We consider a mixture of single-component bosonic and fermionic atoms with an interspecies interaction that is varied using a Feshbach resonance. By performing a mean-field analysis of a two-channel model, which describes both narrow and broad Feshbach resonances, we find an unexpectedly rich phase diagram at zero temperature: Bose-condensed and non-Bose-condensed phases form a variety of phase-separated states that are accompanied by both critical and tricritical points. We discuss the implications of our results for the experimentally observed collapse of Bose-Fermi mixtures on the attractive side of the Feshbach resonance, and we make predictions for future experiments on Bose-Fermi mixtures close to a Feshbach resonance.

Using ${}^{23}\text{N}\text{a}$ NMR measurements on sodium cobaltates at intermediate dopings $\left(0.44\le x\le 0.62\right)$, we establish the qualitative change in behavior of the local magnetic susceptibility at $x^{\ast }=0.63–0.65$, from a low-$x$ Pauli-like regime to the high-$x$ Curie-Weiss regime. For $0.5\le x\le 0.62$, the presence of a maximum $T^{\ast }$ in the temperature dependence of the susceptibility shows the existence of an $x$-dependent energy scale. $T_1$ relaxation measurements establish the predominantly antiferromagnetic character of spin correlations for $x<x^{\ast }$. This contradicts the commonly assumed uncorrelated Pauli behavior in this $x$ range and is at odds with the observed ferromagnetic correlations for $x>x^{\ast }$. It is suggested that at a given $x$ the ferromagnetic correlations might dominate the antiferromagnetic ones above $T^{\ast }$. From ${}^{59}\text{C}\text{o}$ NMR data, it is shown that moving toward higher $x$ away from $x=0.5$ results in the progressive appearance of nonmagnetic ${\text{Co}}^{3+}$ sites, breaking the homogeneity of Co states encountered for $x\le 0.5$. The main features of the NMR-detected ${}^{59}\text{C}\text{o}$ quadrupolar effects, together with indications from the powder x-ray diffraction data, lead us to sketch a possible structural origin for the ${\text{Co}}^{3+}$ sites. In light of this ensemble of experimental observations, a phase diagram taking into account the systematic presence of correlations and their $x$ dependence is proposed.

We report density functional calculations of the electronic structure, Fermi surface, phonon spectrum, magnetism, and electron-phonon coupling for the superconducting phase FeSe, as well as the related compounds FeS and FeTe. We find that the Fermi-surface structure of these compounds is very similar to that of the Fe-As based superconductors, with cylindrical electron sections at the zone corner, cylindrical hole surface sections, and depending on the compound, other small hole sections at the zone center. As in the Fe-As based materials, these surfaces are separated by a two-dimensional nesting vector at $\left(\pi ,\pi \right)$. The density of states, nesting, and Fermi-surface size increase, going from FeSe to FeTe. Both FeSe and FeTe show spin-density wave (SDW) ground states, while FeS is close to instability. In a scenario where superconductivity is mediated by spin fluctuations at the SDW nesting vector, the strongest superconductor in this series would be doped FeTe.

We present temperature- and field-dependent inelastic light-scattering studies of multiferroic ${\text{TbMnO}}_3$. By carefully examining the evolution of magneto-elastic modes in various phases of ${\text{TbMnO}}_3$, our study reveals several features of the field-induced incommensurate-commensurate (IC-C) transition in ${\text{TbMnO}}_3$. We find that, for fields applied along the $b$ axis, there is a coexistence of distinct structural phases in the intermediate field regime $\left(H=4–7\text{T}\right)$ around the IC-C-phase transition. We present evidence for the existence of dynamical fluctuations of the C phase for fields lower than the critical field for $\mathbf{H}$ along the $b$ axis, $H<H_c^b$. Furthermore, we present evidence for strong spin-lattice coupling effects in ${\text{TbMnO}}_3$ in the form of zone-boundary phonon modes that strongly couple to the spins by modulating the exchange interaction in this material.

We analyze antiferromagnetism and superconductivity in novel Fe-based superconductors within the itinerant model of small electron and hole pockets near (0,0) and $\left(\pi ,\pi \right)$. We argue that the effective interactions in both channels logarithmically flow toward the same values at low energies; i.e., antiferromagnetism and superconductivity must be treated on equal footing. The magnetic instability comes first for equal sizes of the two pockets, but loses to superconductivity upon doping. The superconducting gap has no nodes, but changes sign between the two Fermi surfaces (extended $s$-wave symmetry). We argue that the $T$ dependencies of the spin susceptibility and NMR relaxation rate for such a state are exponential only at very low $T$, and can be well fitted by power laws over a wide $T$ range below $T_c$.

