Field-induced magnetic ordering in the Haldane chain compound SrNi${}_2$V${}_2$O${}_8$ and the effect of anisotropy have been investigated using single crystals. Static susceptibility, inelastic neutron scattering, high-field magnetization, and low-temperature heat-capacity studies confirm a nonmagnetic spin-singlet ground state and a gap between the singlet ground state and triplet excited states. The intrachain exchange interaction is estimated to be $J\sim 8.9\pm 0.1$ meV. Splitting of the dispersions into two modes with minimum energies 1.57 and 2.58 meV confirms the existence of single-ion anisotropy $D\left(S^z\right){}^2$. The value of $D$ is estimated to be $-0.51\pm 0.01$ meV and the easy axis is found to be along the crystallographic $c$ axis. Field-induced magnetic ordering has been found with two critical fields (${\mu }_0{H}_c^{\perp c}=12.0\pm 0.2$ T and ${\mu }_0{H}_c^{\parallel c}=20.8\pm 0.5$ T at 4.2 K). Field-induced three-dimensional magnetic ordering above the critical fields is evident from the heat-capacity, susceptibility, and high-field magnetization study. The phase diagram in the H-T plane has been obtained from the high-field magnetization. The observed results are discussed in the light of theoretical predictions as well as earlier experimental reports on Haldane chain compounds.

We report on optical transmission spectroscopy of the Cr-based frustrated triangular antiferromagnets CuCrO${}_2$ and $\alpha$-CaCr${}_2$O${}_4$, and the spinels CdCr${}_2$O${}_4$ and ZnCr${}_2$O${}_4$ in the near-infrared to visible-light frequency range. We explore the possibility to search for spin correlations far above the magnetic ordering temperature and for anomalies in the magnon lifetime in the magnetically ordered state by probing exciton-magnon sidebands of the spin-forbidden crystal-field transitions of the Cr${}^{3+}$ ions (spin $S=3/2$). In CuCrO${}_2$ and $\alpha$-CaCr${}_2$O${}_4$ the appearance of fine structures below $T_{\text{N}}$ is assigned to magnon sidebands by comparison with neutron-scattering results. The temperature dependence of the linewidth of the most intense sidebands in both compounds can be described by an Arrhenius law. For CuCrO${}_2$ the sideband associated with the ${}^4{A}_{\mathsf{2}}\to {}^2{T}_{\mathsf{2}}$ transition can be observed even above $T_{\text{N}}$. Its linewidth does not show a kink at the magnetic ordering temperature and can alternatively be described by a $Z_2$ vortex scenario proposed previously for similar materials. The exciton-magnon features in $\alpha$-CaCr${}_2$O${}_4$ are more complex due to the orthorhombic distortion. While for CdCr${}_2$O${}_4$ magnon sidebands are identified below $T_{\text{N}}$ and one sideband excitation is found to persist across the magnetic ordering transition, only a weak fine structure related to magnetic ordering has been observed in ZnCr${}_2$O${}_4$.

We compare ground-state energies by variational Monte Carlo of the spin unpolarized Halperin 331 and the spin polarized Moore-Read (MR) Pfaffian fractional quantum Hall states at half filling of the lowest Landau level (LLL) and the second Landau level (SLL) as a function of small deviations around the Coulomb point via the finite-thickness effect and direct alterations to the the first two Haldane pseudopotentials. In the comparison we find that in the LLL, either the 331 state or the MR Pfaffian may be lower in energy depending on the deviations. In the SLL, however, the MR Pfaffian is consistently lower in energy except for large deviations. These results suggest that even under moderate deviations in the interaction potential (through various physical processes such as finite thickness, Landau-level mixing, etc.), the MR Pfaffian description is more energetically favorable than the Halperin 331 state in the half-filled SLL (i.e., $\nu =5/2$), consistent with recent experimental investigations.

