Unsupervised learning is a discipline of machine learning which aims at discovering patterns in large data sets or classifying the data into several categories without being trained explicitly. We show that unsupervised learning techniques can be readily used to identify phases and phases transitions of many-body systems. Starting with raw spin configurations of a prototypical Ising model, we use principal component analysis to extract relevant low-dimensional representations of the original data and use clustering analysis to identify distinct phases in the feature space. This approach successfully finds physical concepts such as the order parameter and structure factor to be indicators of a phase transition. We discuss the future prospects of discovering more complex phases and phase transitions using unsupervised learning techniques.

The method for calculating the isotropic exchange interactions in the paramagnetic phase is proposed. It is based on the mapping of the high-temperature expansion of the spin-spin correlation function calculated for the Heisenberg model onto the Hubbard Hamiltonian one. The resulting expression for the exchange interaction has a compact and transparent formulation. The quality of the calculated exchange interactions is estimated by comparing the eigenvalue spectra of the Heisenberg model and low-energy magnetic part of the Hubbard model. By the example of quantum rings at half-filling with different hopping setups, we analyze contributions from different parts of the Hubbard model spectrum to the resulting exchange interaction. The developed method can be applied for simulating magnetic couplings in correlated materials and surface nanostructures.

The two-dimensional quantum XY model, with a Caldeira-Leggett form of dissipation, is applicable to the quantum-critical properties of diverse experimental systems, ranging from superconductor to insulator transitions, ferromagnetic and antiferromagnetic transitions in metals, to the loop-current order transition in cuprates. We solve the reexpression of this model in terms of orthogonal topological excitations, vortices, and a variety of instantons, by renormalization group methods. The calculations explain the extraordinary properties of the model discovered in Monte Carlo calculations: the product form of the quantum-critical fluctuations in space and time, a spatial correlation length proportional to the logarithm of the temporal correlation length near the transition from a disordered to a fully ordered state, and the occurrence of a phase with spatial order without temporal order. They are intimately related to the flow of the metric of time in relation to the metric of space, i.e., of the dynamical critical exponent $z$. These properties appear to be essential in understanding the strange metallic phase found in a variety of quantum-critical transitions as well as the accompanying high-temperature superconductivity.

In conventional metals, electronic transport in a magnetic field is characterized by the motion of electrons along orbits on the Fermi surface, which usually causes an increase in the resistivity through averaging over velocities. Here, we show that large deviations from this behavior can arise in density-wave systems close to their ordering temperature. Specifically, enhanced scattering off collective fluctuations can lead to a change of direction of the orbital motion on reconstructed pockets. In weak magnetic fields, this leads to linear magnetoconductivity, the sign of which depends on the electric-field direction. At a critical magnetic field, the conductivity crosses zero for certain directions, signifying a thermodynamic instability of the density-wave state.

The low-temperature electronic state of the layered organic charge-transfer salt $\kappa -{\left(\mathrm{BETS}\right)}_2{\mathrm{FeCl}}_4$ was probed by interlayer electrical resistance measurements under magnetic field. Both above and below $T_{\mathrm{N}}=0.47$ K, the temperature of antiferromagnetic ordering of $3d$-electron spins of ${\mathrm{Fe}}^{3+}$ localized in the insulating anion layers, a nonsaturating linear $R\left(T\right)$ dependence has been observed. A weak superconducting signal has been detected in the antiferromagnetic state, at temperatures $\le 0.2$ K. Despite the very high crystal quality, only a tiny fraction of the sample appears to be superconducting. Aside from a small kink feature in the resistivity, the impact of the antiferromagnetic ordering of localized ${\mathrm{Fe}}^{3+}$ spins on the conduction $\pi$-electron system is clearly manifested in the Fermi surface reconstruction, as evidenced by Shubnikov–de Haas oscillations. The “magnetic-field–temperature” phase diagrams for the field directions parallel to each of the three principal crystal axes have been determined. For magnetic field along the easy axis, a spin-flop transition has been found. Similarities and differences between the present material and the sister compound $\kappa -{\left(\mathrm{BETS}\right)}_2{\mathrm{FeBr}}_4$ are discussed.

