In their Comment, Refson et al. criticize the use of the “frozen-core” approximation for the Ti $3s$ and $3p$ semicore states in our Brief Report [Phys. Rev. B 84, 132105 (2011)], and they dispute whether the methods employed by us are capable of supporting our conclusions. In this Reply we summarize the main features of our work and we show that indeed none of the conclusions of our Brief Report are affected by the frozen-core treatment of the Ti semicore states. The criticism of Refson et al. seems to be based mostly on a misinterpretation what the main goal of our study is and what the main conclusions of our work are. While the detailed comparison between different pseudopotentials containing different numbers of valence electrons presented in the comment by Refson et al. is very interesting and instructive in its own right, it has no consequences regarding the validity of our work.

Recent experiments have shown that the perovskite to post-perovskite phase transformation in CaIrO${}_3$ occurs more readily at room temperature when a shear stress is applied as compared to isotropic pressure. To understand this mechanistically, we have calculated the minimum-energy pathway of the phase transition with density functional theory under different pressure conditions with the generalized solid-state nudged elastic band method. Our results reveal that shear stress significantly lowers the barrier and stabilizes the product state while isotropic pressure initially raises the barrier and only reduces the barrier at pressures above 90 GPa. The nonmonotonic change in barrier with isotropic pressure is explained in terms of an increase in the activation volume under low pressure and a decrease under high pressure.

We study the temperature dependence of the pressure-induced softening in the negative thermal expansion material Zn(CN)${}_2$ using neutron powder diffraction and molecular dynamics simulations. Both the simulation and experiment show that the pressure-induced softening only occurs above a minimum temperature and also weakens at high temperatures.

Using first-principles calculations we demonstrate sizable exchange coupling between a magnetic molecule and a magnetic substrate via a graphene layer. As a model system we consider cobaltocene (CoCp${}_2$) adsorbed on graphene deposited on Ni(111). We find that the magnetic coupling is antiferromagnetic and is influenced by the molecule structure, the adsorption geometry, and the stacking of graphene on the substrate. We show how the coupling can be tuned by the intercalation of a magnetic monolayer, such as Fe or Co, between graphene and Ni(111). We identify the leading mechanism responsible for the coupling to be the spatial and energy matching of the frontier orbitals of CoCp${}_2$ and graphene close to the Fermi level. Graphene plays the role of an electronic decoupling layer while allowing effective spin communication between molecule and substrate.

The barrier transmission characteristics of a one-dimensional chain of optically linear split-ring resonators (SRRs) containing a barrier composed of optically nonlinear split-ring resonators are studied. (This is an analogy to the quantum mechanical problem of the resonant transmission of a particle through a finite barrier potential.) The SRRs are idealized as inductor-resistor-capacitor-equivalent resonator circuits where the capacitance is either from a linear dielectric medium (optically linear SRRs) or from a Kerr-type nonlinear dielectric medium (optically nonlinear SRRs). The SRRs are arrayed in a one-dimensional chain and interact with one another through weak nearest-neighbor mutually inductive couplings. The transmission maxima of the SRR barrier problem are studied as they are located in a two-dimensional parameter space characterizing the linear mutually inductive coupling and the nonlinear Kerr dielectric of the SRRs of the barrier. The result is a two-dimensional map giving the conditions for the existence of the resonant-barrier modes that are excited in the transmission process. The various lines of transmission maxima in the two-dimensional plot are associated with different types of resonant excitations in the barrier. The map is similar to one recently made in McGurn [Phys. Rev. B 77, 115105 (2008)] for the resonant-transmission modes of a nonlinear barrier in a photonic crystal waveguide. The SRR problem, however, is quite different from the photonic crystal problem as the nonlinear difference equations of the two systems are different in the nature of their nonlinear interactions. Consequently, the results for the two systems are briefly compared. The transmission maxima of the SRR system occur along lines in the two-dimensional plot, which are associated with modes resonantly excited in the barrier. These lines of resonant modes either originate as a simple evolution from the resonant modes of the linear barrier limit or as lines of soliton breather modes of the bright, dark, or gray types. The soliton modes arise either spontaneously at a lower critical value of the nonlinearity of the barrier media or from the breakup of a barrier mode in the linear media limit as the barrier media become increasingly nonlinear. The soliton resonances are identified by comparing the wave functions and energies of the barrier excitations with those of solitons in an infinite chain composed of barrier material. Results for the infinite chain in Giri, Choudhary, Gupta, Bandyopadhyay, and McGurn [Phys. Rev. B 84, 155429 (2011)] for bright solitons are used for this identification, and in the Appendix we present additional solutions for dark and gray solitons that were not included in our previous treatments.

