The wave-vector $\left(\mathbf{q}\right)$ and doping $\left(x,y\right)$ dependences of the magnetic energy, iron moment, and effective exchange interactions in ${\text{LaFeAsO}}_{1-x}{\text{F}}_x$ and ${\text{Ba}}_{1-2y}{\text{K}}_{2y}{\text{Fe}}_2{\text{As}}_2$ are studied by self-consistent LSDA calculations for co-planar spin spirals. For the undoped compounds $\left(x=0,y=0\right)$, the minimum of the calculated total energy, $E\left(\mathbf{q}\right)$, is for $\mathbf{q}$ corresponding to stripe antiferromagnetic order. Already at low levels of electron doping $\left(x\right)$, this minimum becomes flat in ${\text{LaFeAsO}}_{1-x}{\text{F}}_x$ and for $x\gtrsim 5\%$, it shifts to an incommensurate $\mathbf{q}$. In ${\text{Ba}}_{1-2y}{\text{K}}_{2y}{\text{Fe}}_2{\text{As}}_2$, stripe order remains stable for hole doping up to $y=0.3$. These results are explained in terms of the band structure. The magnetic interactions cannot be accurately described by a simple classical Heisenberg model and the effective exchange interactions fitted to $E\left(\mathbf{q}\right)$ depend strongly on doping. The doping dependence of the $E\left(\mathbf{q}\right)$ curves is compared with that of the noninteracting magnetic susceptibility for which similar trends are found.

We demonstrate that dislocations in the graphene lattice give rise to electron Berry phases equivalent to quantized values $\left\{0,\pm \frac{1}{3}\right\}$ in units of the flux quantum but with an opposite sign for the two valleys. An elementary scale consideration of a graphene Aharonov-Bohm ring equipped with valley filters on both terminals, encircling a dislocation, says that in the regime where the intervalley mean-free path is large compared to the intravalley phase coherence length, such that the valley quantum numbers can be regarded as conserved on the relevant scale, the coherent valley-polarized currents sensitive to the topological phases have to traverse the device many times before both valleys contribute, and this is not possible at intermediate temperatures where the latter length becomes of the order of the device size, thus leading to an apparent violation of the basic law of linear transport that magnetoconductance is even in the applied flux. We discuss this discrepancy in the Feynman path picture of dephasing when addressing the transition from quantum to classical dissipative transport. We also investigate this device in the scattering matrix formalism, accounting for the effects of decoherence by the Büttiker dephasing voltage probe type model which conserves the valleys, where the magnetoconductance remains even in the flux, also when different decoherence times are allowed for the individual, time-reversal connected, valleys.

We present a comprehensive study of the dynamical properties of the quantum Heisenberg antiferromagnet on a triangular lattice within the framework of spin-wave theory. The distinct features of spin-wave excitations in the triangular lattice antiferromagnet are (i) finite lifetime at zero temperature due to spontaneous two-magnon decays, (ii) strong renormalization of magnon energies ${\epsilon }_{\mathbf{k}}$ with respect to the harmonic result, and (iii) logarithmic singularities in the decay rate ${\Gamma }_{\mathbf{k}}$. Quantum corrections to the magnon spectrum are obtained using both the on-shell and off-shell solutions of the Dyson equation with the lowest-order magnon self-energy. At low-energies magnon excitations remain well defined albeit with the anomalous decay rate ${\Gamma }_{\mathbf{k}}\propto k^2$ at $\mathbf{k}\to 0$ and ${\Gamma }_{\mathbf{k}}\propto {\left|\mathbf{k}-{\mathbf{Q}}_{\text{AF}}\right|}^{7/2}$ at $\mathbf{k}\to {\mathbf{Q}}_{\text{AF}}$. At high energies, magnons are heavily damped with the decay rate reaching $\left(2{\Gamma }_{\mathbf{k}}/{\epsilon }_{\mathbf{k}}\right)\sim 0.3$ for the case $S=1/2$. The on-shell solution shows logarithmic singularities in ${\Gamma }_{\mathbf{k}}$ with the concomitant jumplike discontinuities in $\text{Re}\left[{\epsilon }_{\mathbf{k}}\right]$ along certain contours in the momentum space. Such singularities are even more prominent in the magnon spectral function $A\left(\mathbf{k},\omega \right)$. Although the off-shell solution removes such log singularities, the decay rates remain strongly enhanced. We also discuss the role of higher-order corrections and show that such singularities may lead to complete disappearance of the spectrum in the vicinity of certain $\mathbf{k}$ points. The kinematic conditions for two-magnon decays are analyzed for various generalizations of the triangular lattice antiferromagnet as well as for the $XXZ$ model on a kagomé lattice. Our results suggest that decays and singularities in the spin-wave spectra must be ubiquitous in all these systems. In addition, we give a detailed introduction in the spin-wave formalism for noncollinear Heisenberg antiferromagnets and calculate several quantities for the triangular lattice model including the ground-state energy and the sublattice magnetization.