We review how a magnetic-resonance force microscope (MRFM) can be applied to perform ferromagnetic resonance spectroscopy of individual submicron-size samples. We restrict our attention to a thorough study of the spin-wave eigenmodes excited in Permalloy (Py) disks patterned out of the same 43.3-nm-thin film. The disks have a diameter of either 1.0 or $0.5\mu \text{m}$ and are quasisaturated by a perpendicularly applied magnetic field. It is shown that quantitative spectroscopic information can be extracted from the MRFM measurements. In particular, the data are extensively compared with complementary approximate models of the dynamical susceptibility: (i) a two-dimensional analytical model, which assumes a homogeneous magnetization dynamics along the thickness, and ii) a full three-dimensional micromagnetic simulation, which assumes a homogeneous magnetization dynamics below a characteristic length scale $c$ and approximates the cylindrical sample volume by a discretized representation with regular cubic mesh of lateral size $c=3.9\text{nm}$. In our analysis, the distortions due to a breaking of the axial symmetry are taken into account; both models incorporating the possibility of a small misalignment between the applied field and the normal of the disks.

We use time-resolved charge-detection techniques to probe virtual tunneling processes in a double quantum dot. The process involves an energetically forbidden state separated by an energy $\delta$ from the Fermi energy in the leads. The nonzero tunneling probability can be interpreted as cotunneling, which occurs as a direct consequence of time-energy uncertainty. For small energy separation the electrons in the quantum dots delocalize and form molecular states. In this regime we establish the experimental equivalence between cotunneling and sequential tunneling into molecular states for electron transport in a double quantum dot. Finally, we investigate inelastic cotunneling processes involving excited states of the quantum dots. Using the time-resolved charge-detection techniques, we are able to extract the shot noise of the current in the cotunneling regime.

We use neutron scattering to study the spin and lattice structure of single-crystal ${\text{SrFe}}_2{\text{As}}_2$, the parent compound of the FeAs-based superconductor $\left(\text{Sr},\text{K}\right){\text{Fe}}_2{\text{As}}_2$. We find that ${\text{SrFe}}_2{\text{As}}_2$ exhibits an abrupt structural phase transition at 220 K, where the structure changes from tetragonal with lattice parameters $c>a=b$ to orthorhombic with $c>a>b$. At almost the same temperature, Fe spins develop a collinear antiferromagnetic structure along the orthorhombic $a$ axis with spin direction parallel to this $a$ axis. These results are consistent with earlier work on the $R\text{FeAsO}$ ($R=\text{rare}$ earth) families of materials and on ${\text{BaFe}}_2{\text{As}}_2$, and therefore suggest that static antiferromagnetic order is ubiquitous for the parent compounds of these FeAs-based high-transition temperature superconductors.

Our studies have significantly modified the conventionally held view of the phase diagram of ${\text{La}}_{2-2x}{\text{Sr}}_{1+2x}{\text{Mn}}_2{\text{O}}_{7-\delta }$ for two compositions exhibiting charge (and orbital) order (CO), i.e., at hole-doping levels, $h=x-\delta$, of $\sim 0.5$ and $\sim 0.6$. These CO states are stable over very narrow doping ranges $\left(\Delta h\sim \pm 0.005\right)$ at the lowest temperatures, but those ranges increase at higher temperatures (to $\Delta h\sim \pm 0.02$) in a manner consistent with simple entropy considerations. Such narrow ranges dictate the crucial need for crystal homogeneity. Attesting to such homogeneity is a conductivity ratio of $>{10}^{10}$ upon crossing the first-order phase boundary from CO at $h=0.60$ to $\text{A}$-type antiferromagnetic (AAFM) at $h\sim 0.59$ or $h\sim 0.61$ plus two findings that were missed in the existing literature: that these CO phases are the ground state at the lowest temperatures, and for $h\sim 0.5$, that coexistence of the CO and AAFM phase is absent at any temperature.