Here, building on our previous work [Phys. Rev. B 92, 125153 (2015)], it is shown that the propagation of unidirectional gapless edge states at an interface of two topologically distinct electromagnetic continua with a well-behaved asymptotic electromagnetic response is rigorously predicted by the bulk-edge correspondence principle. We work out detailed examples demonstrating that when the spatial cutoff of the nonreciprocal part of the material response is considered self-consistently in the solution of the relevant electromagnetic problem, the number of unidirectional gapless edge modes is identical to the difference of the Chern numbers of the bulk materials. Furthermore, it is shown how the role of the spatial cutoff can be imitated in realistic systems using a tiny air gap with a specific thickness. This theory provides a practical roadmap for the application of topological concepts to photonic platforms formed by nonreciprocal electromagnetic continua.

We investigate the electrical conductivity and thermoelectric effects in topological crystalline insulators in the presence of short- and long-range impurity interactions. We employ the generalized Boltzmann formalism for anisotropic Fermi surface systems. The conductivity exhibits a local minimum as doping varies owing to the Van Hove singularity in the density of states originated from the saddle point in the surface states' band structure. Suppression of the interband scattering of the charge carriers at high-energy Dirac points results in a maximum in the electrical conductivity. Whenever the Fermi level passes an extremum in the conductivity, the Seebeck coefficient changes sign. In addition, it is revealed that profound thermoelectric effects can be attained around these extrema points.

A structural and magnetic characterization of Gd-based bulk metallic glasses, ${\mathrm{GdFe}}_2, {\mathrm{GdCo}}_2$, and ${\mathrm{GdNi}}_2$, was performed. Models for the amorphous structures for two magnetic configurations, ferromagnetic and ferrimagnetic, were obtained by means of a first-principles-based method, the stochastic quenching. In all three cases, the ferrimagnetic configuration was energetically more stable than the ferromagnetic one, in perfect agreement with experiments. In the structural analysis, radial and angle distribution functions as well as calculations of bond lengths and average coordination numbers were included. Structural properties are in good agreement with experiments and do not depend on the magnetic configuration. The distribution of magnetic moments shows that amorphous ${\mathrm{GdFe}}_2$ and ${\mathrm{GdCo}}_2$ are both ferrimagnets, with antiparallel alignment of the magnetic moments of the two magnetic sublattices, whereas Ni nearly loses its magnetic moment in amorphous ${\mathrm{GdNi}}_2$, similar to the situation in its crystalline counterpart.

${\mathrm{Ba}}_3{\mathrm{BiRu}}_2{\mathrm{O}}_9$ is a 6H-type perovskite compound containing face-sharing octahedral $M_2{\mathrm{O}}_9$ ($M=\mathrm{Ir}$, Ru) dimers, which are magnetically frustrated at low temperatures. On cooling through $T^{*}=176$ K, it undergoes a pronounced magnetostructural transition, which is not accompanied by any change in space group symmetry, long-range magnetic ordering, or charge ordering. Here, we report the first direct evidence from inelastic neutron scattering that this transition is due to an opening of a gap in the excitation spectra of dimers of low-spin ${\mathrm{Ru}}^{4+}$ ($S=1$) ions. X-ray absorption spectroscopy reveals a change in Ru-Ru orbital overlap at $T^{*}$, linking the emergence of this spin-gap excitation to the magnetostructural transition. Ab initio calculations point to a geometrically frustrated magnetic ground state due to antiferromagnetic interdimer exchange on a triangular ${\mathrm{Ru}}_2{\mathrm{O}}_9$ dimer lattice. X-ray total-scattering data rule out long-range magnetic ordering at low temperatures, consistent with this geometrically frustrated model.