In the insulating phase the cuprates exhibit long-ranged antiferromagnetic order which, however, breaks down when they are doped to become metallic. Neutron scattering data show that upon doping the width $w$ of the magnetic structure factors $S\left(\vec{q}\right)$ becomes broader and that their centers shift away from the antiferromagnetic wave vector by an amount $\delta$ which grows with increasing doping concentration. The spatial two-point spin correlation can directly be determined from $S\left(\vec{q}\right)$. Using the information available from the position and width of $S\left(\vec{q}\right)$ and assuming random spin phase distributions, we calculated the spin arrangement ${\vec{s}}_m$ in direct space. ${\vec{s}}_m$ exhibits patterns of vertical and horizontal stripes of finite length such as a two-dimensional nematic fluid. The finite length depends on the width $w$ whereas the distance between two neighboring stripes is proportional to $\delta$. Furthermore, the differences between experimental results obtained by neutron scattering and by nuclear magnetic resonance are discussed.

We propose a fully ab initio based integrated approach to determine the volume and temperature dependent free-energy surface of nonmagnetic crystalline solids up to the melting point. The approach is based on density-functional theory calculations with a controlled numerical accuracy of better than 1 meV/atom. It accounts for all relevant excitation mechanisms entering the free energy including electronic, quasiharmonic, anharmonic, and structural excitations such as vacancies. To achieve the desired accuracy of $<1\text{meV}/\text{atom}$ for the anharmonic free-energy contribution without losing the ability to perform these calculations on standard present-day computer platforms, we develop a numerically highly efficient technique: we propose a hierarchical scheme—called upsampled thermodynamic integration using Langevin dynamics—which allows for a significant reduction in the number of computationally expensive ab initio configurations compared to a standard molecular dynamics scheme. As for the vacancy contribution, concentration-dependent pressure effects had to be included to achieve the desired accuracy. Applying the integrated approach gives us direct access to the free-energy surface $F\left(V,T\right)$ for aluminum and derived quantities such as the thermal expansion coefficient or the isobaric heat capacity and allows a direct comparison with experiment. A detailed analysis enables us to tackle the long-standing debate over which excitation mechanism (anharmonicity vs vacancies) is dominant close to the melting point.

The magnetic properties of an odd spin number antiferromagnetic ring ${\text{Cr}}_8\text{Ni}$ have been investigated by high-field magnetization, specific-heat, and nuclear-magnetic-resonance measurements at very low temperatures (below 1 K). It is found that the ground state of this frustrated spin ring is a singlet state with total spin value $S_{\text{T}}=0$ and zero expectation value of the local spins. The energy-level structure for low-lying excited total spin state $S_{\text{T}}\ne 0$ shows a breakdown of the Landé interval rule in agreement with theoretical results. Evidences of sizeable Dzyaloshinski-Moriya interactions have been found in the magnetic-field dependence of low-temperature specific-heat and magnetization data.