We consider the spin-orbital model for a magnetic system with singly occupied but triply degenerate $t_{2g}$ orbitals coupled into a planar, triangular lattice, as would be exemplified by ${\text{NaTiO}}_2$. We investigate the ground states of the model for interactions which interpolate between the limits of pure superexchange and purely direct-exchange interactions. By considering ordered and dimerized states at the mean-field level, and by interpreting the results from exact diagonalization calculations on selected finite systems, we demonstrate that orbital interactions are always frustrated and that orbital correlations are dictated by the spin state, manifesting an intrinsic entanglement of these degrees of freedom. In the absence of Hund coupling, the ground state changes from a highly resonating, dimer-based, symmetry-restored spin and orbital-liquid phase to one based on completely static, spin-singlet valence bonds. The generic properties of frustration and entanglement survive even when spins and orbitals are nominally decoupled in the ferromagnetic phases stabilized by a strong Hund coupling. By considering the same model on other lattices, we discuss the extent to which frustration is attributable separately to geometry and to interaction effects.

For a linear chain of diamondlike elements, we show that the Rashba spin-orbit interaction (which can be tuned by a perpendicular gate voltage) and the Aharonov-Bohm flux (due to a perpendicular magnetic field) can combine to select only one propagating ballistic mode, for which the electronic spins are fully polarized along a direction that can be controlled by the electric and magnetic fields and by the electron energy. All the other modes are evanescent. For a wide range of parameters, this chain can serve as a spin filter.

Classical Heisenberg antiferromagnets on two-dimensional kagome and three-dimensional hyperkagome lattices are investigated by Monte Carlo simulations. For both models the symmetry-breaking states at low temperatures are described by nonzero octupole moments or third-rank spin tensor order parameters. In the case of the two-dimensional kagome antiferromagnet, a sharp crossover into a coplanar state takes place at $T_k\approx 0.004J$, which we attribute to proliferation of fractional vortices. The three-dimensional model exhibits a first-order transition at $T_c\approx 0.002J$ into a phase with critical spin correlations, which possesses a long-range order of octupole moments.

We calculate the dynamical spin response of Kondo impurity and Kondo lattice systems within a semiphenomenological Fermi-liquid description, at low temperatures $T<T_K$, the Kondo temperature, and low magnetic fields $B⪡k_B{T}_K/g{\mu }_B$. Fermi-liquid parameters are determined by comparison (i) with microscopic theory (numerical renormalization group) for the impurity model and (ii) with experiment for the lattice model. We find in the impurity case that the true impurity spin resonance has a width of the order of $T_K$ and disappears altogether if the $g$ factors of impurity spin and conduction-electron spin are equal. However, there is an impurity-induced resonance contribution at the conduction-electron resonance. The latter is broadened by spin-lattice relaxation and is usually unobservable. In contrast, for the Anderson lattice in the Kondo regime we find a sharp electron-spin resonance (ESR) line only slightly shifted from the local resonance and broadened by spin-lattice relaxation, the latter significantly reduced by both the effects of heavy-fermion physics and ferromagnetic fluctuations. We conjecture that our findings explain the sharp ESR lines recently observed in several heavy-fermion compounds.

Resonant scattering of electrons with low energies (as compared to the bandwidth) on a single neutral short-range impurity in graphene is analyzed theoretically, taking into account the valley degeneracy. Resonances dramatically increase the scattering cross section and introduce a strong energy dependence. Analysis of the tight-binding model shows that resonant scattering is typical for generic impurities as long as they are sufficiently strong (the potential is of the order of the electron bandwidth or higher).

The electronic response of doped manganites at the transition from the paramagnetic insulating to the ferromagnetic metallic state in ${\text{La}}_{1-x}{\text{Ca}}_x{\text{MnO}}_3$ for $x=0.3$ and 0.2 was investigated by dc conductivity, ellipsometry, and vacuum ultraviolet reflectance for energies between 0 and 22 eV. A stabilized Kramers-Kronig transformation yields the optical conductivity and reveals changes in the optical spectral weight up to 22 eV at the metal-to-insulator transition. In the observed energy range, the spectral weight is conserved within 0.3%. The redistribution of spectral weight in this surprisingly broad energy range has important ramifications for the effective low-energy physics. We discuss the importance of the charge-transfer, Coulomb on-site, Jahn-Teller, and long-range Coulomb screening effects to the electronic structure.