We performed magnetic susceptibility, dielectric constant, neutron-diffraction, and synchrotron radiation x-ray diffraction measurements on a spin-lattice coupling system ${\mathrm{CuFeO}}_2$ under applied uniaxial pressure $p$ up to 600 MPa. We found that the phase-transition temperature $T_{\mathrm{N}1}$ from the paramagnetic phase to the partially disordered phase increases by as much as 5 K from the original $T_{\mathrm{N}1}\simeq 14\mathrm{K}$ under applied $p$ of 600 MPa, and that the lattice constant $b_{\mathrm{m}}$ of ${\mathrm{CuFeO}}_2$ changes significantly. In contrast, the value of $q_0$, which is the magnetic modulation wave number at $T_{\mathrm{N}1}$ and which should reflect the ratios of the exchange coupling constants, is not changed, even by applied $p$ of 600 MPa. Based on these results, we show that an explanation using only the exchange striction effect is not suitable for the magnetic phase transition in ${\mathrm{CuFeO}}_2$. These results suggest that a lattice degree of freedom via a spin-lattice coupling is indispensable for the determination of the magnetic properties of ${\mathrm{CuFeO}}_2$. A dielectric anomaly under applied $p$ of 600 MPa is also briefly discussed.

In a section of a recent paper [Phys. Rev. B 91, 104432 (2015)], the authors discuss some of the arguments in the paper by Parisi and Temesvári [Nucl. Phys. B 858, 293 (2012)]. In this Comment, it is shown how these arguments are misinterpreted and the existence of the Almeida-Thouless transition $\mathit{in}$ the upper critical dimension six reasserted.

In his Comment, Temesvári objects to a remark in our paper [Phys. Rev. B 91, 104432 (2015)] that his result for the form of the Almeida-Thouless (AT) line obtained in an earlier paper by Parisi and Temevári [Nucl. Phys. B 858, 293 (2012)] in six dimensions can be obtained by taking the limit of $d\to 6$ in the equations valid for $d>6$ but that this violated one of the inequalities needed for their validity. He is just pointing out that they gave a derivation of the form of the AT line in six dimensions in Parisi and Temevári [Nucl. Phys. B 858, 293 (2012)] which avoided this difficulty. However, it is still a perturbative approach and does not deal with the lack of a perturbative fixed point found by Bray and Roberts [J. Phys. C 13, 5405 (1980)] long ago.

The band structure of TaAs provides the necessary conditions for the emergence of Weyl fermions. Measurements verifying this fact are remarkably robust, given the reported levels of nonstoichiometry in typical single crystals. Here we demonstrate the surprising fact that a small degree of nonstoichiometry is essential for such observations in a wide range of temperatures. From first principles, we compute how crystal defects influence the position of the Fermi level relative to the so-called Weyl points, a key factor in allowing the detection of these particles. We show that observations of Weyl fermions depend crucially on nonstoichiometry and only occur within narrow ranges of elemental composition and temperature, indicating a considerable degree of fortuity in their discovery. Our approach suggests that in some cases the drive to produce ultra-pure crystals for measurements of exotic emergent phenomena may be misplaced.

We study the frequency dependence of the optical conductivity $\text{Re}\sigma \left(\omega \right)$ of the Heisenberg spin-$\frac{1}{2}$ chain in the thermal and near the transition to the many-body localized phase induced by the strength of a random $z$-directed magnetic field. Using the method of dynamical quantum typicality, we calculate the real-time dynamics of the spin-current autocorrelation function and obtain the Fourier transform $\text{Re}\sigma \left(\omega \right)$ for system sizes much larger than accessible to standard exact-diagonalization approaches. We find that the low-frequency behavior of $\text{Re}\sigma \left(\omega \right)$ is well described by $\text{Re}\sigma \left(\omega \right)\approx {\sigma }_{\text{dc}}+a{\left|\omega \right|}^{\alpha }$, with $\alpha \approx 1$ in a wide range within the thermal phase and close to the transition. We particularly detail the decrease of ${\sigma }_{\text{dc}}$ in the thermal phase as a function of increasing disorder for strong exchange anisotropies. We further find that the temperature dependence of ${\sigma }_{\text{dc}}$ is consistent with the existence of a mobility edge.