We demonstrate the importance of thermal effects such as temperature-induced electronic, magnetic and vibrational excitations, as well as structural defects in the first-principles calculations of the magnetic critical temperature of complex alloys using half-Heusler ${\text{Ni}}_{1-x}{\text{Cu}}_x\text{MnSb}$ alloys as a case study. The thermal lattice expansion and one-electron excitations have been accounted for self-consistently in the Curie temperature calculations. In the Ni-rich region, electronic excitations, thermal expansion, and structural defects substantially decrease the calculated Curie temperature. At the same time, some defects are shown to increase $T_C$ in Cu-rich samples.

We propose a theory for the underdoped hole-doped cuprates, focusing on the “nodal-antinodal dichotomy” observed in recent experiments. Our theory begins with an ordered antiferromagnetic Fermi liquid with electron and hole pockets. We argue that it is useful to consider a quantum transition at which the loss of antiferromagnetic order leads to a hypothetical metallic “algebraic charge liquid” (ACL) with pockets of charge $-e$ and $+e$ fermions, and an emergent U(1) gauge field; the instabilities of the ACL lead to the low-temperature phases of the underdoped cuprates. The pairing instability leads to a superconductor with the strongest pairing within the $-e$ Fermi pockets, a $d$-wave pairing signature for electrons, and very weak nodal-point pairing of the $+e$ fermions near the Brillouin-zone diagonals. The influence of an applied magnetic field is discussed using a proposed phase diagram as a function of field strength and doping. We describe the influence of gauge field and pairing fluctuations on the quantum Shubnikov–de Haas oscillations in the normal states induced by the field. For the finite-temperature pseudogap region, our theory has some similarities to the phenomenological two-fluid model of $-2e$ bosons and $+e$ fermions proposed by Geshkenbein et al. [Phys. Rev. B 55, 3173 (1997)], which describes anomalous aspects of transverse transport in a magnetic field.

In underdoped cuprates, only a portion of the Fermi surface survives as Fermi arcs due to pseudogap opening. In hole-doped ${\text{La}}_2{\text{CuO}}_4$, we have deduced the “coherence temperature” $T_{\text{coh}}$ of quasiparticles on the Fermi arc above which the broadened leading edge position in angle-integrated photoemission spectra is shifted away from the Fermi level and the quasiparticle concept starts to lose its meaning. $T_{\text{coh}}$ is found to rapidly increase with hole doping, an opposite behavior to the pseudogap temperature $T^{\ast }$. The superconducting dome is thus located below both $T^{\ast }$ and $T_{\text{coh}}$, indicating that the superconductivity emerges out of the coherent Fermionic quasiparticles on the Fermi arc. $T_{\text{coh}}$ remains small in the underdoped region, indicating that incoherent charge carriers originating from the Fermi arc are responsible for the apparently metallic transport at high temperatures.

Two elastically coupled nanomechanical resonators driven independently near their resonance frequencies show intricate nonlinear dynamics. The dynamics provide a scheme for realizing a nanomechanical system with tunable frequency and nonlinear properties. For large vibration amplitudes, the system develops spontaneous oscillations of amplitude modulation that also show period-doubling transitions and chaos. The complex nonlinear dynamics are quantitatively predicted by a simple theoretical model.

We investigate the possibility of a strongly correlated fractional quantum Hall (FQH) state in bulk three-dimensional (3D) isotropic (not layered) materials. We find that a FQH state can exist at low densities only if it is accompanied by a staging transition in which the electrons reorganize themselves in layers, perpendicular to the magnetic field, at distances of the order of the magnetic length apart. The Hartree energy associated to the staging transition is off set by the correlation Fock energy of the 3D FQH state. We obtain the phase diagram of bulk electrons in a magnetic field subject to Coulomb interactions as a function of carrier density and lattice constant. At very low densities, the 3D FQH state exhibits a transition to a 3D Wigner crystal state stabilized by phonon correlations.