Transport dimensionality of Ti $d$ electrons in (LaTiO${}_3$)${}_1$/(SrTiO${}_3$)${}_N$ superlattices has been investigated using density functional theory with local spin-density approximation + $U$ method. Different spatial distribution patterns have been found between Ti $t_{2g}$ orbital electrons. The $d_{xy}$ orbital electrons are highly localized near interfaces due to the potentials by positively charged LaO layers, while the degenerate $d_{yz}$ and $d_{xz}$ orbital electrons are more distributed inside SrTiO${}_3$ insulators. For $N$ ≥ 3 unit cells (u.c.), the Ti $d_{xy}$ densities of state exhibit the staircaselike increments, which appear at the same energy levels as the $d_{xy}$ flat bands along the Γ-$Z$ direction in band structures. The $k_z$-independent discrete energy levels indicate that the electrons in $d_{xy}$ flat bands are two-dimensional electron gases (2DEGs) which can transport along interfaces, but they cannot transport perpendicularly to interfaces due to the confinements in the potential wells by LaO layers. Unlike the $d_{xy}$ orbital electrons, the $d_{yz}$ and $d_{xz}$ orbital electrons have three-dimensional (3D) transport characteristics, regardless of SrTiO${}_3$ thicknesses. The 2DEG formation by $d_{xy}$ orbital electrons, when $N$ ≥ 3 u.c., indicates the existence of critical SrTiO${}_3$ thickness where the electron transport dimensionality starts to change from 3D to 2D in (LaTiO${}_3$)${}_1$/(SrTiO${}_3$)${}_N$ superlattices.

We develop a theoretical description of the spin dynamics of resident holes in a $p$-doped semiconductor quantum well (QW) subject to a magnetic field slightly tilted from the Voigt geometry. We find the expressions for the signals measured in time-resolved Faraday rotation (TRFR) and resonant spin amplification (RSA) experiments and study their behavior for a range of system parameters. We find that an inversion of the RSA peaks can occur for long hole spin dephasing times and tilted magnetic fields. We verify the validity of our theoretical findings by performing a series of TRFR and RSA experiments on a $p$-modulation doped GaAs/Al${}_{0.3}$Ga${}_{0.7}$As single QW and showing that our model can reproduce experimentally observed signals.

We report on investigations of optical carrier generation in silicon nanocrystals embedded in an SiO${}_2$ matrix. Carrier relaxation and recombination processes are monitored by means of time-resolved induced absorption, using a conventional femtosecond pump-probe setup for samples containing different average sizes of nanocrystals ($d_{\mathrm{NC}}$ $=$ 2.5–5.5 nm). The electron-hole pairs generated by the pump pulse are probed by a second pulse over a broad spectral range ($E_{\mathrm{probe}}$ $=$ 0.95–1.35 or 1.6–3.25 eV), by which information on excited states is obtained. Under the same excitation conditions, we observe that the induced absorption intensity in the near-infrared range is a factor of $\sim$10 higher than in the visible range. To account for these observations, we model the spectral dependence of the induced absorption signal using an empirical $s{p}^3{d}^5{s}^{*}$ tight-binding technique, by which the spectrum can be well reproduced up to a certain threshold. For probe photon energies above this threshold (dependent on nanocrystal size), the induced absorption signal is found to feature a long-standing component, whereas the induced absorption signal for probe photon energies below this value vanishes within 0.5 ns. We explain this by self-trapping of excitons on surface-related states.

We investigate by means of the time-dependent Gutzwiller variational approach the out-of-equilibrium dynamics of an antiferromagnetic state evolved with the Hubbard model Hamiltonian after a sudden change of the repulsion strength $U$. We find that magnetic order survives more than what is expected on the basis of thermalization arguments, in agreement with recent dynamical mean field theory calculations. In addition, we find evidence of a dynamical transition for quenches to large values of $U$ between a coherent antiferromagnet characterized by a finite quasiparticle residue to an incoherent one with vanishing residue, which finally turns into a paramagnet for even larger $U$.