We identify and analyze dephasing mechanisms that broaden the optical transitions of rare-earth ions in randomly oriented transparent ceramics. The study examines the narrow ${}^{7}F_0\leftrightarrow {}^{5}D_0$ transition of ${\mathrm{Eu}}^{3+}$ dopants in a series of ${\mathrm{Y}}_2{\mathrm{O}}_3$ ceramic samples prepared under varying conditions. We characterize the temperature and magnetic field dependence of the homogeneous linewidth, as well as long-term spectral diffusion on time scales up to 1 s. The results highlight significant differences between samples with differing thermal treatments and ${\mathrm{Zr}}^{4+}$ additive concentrations. In particular, several distinct magnetic interactions from defect centers are observed, which are clearly distinguished from the broadening due to interactions with two-level systems and phonons. By minimizing the broadening due to the different defect centers, linewidths of the order of 4 kHz are achieved for all samples. The linewidths are limited by temperature-dependent interactions and by an interaction that is yet to be identified. Although the homogeneous linewidth can be narrowed further in these ceramic samples, the broadening is now comparable to the linewidths achieved in rare-earth-ion–doped single crystals. Thus, this work emphasizes the usefulness of studying ceramics to gain insights into dephasing mechanisms relevant to single crystals and suggests that ceramics may be an interesting alternative for applications in classical and quantum information processing.

The magnetization dynamics induced by standing elastic waves excited in a thin ferromagnetic film is described with the aid of micromagnetic simulations taking into account the magnetoelastic coupling between spins and lattice strains. Our calculations are based on the numerical solution of the Landau-Lifshitz-Gilbert equation comprising the damping term and the effective magnetic field with all relevant contributions. The simulations have been performed for 2-nm-thick $\mathrm{F}{\mathrm{e}}_{81}\mathrm{G}{\mathrm{a}}_{19}$ film dynamically strained by longitudinal and transverse standing waves with various frequencies, which span a wide range around the resonance frequency ${\nu }_{\mathrm{res}}$ of coherent magnetization precession in unstrained $\mathrm{F}{\mathrm{e}}_{81}\mathrm{G}{\mathrm{a}}_{19}$ film. It is found that standing elastic waves give rise to complex local magnetization dynamics and spatially inhomogeneous dynamic patterns in the form of standing spin waves with the same wavelength. Remarkably, the amplitude of magnetization precession does not go to zero at nodes of these spin waves, which cannot be precisely described by simple analytical formulae. In the steady-state regime, magnetization oscillates with the frequency of the elastic wave, except in the case of longitudinal waves with frequencies well below ${\nu }_{\mathrm{res}}$, where the magnetization precesses with variable frequency strongly exceeding the wave frequency. The results obtained for the magnetization dynamics driven by elastic waves are used to calculate the spin current pumped from the dynamically strained ferromagnet into adjacent paramagnetic metal. Numerical calculations demonstrate that the transverse charge current in the paramagnetic layer, which is created by the spin current via inverse spin Hall effect, is high enough to be measured experimentally.

