) appears over a wide window of temperature and magnetic field, regardless of crystal orientation, while the SkX phase region shrinks to a small pocket near the helical transition temperature $T_{\mathrm{N}}$ in a (111) plate with the thickness above $t_{\mathrm{c}}$, in contrast to the stable SkX in (110) and (001) plates. This observation indicates the importance of the magnetic anisotropy and thermal fluctuation effects for the skyrmion stability. Furthermore, the forms of skyrmions have been found to change from multidomain state of SkX to skyrmion glass structure via single domain state of SkX with increasing magnetic field.

We report a sudden reversal in the pressure dependence of $T_{\mathrm{c}}$ in the iron-based superconductor ${\text{RbFe}}_2{\text{As}}_2$, at a critical pressure $P_{\mathrm{c}}$ $=11$ kbar. Combined with our prior results on ${\text{KFe}}_2{\text{As}}_2$ and ${\text{CsFe}}_2{\text{As}}_2$, we find a universal V-shaped phase diagram for $T_{\mathrm{c}}$ versus $P$ in these fully hole-doped 122 materials, when measured relative to the critical point $(P_{\mathrm{c}},T_{\mathrm{c}})$. From measurements of the upper critical field $H_{\mathrm{c}2}\left(T\right)$ under pressure in ${\text{KFe}}_2{\text{As}}_2$ and ${\text{RbFe}}_2{\text{As}}_2$, we observe the same twofold jump in $(1/T_{\mathrm{c}}){\left(-\partial H_{\text{c}2}/\partial T\right)}_{T_{\mathrm{c}}}$ across $P_{\mathrm{c}}$, compelling evidence for a sudden change in the structure of the superconducting gap. We argue that this change is due to a transition from one pairing state to another, with different symmetries on either side of $P_{\mathrm{c}}$. We discuss a possible link between scattering and pairing, and a scenario where a $d$-wave state favored by high-$Q$ scattering at low pressure changes to a state with $s_{\pm }$ symmetry favored by low-$Q$ scattering at high pressure.

Here we study the magnetotransport properties of the ferropnictide crystals ${\text{BaFe}}_2{\text{As}}_2$ and ${\text{BaFe}}_{1.985}{\text{Co}}_{0.015}{\text{As}}_2$. These materials exhibit a high field linear magnetoresistance that has been attributed to the quantum linear magnetoresistance model. In this model, the linear magnetoresistance is dependent on the concentration of scattering centers in the material. By using proton-beam irradiation to change the defect scattering density, we find that the dependence of the magnitude of the linear magnetoresistance on scattering quite clearly contravenes this prediction. A number of other scaling trends in the magnetoresistance and high field Hall data are observed and discussed.