A subtle relation between quantum Hall physics and the phenomenon of pairing is unveiled. By use of second quantization, we establish a connection between (i) a broad class of rotationally symmetric two-body interactions within the lowest Landau level and (ii) integrable hyperbolic Richardson-Gaudin-type Hamiltonians that arise in $(p_x+i{p}_y)$ superconductivity. Specifically, we show that general Haldane pseudopotentials (and their sums) can be expressed as a sum of repulsive noncommuting $(p_x+i{p}_y)$-type pairing Hamiltonians. The determination of the spectrum and individual null spaces of each of these noncommuting Richardson-Gaudin-type Hamiltonians is nontrivial yet is Bethe ansatz solvable. For the Laughlin sequence, it is observed that this problem is frustration free and zero-energy ground states lie in the common null space of all of these noncommuting Hamiltonians. This property allows for the use of a new truncated basis of pairing configurations in which to express Laughlin states at general filling factors. We prove separability of arbitrary Haldane pseudopotentials, providing explicit expressions for their second quantized forms, and further show by explicit construction how to exploit the topological equivalence between different geometries (disk, cylinder, and sphere) sharing the same topological genus number, in the second quantized formalism, through similarity transformations. As an application of the second quantized approach, we establish a “squeezing principle” that applies to the zero modes of a general class of Hamiltonians, which includes but is not limited to Haldane pseudopotentials. We also show how one may establish (bounds on) “incompressible filling factors” for those Hamiltonians. By invoking properties of symmetric polynomials, we provide explicit second quantized quasihole generators; the generators that we find directly relate to bosonic chiral edge modes and further make aspects of dimensional reduction in the quantum Hall systems precise.

Modeling point defects at an atomic scale requires careful treatment of the long-range atomic relaxations. This elastic field can strongly affect point defect properties calculated in atomistic simulations because of the finite size of the system under study. This is an important restriction for ab initio methods which are limited to a few hundred atoms. We propose an original approach coupling ab initio calculations and linear elasticity theory to obtain the properties of an isolated point defect for reduced supercell sizes. The reliability and benefit of our approach are demonstrated for three problematic cases: the self-interstitial in zirconium, clusters of self-interstitials in iron, and the neutral vacancy in silicon.

GdSi exhibits spin-density-wave (SDW) order arising from the cooperative interplay of sizeable local moments and a partially nested Fermi sea of itinerant electrons. Using magnetotransport, magnetization, and nonresonant magnetic x-ray diffraction techniques, we determine the H-T phase diagrams of GdSi for magnetic fields up to 21 T, where antiferromagnetic order is no longer stable, and field directions along each of the three major crystal axes. While the incommensurate magnetic ordering vector that characterizes the SDW is robust under magnetic field, the multiple spin structures of this compound are highly flexible and rotate relative to the applied field via either canting or spin-flop processes. The antiferromagnetic spin densities always arrange themselves transverse to the applied magnetic field direction. The phase diagrams are delineated by two types of phase boundaries: one separates a collinear from a planar spin structure associated with a lattice structural transition, and the other defines a spin flop transition that is only weakly temperature dependent. The major features of the phase diagrams along each of the crystal axes can be explained by the combination of local moment and global Fermi surface physics at play.

We studied the electronic structure of a Shastry-Sutherland lattice system, HoB${}_4$ employing high-resolution photoemission spectroscopy and ab initio band-structure calculations. The surface and bulk borons exhibit subtle differences and loss of boron compared to the stoichiometric bulk. However, the surface and bulk conduction bands near Fermi level are found to be similar. Evolution of the electronic structure with temperature is found to be similar to that observed in a typical charge-disordered system. A sharp dip is observed at the Fermi level in the low-temperature spectra revealing a signature of antiferromagnetic gap. Asymmetric spectral weight transfer with temperature manifests particle-hole asymmetry that may be related to the exotic properties of these systems.

We present a micromagnetic analysis of spin-wave propagation in a magnonic crystal realized as a permalloy spin-wave waveguide with a spatial periodical variation of its saturation magnetization. Frequency band gaps were clearly observed in the spin-wave transmission spectra, and their origin is traced back to an overlap of individual band gaps of the fundamental and higher-order spin-wave width modes. The control of the depth, width, and position in frequency and space of the rejection band gaps by the width areas with a reduced magnetization and by the modulation level is discussed in this study.

$M$-doped IrTe${}_2$ ($M$ = Mn, Fe, Co, Ni) compounds were synthesized by solid-state reaction. Single crystal x-ray diffraction experiments indicate that part of the doped $M$ ions ($M$ = Fe, Co, and Ni) substitute for Ir, and the rest intercalate into the octahedral interstitial sites located in between IrTe${}_2$ layers. Due to the lattice mismatch between MnTe${}_2$ and IrTe${}_2$, Mn has limited solubility in IrTe${}_2$ lattice. The trigonal structure is stable in the whole temperature range 1.80 K$\le$ $T$ $\le$ 300 K for all doped compositions. No long-range magnetic order or superconductivity was observed in any doped compositions above 1.80 K. A spin glass behavior below 10 K was observed in Fe-doped IrTe${}_2$ from the temperature dependence of magnetization, electrical resistivity, and specific heat. The low temperature specific heat data suggest the electron density of states is enhanced in Fe- and Co-doped compositions but reduced in Ni-doped IrTe${}_2$. With the 3$d$ transition metal doping the trigonal $a$-lattice parameter increases but the $c$-lattice parameter decreases. Detailed analysis of the single crystal x-ray diffraction data shows that interlayer Te-Te distance increases despite a reduced $c$ lattice. The importance of the Te-Te, Te-Ir, and Ir-Ir bonding is discussed.