The origin of the unusual $90°$ ferroelectric/ferroelastic domains, consistently observed in recent studies on mesoscale and nanoscale free-standing single crystals of ${\text{BaTiO}}_3$ [Schilling et al., Phys. Rev. B 74, 024115 (2006); Schilling et al., Nano Lett. 7, 3787 (2007)], has been considered. A model has been developed which postulates that the domains form as a response to elastic stress induced by a surface layer which does not undergo the paraelectric-ferroelectric cubic-tetragonal phase transition. This model was found to accurately account for the changes in domain periodicity as a function of size that had been observed experimentally. The physical origin of the surface layer might readily be associated with patterning damage, seen in experiment; however, when all evidence of physical damage is removed from the ${\text{BaTiO}}_3$ surfaces by thermal annealing, the domain configuration remains practically unchanged. This suggests a more intrinsic origin, such as the increased importance of surface tension at small dimensions. The effect of surface tension is also shown to be proportional to the difference in hardness between the surface and the interior of the ferroelectric. The present model for surface-tension induced twinning should also be relevant for finely grained or core-shell structured ceramics.

We used polarized inelastic neutron-scattering measurements to shed light on the spin-lattice quantum entanglement in multiferroic materials. We report an evidence for hybrid elementary excitations made of a mixing between spin waves and phonons, which can be considered as multiferroic Goldstone modes. We argue that the Dzyaloshinskii-Moriya interaction could be at the origin of this hybridization.

We investigated theoretically the phonon thermal conductivity of single-layer graphene. The phonon dispersion for all polarizations and crystallographic directions in graphene lattice was obtained using the valence-force field method. The three-phonon Umklapp processes were treated exactly using an accurate phonon dispersion and Brillouin zone, and accounting for all phonon relaxation channels allowed by the momentum and energy conservation laws. The uniqueness of graphene was reflected in the two-dimensional phonon density of states and restrictions on the phonon Umklapp scattering phase-space. The phonon scattering on defects and graphene edges has also been included in the model. The calculations were performed for the Gruneisen parameter, which was determined from the ab initio theory as a function of the phonon wave vector and polarization branch, and for a range of values from experiments. It was found that the near room-temperature thermal conductivity of single-layer graphene, calculated with a realistic Gruneisen parameter, is in the range $\sim 2000–5000\text{W}/\text{mK}$ depending on the flake width, defect concentration and roughness of the edges. Owing to the long phonon mean free path the graphene edges produce strong effect on thermal conductivity even at room temperature. The obtained results are in good agreement with the recent measurements of the thermal conductivity of suspended graphene.

Heat capacity, magnetic susceptibility, NMR, and resistivity of ${\text{SrNi}}_2{\text{P}}_2$ single crystals are presented, illustrating a purely structural transition at 325 K with no magnetism. Bulk superconductivity is found at 1.4 K. The magnitude of the transition temperature $T_c$, fits to the heat-capacity data, the small upper critical field $H_{c2}=390\text{Oe}$, and Ginzburg-Landau parameter $\kappa =2.1$ suggest a conventional fully gapped superconductor. With applied pressure a second structural phase transition occurs which results in an 8% reduction in the $c/a$ ratio of lattice parameters. We find that superconductivity persists into this high-pressure phase, although the transition temperature is monotonically suppressed with increasing pressure. Comparison of these Ni-P data as well as layered Fe-As and Ni-As superconductor indicates that reduced dimensionality can be a mechanism for increasing the transition temperature.

In this article, we present a comprehensive theoretical study of solubilities of alkali (Li, Na, K, Rb, Cs) and alkaline-earth (Be, Ca, Sr, Ba) metals in the boron-rich Mg-B system. The study is based on first-principles calculations of solutes formation energies in ${\text{MgB}}_2$, ${\text{MgB}}_4$, ${\text{MgB}}_7$ alloys and subsequent statistical-thermodynamical evaluation of solubilities. The advantage of the approach consists in considering all the known phase boundaries in the ternary phase diagram. Substitutional Na, Ca, and Li demonstrate the largest solubilities, and Na has the highest (0.5%–1% in ${\text{MgB}}_7$ at $T=650–1000\text{K}$). All the considered interstitials have negligible solubilities. The solubility of Be in ${\text{MgB}}_7$ cannot be determined because the corresponding low-solubility formation energy is negative indicating the existence of an unknown ternary ground state. We have performed a high-throughput search of ground states in binary Mg-B, $\text{Mg-}A$, and $\text{B-}A$ systems, and we construct the ternary phase diagrams of $\text{Mg-B-}A$ alloys based on the stable binary phases. Despite its high-temperature observations, we find that ${\text{Sr}}_9{\text{Mg}}_{38}$ is not a low-temperature equilibrium structure. We also determine two possible ground states ${\text{CaB}}_4$ and ${\text{RbB}}_4$, not yet observed experimentally.