We study the temperature dependence as well as anisotropy of optical conductivity (${\sigma }_1$) in the pseudocubic single crystal Pr${}_{0.5}$Ca${}_{1.5}$MnO${}_4$ using spectrocopic ellipsometry. Three transition temperatures are observed and can be linked to charge-orbital ($T_{\mathrm{CO}/\mathrm{OO}}\sim$320 K), two-dimensional-antiferromagnetic (2D-AFM) ($\sim$200 K), and three-dimensional AFM ($T_{\mathrm{N}}\sim$125 K) orderings. Below $T_{\mathrm{CO}/\mathrm{OO}}$, ${\sigma }_1$ shows a charge-ordering peak ($\sim$0.8 eV) with a significant blue shift as the temperature decreases. Calculations based on a model that incorporates a static Jahn-Teller distortion and assumes the existence of a local charge imbalance between two different sublattices support this assignment and explain the blue shift. This view is further supported by the partial spectral weight analysis showing the onset of optical anisotropy at $T_{\mathrm{CO}/\mathrm{OO}}$ in the charge-ordering region (0.5–2.5 eV). Interestingly, in the charge-transfer region (2.5–4 eV), the spectral weight shows anomalies around the $T_{2\mathrm{D}-\mathrm{AFM}}$ that we attribute to the role of oxygen-$p$ orbitals in stabilizing the CE-type magnetic ordering. Our result shows the importance of spin, charge, orbital, and lattice degrees of freedom in this layered manganite.

We present first-principles calculations of the nontrivial surface states and their spin textures in the topological crystalline insulator SnTe. The surface state dispersion on the [001] surface exhibits four Dirac cones centered along the intersection of the mirror plane and the surface plane. We propose a simple model of two interacting coaxial Dirac cones to describe both the surface state dispersion and the associated spin texture. The out-of-plane spin polarization is found to be zero due to the crystalline and time-reversal symmetries. The in-plane spin texture shows helicity with some distortion due to the interaction of the two coaxial Dirac cones, indicating a nontrivial mirror Chern number of $-2$, distinct from the value of $-1$ in a $Z_2$ topological insulator such as Bi/Sb alloys or Bi${}_2$Se${}_3$. The surface state dispersion and its spin texture would provide an experimentally accessible signature for determining the nontrivial mirror Chern number.

The problem of two-dimensional, independent electrons subject to a periodic potential and a uniform perpendicular magnetic field unveils surprisingly rich physics, as epitomized by the fractal energy spectrum known as Hofstadter's butterfly. It has hitherto been addressed using various approximations rooted in either the strong potential or the strong field limiting cases. Here, we report calculations of the full spectrum of the single-particle Schrödinger equation without further approximations. Our method is exact, up to numerical precision, for any combination of potential and uniform field strength. We first study a situation that corresponds to the strong potential limit, and compare the exact results to the predictions of a Hofstadter-like model. We then go on to analyze the evolution of the fractal spectrum from a Landau-like nearly free electron system to the Hofstadter tight-binding limit by tuning the amplitude of the modulation potential.

Hard x-ray photoemission studies of Ca${}_3$(Ru${}_{1-x}$Ti${}_x$)${}_2$O${}_7$ with $x$ $=$ 0, 0.003, and 0.005 have been carried out to clarify the origin of the extremely high sensitivity of the metal-insulator (M-I) transition to the amount of Ti substitution. All the compounds show an antiferromagnetic transition followed by a structural transition at a temperature $T_{\mathrm{S}}$, with decreasing temperature. For $x$ > 0, the structural transition is accompanied with a drastic M-I transition and the intensities of the screened peaks in the Ru 3$d$ core-level spectra are significantly reduced below $T_{\mathrm{S}}$. The spectral weight of the valence band is concurrently shifted toward the higher binding energy side by an order of 2 eV, which shows that a strong electron correlation plays an essential role for the M-I transition at $T_{\mathrm{S}}$ for $x$ > 0. These results provide strong evidence that Mott transition is induced by a minute amount of the Ti substitution in Ca${}_3$Ru${}_2$O${}_7$.