The resistivity vs temperature of annealed and unannealed single crystals of Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ over a broad range of nominal compositions between $x$ $=$ 0.05 and 0.30, with special focus on compositions around that ($x_{\mathrm{opt}}$) of the optimal superconducting transition temperature, is reported. Above any transition temperature, either superconducting ($T_c$) or structural ($T_S$) for $x$ < $x_{\mathrm{opt}}$, the low temperature resistivity, ρ, behaves approximately linearly with temperature from $x$ $=$ 0.05 up to at least $x$ $=$ 0.095, with $\rho \propto T^2$ starting for $x$ $=$ 0.14. The apparent constancy of the temperature dependence over a broad composition range argues strongly for the presence of a quantum critical point (QCP) underneath the superconducting dome. However, the temperature dependences measured down to $T_c$ leave the exact location of the QCP open. Interestingly, although the superconducting transition temperature rises by ≈1.5 K with annealing, the temperature dependence of ρ appears unaffected by annealing, i.e., the QCP appears insensitive to small amounts of lattice disorder.

We study superconductivity in a Weyl semimetal with broken time-reversal symmetry and stabilized by a point-group symmetry. The resulting superconducting phase is characterized by topologically protected bulk nodes and surface states with Fermi arcs. The topological invariant governing the system is calculated using changes in eigenvalues of the point-group operator along high-symmetry momentum lines. We show that this invariant is determined by the Fermi surface topology of the Weyl semimetal. We discuss the effect of surface orientation and $C_4$-breaking strain as possible experimental consequences.

We have measured the relaxation of charge-density waves in chromium from out-of-equilibrium states achieved through rapid thermal quenching. Although pinned density waves have been predicted to relax through stick-slip dynamics, in which long-lived metastable states are linked by abrupt rearrangements of the microscopic structure, these microscopic behaviors have not been observed. Using synchrotron x rays, we have measured metastability of the order parameter and microscopic pinning phenomena including an avalanche of the charge-density wave phase. Molecular dynamical simulations based on the Fukuyama-Lee-Rice model show that these behaviors may be attributed to nucleation, pinning, and propagation of phase solitons.

The superconductor Sn${}_{1-x}$In${}_x$Te is a doped topological crystalline insulator and has become important as a candidate topological superconductor, but its superconducting phase diagram is poorly understood. By measuring about 50 samples of high-quality, vapor-grown single crystals, we found that the dependence of the superconducting transition temperature $T_c$ on the In content $x$ presents a qualitative change across the critical doping $x_c\simeq 3.8\%$, at which a structural phase transition takes place. Intriguingly, in the ferroelectric rhombohedral phase below the critical doping, $T_c$ is found to be strongly enhanced with impurity scattering. It appears that the nature of electron pairing changes across $x_c$ in Sn${}_{1-x}$In${}_x$Te.

Thermal fluctuations of nanomagnets driven by spin-polarized currents are treated via the Landau-Lifshitz-Gilbert equation generalized to include both the random thermal noise field and the Slonczewski spin-transfer torque term. By averaging this stochastic (Langevin) equation over its realizations, the explicit infinite hierarchy of differential-recurrence relations for statistical moments (averaged spherical harmonics) is derived for arbitrary demagnetizing factors and magnetocrystalline anisotropy for the generic nanopillar model of a spin-torque device comprising two ferromagnetic strata representing the free and fixed layers and a nonmagnetic conducting spacer all sandwiched between two ohmic contacts. The influence of thermal fluctuations and spin-transfer torques on relevant switching characteristics, such as the stationary magnetization, the magnetization reversal time, etc., is calculated by solving the hierarchy for wide ranges of temperature, damping, external magnetic field, and spin-polarized current, indicating new spin-torque effects in the thermally assisted magnetization reversal comprising several orders of magnitude. In particular, a pronounced dependence of the switching characteristics on the directions of the external magnetic field and the spin polarization exists.