A suitable definition for the local potential felt by local modes in the paraelectric phase of barium titanate is proposed. It is defined as the potential of mean force (free energy) acting on a given local mode $\vec{u}$. This free energy $\tilde{F}\left(\vec{u}\right)$ is computed by constrained molecular dynamics coupled to the method of the thermodynamic integration. It is shown that this free-energy landscape is directly related to the density of probability of the local modes $\Pi \left(\vec{u}\right)$ by $\Pi \left(\vec{u}\right)={\Pi }_0{e}^{-\left[\tilde{F}\left(\vec{u}\right)-{\tilde{F}}_0\right]/k_{B}T}$. From $T_c$ to $\approx T_c+400\text{K}$, the free-energy landscape obtained exhibits eight minima along the $⟨111⟩$ directions, confirming the existence of off-center dipoles in the paraelectric phase of barium titanate in this range of temperature. Only above this temperature, the free energy has a single minimum for $\vec{u}=\vec{0}$. An analytical expression of $\tilde{F}\left(\vec{u}\right)$ is provided under the form of a fourth-order polynomial function in $u_{\alpha }$.

We report here the observation of ferromagnetism (FM) at 300 K in mixtures of ${\text{TiO}}_2$ and ${\text{Co}}_3{\text{O}}_4$ powders despite the antiferromagnetic and diamagnetic characters of both oxides, respectively. The ferromagnetic behavior is found in the early stages of reaction and only for ${\text{TiO}}_2$ in anatase structure; no FM is found for identical samples prepared with rutile-${\text{TiO}}_2$. Optical spectroscopy and x-ray absorption spectra confirm a surface reduction of octahedral ${\text{Co}}^{+3}\to {\text{Co}}^{+2}$ in the mixtures which is in the origin of the observed magnetism.

We report density functional calculations of electronic structure and magnetic properties of ternary iron chalcogenide ${\text{TlFe}}_2{\text{Se}}_2$, which occurs in the ${\text{ThCr}}_2{\text{Si}}_2$ structure and discuss the results in relation to the iron-based superconductors. The ground state is antiferromagnetic with checkerboard order and Fe moment $\sim 1.90{\mu }_B$. There is strong magnetoelastic coupling similar to the Fe-based superconductors, reflected in a sensitivity of the Se position to magnetism. Tl is monovalent in this compound, providing heavy electron doping of 0.5 additional carriers per Fe relative to the parent compounds of the Fe-based superconductors. Other than the change in electron count, the electronic structure is rather similar to those materials. In particular, the Fermi surface is closely related to those of the Fe-based superconductors, except that the electron cylinders are larger, and the hole sections are suppressed. This removes the tendency toward a spin-density wave.

By performing heat-capacity, magnetocaloric effect, torque magnetometry, and force magnetometry measurements up to 33 T, we have mapped out the $T\text{−}H$ phase diagram of the $S=1/2$ spin dimer compound ${\text{Ba}}_3{\text{Cr}}_2{\text{O}}_8$. We found evidence for field-induced magnetic order between $H_{c1}=12.52\left(2\right)\text{T}$ and $H_{c2}=23.60\left(5\right)\text{T}$, with the maximum transition temperature $T_c\sim 2.7\text{K}$ at $H\sim 18\text{T}$. The lower transition can likely be described by Bose-Einstein condensation of triplons theory, and this is consistent with the absence of any magnetization plateaus in our magnetic torque and force measurements. In contrast, our measurements uncovered magnetic field irreversibility associated with a symmetric specific heat versus temperature near $H_{c2}$ suggesting that the upper transition is first order.