In mixed-valence or heavy-fermion systems, the hybridization between local $f$ orbitals and conduction band states can cause the suppression of long-range magnetic order, which competes with strong spin fluctuations. Ce- and Yb-based systems have been found to exhibit fascinating physical properties (heavy-fermion superconductivity, non-Fermi-liquid states, etc.) when tuned to the vicinity of magnetic quantum critical points by use of various external control parameters (temperature, magnetic field, chemical composition). Recently, similar effects (mixed-valence, Kondo fluctuations, heavy Fermi liquid) have been reported to exist in some Eu-based compounds. Unlike Ce (Yb), Eu has a multiple electron (hole) occupancy of its $4f$ shell, and the magnetic ${\mathrm{Eu}}^{2+}$ state ($4f^7$) has no orbital component in the usual $LS$ coupling scheme, which can lead to a quite different and interesting physics. In the ${\mathrm{EuCu}}_2{(\mathrm{Si}}_x{\mathrm{Ge}}_{1-x}{)}_2$ series, where the valence can be tuned by varying the Si/Ge ratio, it has been reported that a significant valence fluctuation can exist even in the magnetic order regime. This paper presents a detailed study of the latter material using different microscopic probes (XANES, Mössbauer spectroscopy, elastic and inelastic neutron scattering), in which the composition dependence of the magnetic order and dynamics across the series is traced back to the change in the Eu valence state. In particular, the results support the persistence of valence fluctuations into the antiferromagnetic state over a sizable composition range below the critical Si concentration $x_c\approx 0.65$. The sequence of magnetic ground states in the series is shown to reflect the evolution of the magnetic spectral response.

Chemical substitution plays a key role in controlling the electronic and magnetic properties of complex materials. For instance, in EuO, carrier doping can induce a spin-polarized metallic state and colossal magnetoresistance, and significantly enhance the Curie temperature. Here, we employ a combination of molecular-beam epitaxy, angle-resolved photoemission spectroscopy, and an effective model calculation to investigate and understand how semilocalized states evolve in lightly electron-doped ${\mathrm{Eu}}_{1-x}{\mathrm{Gd}}_x\mathrm{O}$ above the ferromagnetic Curie temperature. Our studies reveal a characteristic length scale for the spatial extent of the donor wave functions which remains constant as a function of doping, consistent with recent tunneling studies of doped EuO. Our work sheds light on the nature of the semiconductor-to-metal transition in ${\mathrm{Eu}}_{1-x}{\mathrm{Gd}}_x\mathrm{O}$ and should be generally applicable for doped complex oxides.

The Coulomb interaction is widely known to enhance the effective mass of interacting particles and therefore tends to favor a localized state at commensurate filling. Here, we will show that, in contrast to this consensus, in a van der Waals heterostructure consisting of graphene and hexagon boron nitride (h-BN), the onsite Coulomb repulsion will at first destroy the localized state. This is due to the fact that the onsite Coulomb repulsion tends to suppress the asymmetry between neighboring carbons induced by h-BN substrate. We corroborate this surprising phenomenon by solving a tight-binding model with onsite Coulomb repulsion treated within coherent potential approximation, where hopping parameters are derived from density functional theory calculations based on the graphene/h-BN heterostructure. Our results indicate that both gapless and gapped states observed experimentally in graphene/h-BN heterostructures can be understood after a realistic value of the onsite Coulomb repulsion, as well as different interlayer distances, is taken into account. Finally, we propose ways to enhance the gapped state which is essential for potential application of graphene to next-generation electronics. Furthermore, we argue that band gap suppressed by many-body effect should happen in other van der Waals heterostructures.

Graphene on an insulating ferromagnetic substrate—ferromagnetic insulator or ferromagnetic metal with a tunnel barrier—is expected to exhibit large exchange and spin-orbit couplings due to proximity effects. We use a realistic transport model of charge-disorder scattering and solve the linearized Boltzmann equation numerically exactly for the anisotropic Fermi contours of modified Dirac electrons to find magnetotransport signatures of these proximity effects: proximity anisotropic magnetoresistance, inverse spin-galvanic effect, and the planar Hall resistivity. We establish the corresponding anisotropies due to the exchange and spin-orbit couplings, with respect to the magnetization orientation. We also present parameter maps guiding towards optimal regimes for observing transport magnetoanisotropies in proximity graphene.