We study the effect of transition-metal intercalation of graphene on the formation of a two-dimensional topological insulator with experimentally measurable edge states. Our first-principles calculations reveal that the spin-orbit-coupling (SOC) gap in Re-intercalated graphene on SiC(0001) substrate can be as large as 100 meV. This value is five orders of magnitude larger than that of pristine graphene. A similar effect should also exist in Mn- or Tc-intercalated graphene. A tight-binding model Hamiltonian analysis establishes the role of orbital coupling between graphene $p$ states and transition-metal $d$ states on the formation of the SOC gap. Remarkably, the gap can be larger than atomic SOC, as is the case for Mn. This finding opens the possibility of designing topological insulators comprised of only relatively light elements. Our study also reveals that the presence of the substrate should induce a splitting between the $K$ and $K^{\prime }$ valleys with the potential to integrate spintronics with valleytronics.

We describe a method for deriving effective low-energy theories of electronic interactions at graphene edges. Our method is applicable to general edges of honeycomb lattices (zigzag, chiral, and even disordered) as long as localized low-energy states (edge states) are present. The central characteristic of the effective theories is a dramatically reduced number of degrees of freedom. As a consequence, the solution of the effective theory by exact diagonalization is feasible for reasonably large ribbon sizes. The quality of the involved approximations is critically assessed by comparing the correlation functions obtained from the effective theory with numerically exact quantum Monte-Carlo calculations. We discuss effective theories of two levels: a relatively complicated Fermionic edge state theory and a further reduced Heisenberg spin model. The latter theory paves the way to an efficient description of the magnetic features in long and structurally disordered graphene edges beyond the mean-field approximation.

We present an efficient method for calculating the prefactors of harmonic transition state theory rates. We reformulate the prefactors in terms of the density of states (DOS) of the Hessian matrices at the basin minimum and the saddle point. The DOS is then approximated using the kernel polynomial method as an expansion in terms of Chebyshev polynomials. The cost of the calculation scales linearly with the number of atoms, in contrast with the cubic scaling of the direct method. This approach hence greatly facilitates the investigations of kinetic processes in very large systems. We demonstrate the method by calculating the prefactors of the transition rates for two processes in bulk silver: vacancy hopping and Frenkel pair formation.

Stick-slip phenomenon is generally associated with a wide range of dynamical systems. Here we report a unique quasistatic form of the stick-slip characterized in terms of bursts in structural relaxation. This is demonstrated for the case of a dislocation core and its one-dimensional representation, namely, the Frenkel-Kontorova chain. The correspondence between these two is also established through the technique of dimensionality reduction.

We present measurements of thermal transport in 500-nm-thick, 35-$\mu$m-wide, and 806-$\mu$m-long micromachined suspended silicon nitride (Si-N) bridges over the temperature range of 77 to 325 K. The measured thermal conductivity of Si-N (for material grown by low-pressure chemical vapor deposition in two different furnaces) deviates somewhat from previously reported measurements and also shows surprising dependence on surface variation at these relatively high temperatures. Addition of discontinuous gold films causes the thermal conductance of Si-N bridges to drop through the entire measured temperature range, before rising again when thicker, continuous films are added. Similar effects occur when continuous but very low-thermal-conductivity alumina films are deposited. The reduction in thermal conductance upon modification of the Si-N surface is strong evidence that vibrational excitations with long mean free paths carry significant heat even at these high temperatures. By measuring a series of film thicknesses the surface-scattering effects can be mitigated, and the resulting experimental values of the thermal conductivity of alumina and Au thin films compare very well to known values or to predictions of the Wiedemann-Franz law. We also present a modified model for the phonon mean free path in thin-film geometries, and use it along with atomic force microsope scans to show that a very small population of phonons with mean free path on the order of 1 $\mu$m and wavelength much longer than the expected thermal wavelengths carry up to $50\%$ of the heat in Si-N at room temperature.