In order to elucidate the origin of the ferromagnetism found in underdoped $\mathrm{L}{\mathrm{a}}_{1-x}\mathrm{S}{\mathrm{r}}_x\mathrm{Mn}{\mathrm{O}}_3$, we have grown a series of single crystals with a fine step of doping and characterized them with a structural study and measurements of magnetization, resistivity, thermoelectric power, and thermal conductivity. The paramagnetic phase of the underdoped $\mathrm{L}{\mathrm{a}}_{1-x}\mathrm{S}{\mathrm{r}}_x\mathrm{Mn}{\mathrm{O}}_3$ is a small-polaron conductor. However, the Weiss constant extracted from the paramagnetic susceptibility shows a ferromagnetic coupling and tracks the Curie temperature. Given that the double exchange interaction cannot be delivered by the hopping motion of small polarons, we have made a systematic analysis of the structural changes with $x$ and studied whether the superexchange interaction can account for the ferromagnetic coupling found in the paramagnetic phase. Intrinsic local site distortions in $\mathrm{LaMn}{\mathrm{O}}_3$ change as $x$ increases in $\mathrm{L}{\mathrm{a}}_{1-x}\mathrm{S}{\mathrm{r}}_x\mathrm{Mn}{\mathrm{O}}_3$. The influence of the local structural distortion and the cooperative orbital ordering on lattice parameters have been demonstrated by a comparison between the measured change of lattice parameters versus hole doping and a simulation with the software SPuDs, in which rigid octahedra are assumed. Changes with $x$ of the bond length splitting in $\mathrm{Mn}{\mathrm{O}}_6$ octahedra induces an orbital mixing of $(3x^2-r^2)+(y^2-z^2)\mathrm{or}(3y^2-r^2)+(z^2-x^2)$, which progressively converts two-dimensional ferromagnetism in the parent perovskite $\mathrm{LaMn}{\mathrm{O}}_3$ into three-dimensional ferromagnetism. The correlation between the particular lattice distortions and the cooperative orbital ordering and orbital mixing can in turn be used to test the superexchange model by measuring the change of transition temperatures under uniaxial stress. Nearly identical uniaxial stress effects found in crystals of the mixed-valent $\mathrm{L}{\mathrm{a}}_{0.875}\mathrm{S}{\mathrm{r}}_{.125}\mathrm{Mn}{\mathrm{O}}_3$ and single-valent $\mathrm{LaM}{\mathrm{n}}_{0.5}\mathrm{G}{\mathrm{a}}_{0.5}{\mathrm{O}}_3$ confirm unambiguously that superexchange interactions play the dominant role in the ferromagnetic coupling of underdoped $\mathrm{L}{\mathrm{a}}_{1-x}\mathrm{S}{\mathrm{r}}_x\mathrm{Mn}{\mathrm{O}}_3$.

Optimizing translationally invariant infinite-projected entangled pair states, we investigate the spin-2 Affleck-Kennedy-Lieb-Tasaki and spin-1 Heisenberg models on the kagome lattice as a function of magnetic field. We found that the magnetization curves offer a wide variety of compressible and incompressible phases. Incompressible nematic phases breaking the lattice $C_3$ rotation, for which we propose simple qualitative pictures, give rise to magnetization plateaus at reduced magnetization $m_z=\frac{5}{6}$ and $\frac{1}{3}$ for spin-2 and -1, respectively, in addition to the $m_z=0$ plateaus characteristic of zero-field gapped spin liquids. Moving away from the plateaus, we observe a rich variety of compressible superfluid nematic, named “supernematic,” phases breaking spontaneously both point group and spin-U(1) symmetries, as well as a superfluid phase preserving lattice symmetries. We also identify the nature, continuous or first order, of the various phase transitions. Possible connections to experimental spin-1 systems are discussed.

We study spin-wave spectra of mesoscopic ferromagnetic Sierpinski carpets by means of broadband-ferromagnetic resonance measurements and micromagnetic simulations. Sierpinski carpets are self-similar fractals with noninteger Hausdorff dimension that are constructed via a deterministic iteration process. The number of quantized spin-wave modes in the spectra increases with the iteration level of the carpets and the frequency splitting resembles bandpass characteristics known from fractal antennas. We find that the splitting is sensitive to the fractal dimension as well as to the relative alignment of the magnetic field and the sides of the fractals. Micromagnetic simulations provide the localization of individual spin-wave modes determined by the confinement and the inhomogeneity of the internal field.