Temperature (5–250 K) and magnetic-field (0–70 kOe) variations of the low-energy (1–10 meV) electrodynamics of spin excitations have been investigated for a complete set of light-polarization configurations for a ferroelectric magnet ${\text{DyMnO}}_3$ by using terahertz time-domain spectroscopy. We identify the pronounced absorption continuum (1–8 meV) with a peak feature around 2 meV, which is electric-dipole active only for the light $E$ vector along the $a$ axis. This absorption band grows in intensity with lowering temperature from the spin-collinear paraelectric phase above the ferroelectric transition but is independent of the orientation of spiral spin plane ($bc$ or $ab$), as shown on the original $P_{\text{s}}$ (ferroelectric polarization) $\parallel c$ phase as well as the magnetic-field induced $P_{\text{s}}\parallel a$ phase. The possible origin of this electric-dipole active band is argued in terms of the large fluctuations of spins and spin current.

The ground-state properties of a spin $S=1/2$ tetrameric Heisenberg antiferromagnetic chain with alternating couplings ${\text{AF}}_1{\text{-AF}}_2{\text{-AF}}_1\text{-F}$ (AF and F denote antiferromagnetic and ferromagnetic couplings, respectively) are studied by means of the density-matrix renormalization-group method. Two plateaus of magnetization $m$ are found at $m=0$ and 1/4. It is shown that in such a spin-1/2 AF system, there is a gap from the singlet ground state to the triplet excited states in the absence of a magnetic field. The spin-spin correlation function decays exponentially, and the gapped states have a nonvanishing string order, which measures a hidden symmetry in the system. By a dual transformation, the string order is transformed into a ferromagnetic order and the hidden symmetry is unveiled to be a $Z_2\times Z_2$ discrete symmetry, which is fully broken in the gapped states. This half-integer spin Heisenberg AF chain is in a Haldane-like phase suggesting that the present findings extend the substance of Haldane’s scenario. A valence-bond-solid state picture is also proposed for the gapped states.

Electrical injection from the Heusler alloy ${\text{Co}}_2\text{FeSi}$ into (Al,Ga)As is investigated for different growth temperatures ${\text{T}}_G$ of the injector layer. Depending on ${\text{T}}_G$, the spin polarization of injected electrons in the semiconductor is determined by two competing mechanisms: actual spin injection at the ${\text{Co}}_2\text{FeSi}/\left(\text{Al},\text{Ga}\right)\text{As}$ interface and ultrafast spin alignment in the (Al,Ga)As layer. This layer is strongly affected by the thermally activated diffusion of Co, Fe, and Si during the growth of the ${\text{Co}}_2\text{FeSi}$ layers. Despite the electrical compensation and magnetic transformation in the underlying semiconductor structure, a spin-injection efficiency of at least 50% is achieved as deduced from the analysis of electroluminescence and time-resolved photoluminescence data.

We report density functional calculations of the electronic structure and Fermi surface of the ${\text{BaFe}}_2{\text{As}}_2$ and LiFeAs phases including doping via the virtual-crystal approximation. The results show that contrary to a rigid-band picture, the density of states at the Fermi energy is only weakly doping dependent and that the main effect of doping is a change in the relative sizes of the electron and hole Fermi surfaces as required by Luttinger’s theory. This is partly a consequence of a change in As height with doping, in particular a shift of As toward Fe as holes are introduced in the Fe plane, as might be expected from simple ionic considerations. The main effect of doping is therefore a reduction in the degree of nesting of the Fermi surface. This provides a framework for understanding the approximate electron-hole symmetry in the phase diagrams of the Fe-As based superconductors.

The structural and the electronic properties of a hypothetical three-dimensional (3D) all-$s{p}^2$ carbon phase, called $K_4$, are investigated using first-principles calculations. The cohesive energy per atom for this structure is found to be 1.3 eV lower than for graphite and diamond, but also more than 0.3 eV lower than for the previously proposed H-6, bct-4, and C-20 phases, also 3D all-$s{p}^2$ carbon forms. The calculated bulk modulus for the $K_4$ crystal is slightly higher than for the C-20 structure but lower than for the H-6 and bct-4 solids. Our analysis reveals that the relatively low cohesive energy and bulk modulus of the $K_4$ phase are due to the disruption of the $\pi$ bonding states. The calculated density of states and band structure show that the $K_4$ phase is metallic.