The hole-doped kagome lattice of Cu${}^{2+}$ ions in LaCuO${}_{2.66}$ was investigated by nuclear quadrupole resonance, electron spin resonance, electrical resistivity, bulk magnetization, and specific-heat measurements. For temperatures above $\sim 180$ K, the spin and charge properties show an activated behavior suggestive of a narrow-gap semiconductor. At lower temperatures, the results indicate an insulating ground state which may or may not be charge ordered. While the frustrated spins in remaining patches of the original kagome lattice might not be directly detected here, the observation of coexisting nonmagnetic sites, free spins, and frozen moments reveals an intrinsically inhomogeneous magnetism. Numerical simulations of a $\frac{1}{3}$-diluted kagome lattice rationalize this magnetic state in terms of a heterogeneous distribution of cluster sizes and morphologies near the site-percolation threshold.

We investigated the magnetic-field-induced phases of a typical three-dimensional frustrated magnet, CdCr${}_2$O${}_4$, in magnetic fields of up to 120 T using both the electromagnetic induction method and magneto-optical spectroscopy of the $d$-$d$ transitions and the exciton-magnon-phonon transitions. Anomalies were observed in the magneto-optical absorption intensity as well as the differential magnetization prior to a fully polarized magnetic phase, revealing a magnetic phase associated with changes in both the crystal and magnetic structures accompanied by the first-order phase transition. A magnetic superfluid state, such as an umbrella-like magnetic structure or a spin-nematic state, is proposed as a candidate for this phase, which is found universally in the series of chromium spinel oxides, $A$Cr${}_2$O${}_4$ ($A$ $=$ Zn, Cd, Hg).

The iron-rich intermetallics $R_2$Fe${}_{17}$ (where $R$ is a rare-earth element) proved unamenable to anisotropy control via interstitial doping. There is only one precedent, Sm${}_2$Fe${}_{17}$N${}_{3-\delta }$ (Sm${}_2$Fe${}_{17}$C${}_{3-\delta }$), where interstitial modification has stabilized an easy-axis anisotropy at all temperatures up to $T_{\mathrm{C}}$. All previous attempts to prepare a usable easy-axis $R_2$Fe${}_{17}$ hydride have failed. Now we have succeeded in preparing a high-quality single-phase Tb${}_2$Fe${}_{17}$H${}_3$ single crystal, which has the required easy-axis anisotropy between 0 K and $T_{\mathrm{C}}$ $=$ 560 K. At $T$ $=$ 300 K, Tb${}_2$Fe${}_{17}$H${}_3$ has the spontaneous magnetic moment $M_{\mathrm{s}}$ of 22.5 μ${}_{\mathrm{B}}$ per formula unit and anisotropy field μ${}_0$$H_{\mathrm{a}}$ of 2.5 T. The main mechanism stabilizing the easy-axis anisotropy in hydrides is the same as in other similar compounds by way of boosting the leading crystal field parameter $A_{20}$. Terbium is rather special in having the Stevens factors such that ${\alpha }_J$ < 0 and ${\beta }_J$ > 0, which is why the easy-axis anisotropy in Tb${}_2$Fe${}_{17}$ hydrides is also assisted by the fourth-order parameter $A_{40}$. This proves a decisive advantage over the compounds with $R$ $=$ Pr, Nd, Dy, or Ho where ${\beta }_J$ < 0 and $A_{40}$ is a hindrance.