Monte Carlo and spin dynamics techniques have been used to perform large-scale simulations of the dynamic behavior of a nanoscale, classical, Heisenberg antiferromagnet on a simple-cubic lattice with linear sizes $L⩽40$ at a temperature below the Néel temperature. Nanoparticles are modeled with completely free boundary conditions, i.e., six free surfaces, and nanofilms are modeled with two free surfaces in the spatial $z$ direction and periodic boundaries parallel to the surfaces in the $xy$ direction, which are compared to the “infinite” system with periodic boundary conditions. The temporal evolutions of spin configurations were determined numerically from coupled equations of motion for individual spins using a fast spin dynamics algorithm with the fourth-order Suzuki-Trotter decomposition of exponential operators, with initial spin configurations generated by Monte Carlo simulations. The local dynamic structure factor $S(q,\omega )$ was calculated from the local space- and time-displaced spin-spin correlation function. Multiple excitation peaks for wave vectors within the first Brillouin zone appear in the spin-wave spectra of the transverse component of dynamic structure factor $S^T(q,\omega )$ in the nanoscale classical Heisenberg antiferromagnet, which are lacking if periodic boundary conditions are used. With the assumption of $q$-space spin-wave reflections with broken momentum conservation due to free-surface confinements, we successfully explained those spectra quantitatively in the linear dispersion region. Meanwhile, we also observed two unexpected quantized spin-wave excitation modes in the spatial $z$ direction in nanofilms for $S^T(q,\omega )$ not expected in bulk systems. The results of this study indicate the presence of unexpected forms of spin-wave excitation behavior that have yet to be observed experimentally but could be directly tested through neutron scattering experiments on nanoscale ${\mathrm{RbMnF}}_3$ particles or films.

We investigate the possibility of realizing a topological state in the impurity band formed by a chain of classical spins embedded in a two-dimensional singlet superconductor with Rashba spin-orbit coupling. In contrast to similar proposals which require a helical spin texture of the impurity spins for a nontrivial topology, here we show that spin-flip correlations due to the spin-orbit coupling in the superconductor produces a topological state for ferromagnetic alignment of the impurity spins. From the Bogoliubov–de Gennes equations we derive an effective tight-binding model for the subgap states which resembles a spinless superconductor with long-range hopping and pairing terms. We evaluate the topological invariant, and show that a topologically nontrivial state is generically present in this model.

The magnetic order of the localized ${\mathrm{Eu}}^{2+}$ spins in optimally doped $\mathrm{Eu}\left({\mathrm{Fe}}_{1-x}{\mathrm{Ir}}_x\right){}_2{\mathrm{As}}_2 \left(\mathit{x}=0.12\right)$ with superconducting transition temperature $T_{\mathrm{SC}}=22$ K was investigated by single-crystal neutron diffraction. The ${\mathrm{Eu}}^{2+}$ moments were found to be ferromagnetically aligned along the $\mathit{c}$ direction with an ordered moment of 7.0(1) ${\mu }_B$ well below the magnetic phase transition temperature $T_C=17$ K. No evidence of the tetragonal-to-orthorhombic structural phase transition was found in this compound within the experimental uncertainty, in which the spin-density-wave (SDW) order of the Fe sublattice is supposed to be completely suppressed and the superconductivity gets fully developed. The ferromagnetic ground state of the ${\mathrm{Eu}}^{2+}$ spins in $\mathrm{Eu}\left({\mathrm{Fe}}_{0.88}{\mathrm{Ir}}_{0.12}\right){}_2{\mathrm{As}}_2$ was supported by the first-principles density functional calculation. In addition, comparison of the electronic structure calculations between $\mathrm{Eu}\left({\mathrm{Fe}}_{0.875}{\mathrm{Ir}}_{0.125}\right){}_2{\mathrm{As}}_2$ and the parent compound ${\mathrm{EuFe}}_2{\mathrm{As}}_2$ indicates stronger hybridization and more expanded bandwidth due to the Ir substitution, which together with the introduction of electrons might work against the Fe-SDW in favor of the superconductivity.

We address the quantum-critical behavior of two-dimensional itinerant ferromagnetic systems described by spin-fermion models in which fermions interact with close-to-critical bosonic modes. We consider Heisenberg ferromagnets, Ising ferromagnets, and the Ising nematic transition. Mean-field theory close to the quantum critical point predicts a superconducting gap with spin-triplet symmetry for the ferromagnetic systems and a singlet gap for the nematic scenario. Studying fluctuations in this ordered phase using a nonlinear sigma model, we find that these fluctuations are not suppressed by any small parameter. As a result, we find that a superconducting quasi-long-range order is still possible in the Ising-like models but long-range order is destroyed in Heisenberg ferromagnets.