The $4f$-electron system YbAl${}_3$C${}_3$ with a nonmagnetic spin-dimer ground state has been studied by neutron diffraction in an applied magnetic field. A long-range magnetic order involving both ferromagnetic and antiferromagnetic components has been revealed above the critical field $H_C\sim 6$ T at temperature $T=0.05$ K. The magnetic structure indicates that the geometrical frustration of the prototype hexagonal lattice is not fully relieved in the low-temperature orthorhombic phase. The suppression of magnetic ordering by the remanent frustration is the key factor stabilizing the nonmagnetic singlet ground state in zero field. Temperature-dependent measurements in the applied field $H=12$ T revealed that the long-range ordering persists up to temperatures significantly higher than the spin gap, indicating that this phase is not directly related to the singlet-triplet excitation. Combining our neutron diffraction results with the previously published phase diagram, we support the existence of an intermediate disordered phase as the first excitation from the nonmagnetic singlet ground state. Based on our results, we propose YbAl${}_3$C${}_3$ as a material for studying the quantum phase transitions of heavy-fermion metals under the influence of geometrical frustration.

We study and classify the proximity-induced superconducting pairing in a topological insulator (TI)-superconductor (SC) hybrid structure for SCs with different symmetries. The Dirac surface state gives a coupling between spin-singlet and spin-triplet pairing amplitudes as well as pairing that is odd in frequency for $p$-wave SCs. We also find that all SCs induce pairing that is odd in both frequency and orbital (band) index, with oddness in frequency and orbital index being completely interchangeable. The different induced pairing amplitudes significantly modify the density of states in the TI surface layer.

Using first-principles methods based on density-functional theory, we investigate the spin relaxation in W(001) ultrathin films. Within the framework of the Elliott-Yafet theory, we calculate the spin mixing of the Bloch states and we explicitly consider spin-flip scattering off self-adatoms. At small film thicknesses, we find an oscillatory behavior of the spin-mixing parameter and relaxation rate as a function of the film thickness, which we trace back to surface-state properties. We also analyze the Rashba effect experienced by the surface states and discuss its influence on the spin relaxation. Finally, we calculate the anisotropy of the spin-relaxation rate with respect to the polarization direction of the excited spin population relative to the crystallographic axes of the film. We find that the spin-relaxation rate can increase by as much as 27$\%$ when the spin polarization is directed out of plane, compared to the case when it is in plane. Our calculations are based on the multiple-scattering formalism of the Korringa-Kohn-Rostoker Green-function method.

The half-doped Pr${}_{0.5}$Sr${}_{0.5}$MnO${}_3$ (PSMO) manganite represents a unique stripe type of charge orbital order that induces transport and magnetic anisotropy. Low-energy charge dynamics in PSMO (110) epitaxial film were investigated along and across two dissimilar in-plane orthogonal axes, [1-10] and [001], by recording the complex refractive index in the energy range of 1–7 meV. We report a novel observation of a gradual crossover from Drude-like metallic conductivity to charge-density-wave (CDW)–like collective excitations as the polarized terahertz excitation field is swept across the orthogonal in-plane axes. This is a rare manifestation of a CDW mode in a highly conducting stripe-type charge-ordered (CO) system, which is fundamentally different from the CDW modes of checkerboard CO. Interestingly, the contrasting charge dynamics along orthogonal in-plane axes form an intrinsic electronic switch, apparently a consequence of the unique CO of PSMO.

We present results for magnetic excitations in doped copper oxides using the random phase approximation and itinerant electrons. In the [1,0] direction the observed excitations resemble dispersive quasiparticles both in the normal and in the superconducting state, similarly to recent resonant inelastic x-ray scattering experiments. In the [1,1] direction the excitations form, except for the critical region near the antiferromagnetic wave vector $\mathbf{Q}=(\pi ,\pi )$, only very broad continua. Using the obtained spin propagators we calculate electron self-energies and their effects on electronic Raman spectra. We show that the recently observed additional peak at about twice the pair breaking in $B_{1g}$ symmetry below $T_c$ in HgBa${}_2$CuO${}_{4+\delta }$ can be explained as a self-energy effect where a broken Cooper pair and a magnetic excitation appear as final states. The absence of this peak in $B_{2g}$ symmetry, which probes mainly electrons near the nodal direction, is explained by their small self-energies compared to those in the antinodal direction.