We study the quantum phase diagram of the spin-$1/2$ Heisenberg model on the kagome lattice with first-, second-, and third-neighbor interactions $J_1,J_2$, and $J_3$ by means of density matrix renormalization group. For small $J_2$ and $J_3$, this model sustains a time-reversal invariant quantum spin-liquid phase. With increasing $J_2$ and $J_3$, we find in addition a $q=(0,0)$ Néel phase, a chiral spin-liquid phase, an apparent valence-bond crystal phase, and a complex noncoplanar magnetically ordered state with spins forming the vertices of a cuboctahedron known as a cuboc1 phase. Both the chiral spin liquid and cuboc1 phase break time-reversal symmetry in the sense of spontaneous scalar spin chirality. We show that the chiralities in the chiral spin liquid and cuboc1 are distinct, and that these two states are separated by a strong first-order phase transition. The transitions from the chiral spin liquid to both the $q=(0,0)$ phase and to time-reversal symmetric spin liquid, however, are consistent with continuous quantum phase transitions.

The electronic structures of ${\mathrm{SrMn}}_{1-x}{\mathrm{Ru}}_x{\mathrm{O}}_3$ $(0\le x\le 1)$ have been investigated by employing soft x-ray absorption spectroscopy (XAS) and soft x-ray magnetic circular dichroism (XMCD). Both Mn and Ru ions are nearly tetravalent $({\mathrm{Mn}}^{4+},{\mathrm{Ru}}^{4+})$ for the end members of $x=0$ $\left({\mathrm{SrMnO}}_3\right)$ and $x=1$ $\left({\mathrm{SrRuO}}_3\right)$. In the Ru-dilute concentration $(x\le \sim 0.2)$, Ru ions are pentavalent $\left({\mathrm{Ru}}^{5+}\right)$, which transform neighboring Mn ions into the trivalent ${\mathrm{Mn}}^{3+}$ states via electron charge transfer. In the intermediate substitution regime, Mn and Ru ions are in the inhomogeneously mixed-valent states $({\mathrm{Mn}}^3-{\mathrm{Mn}}^{4+}$ and ${\mathrm{Ru}}^4-{\mathrm{Ru}}^{5+})$. Finite Mn $2p$ XMCD signals are observed for $x>0$, in agreement with the ferromagnetic, spin-glass, cluster-glass ground states depending on $x$. The unoccupied Mn $3d$ and Ru $4d$ states, determined from the measured O $1s$ XAS spectra and the calculated density of states, support these findings.

Recently we conjectured that a certain set of universal topological quantities characterize topological order in any dimension. Those quantities can be extracted from the universal overlap of the ground-state wave functions. For systems with gapped boundaries, these quantities are representations of the mapping class group $\mathtt{MCG}\left(\mathcal{M}\right)$ of the space manifold $\mathcal{M}$ on which the systems live. We will here consider simple examples in three dimensions and give physical interpretation of these quantities, related to the fusion algebra and statistics of particles and string excitations. In particular, we will consider dimensional reduction from 3+1D to 2+1D, and show how the induced 2+1D topological data contain information on the fusion and the braiding of non-Abelian string excitations in 3D. These universal quantities generalize the well-known modular $S$ and $T$ matrices to any dimension.

The diffusion of particles in solid-state materials generally involves several sequential thermal-activation processes. However, presently, diffusion coefficient theory only deals with a single barrier, i.e., it lacks an accurate description to deal with multiple-barrier diffusion. Here, we develop a general diffusion coefficient theory for multiple-barrier diffusion. Using our diffusion theory and first-principles calculated hopping rates for each barrier, we calculate the diffusion coefficients of Cd, Cu, Te, and Cl interstitials in CdTe for their full multiple-barrier diffusion pathways. We found that the calculated diffusivity agrees well with the experimental measurement, thus justifying our theory, which is general for many other systems.