The in-plane London penetration depth $\Delta \lambda \left(T\right)$ was measured using a tunnel diode resonator technique in single crystals of ${\mathrm{Ba}}_{1-x}$${\mathrm{K}}_x$${\mathrm{Fe}}_2$${\mathrm{As}}_2$ with doping levels $x$ ranging from heavily underdoped, $x=0.16$ $(T_c=7\text{K})$, to nearly optimally doped, $x=0.34$ $(T_c=39\text{K})$. Exponential saturation of $\Delta \lambda \left(T\right)$ in the $T\to 0$ limit is found in optimally doped samples, with the superfluid density ${\rho }_s\left(T\right)\equiv {[\lambda \left(0\right)/\lambda \left(T\right)]}^2$ quantitatively described by a self-consistent $\gamma$ model with two nodeless isotropic superconducting gaps. As the doping level is decreased towards the extreme end of the superconducting dome at $x=0.16$, the low-temperature behavior of $\Delta \lambda \left(T\right)$ becomes nonexponential and is best described by the power law $\Delta \lambda \left(T\right)\propto T^2$, characteristic of strongly anisotropic gaps. The change between the two regimes happens within the range of coexisting magnetic/nematic order and superconductivity, $x<0.25$, and is accompanied by a rapid rise in the absolute value of $\Delta \lambda \left(T\right)$ with underdoping. This effect, characteristic of the competition between superconductivity and other ordered states, is very similar to but of significantly smaller magnitude than what is observed in the electron-doped Ba$({\mathrm{Fe}}_{1-x}$${\mathrm{Co}}_x)$${}_2$${\mathrm{As}}_2$ compounds. Our study suggests that the competition between superconductivity and magnetic/nematic order in hole-doped compounds is weaker than in electron-doped compounds, and that the anisotropy of the superconducting state in the underdoped iron pnictides is a consequence of the anisotropic changes in the pairing interaction and in the gap function promoted by both magnetic and nematic long-range orders.

The London penetration depth $\lambda \left(T\right)$ was measured in single crystals of a ${\mathrm{SrFe}}_2\left({\mathrm{As}}_{1-x}{\mathrm{P}}_x\right){}_2$ $\left(x=0.35\right)$ iron-based superconductor. The influence of disorder on the transition temperature $T_c$ and on $\lambda \left(T\right)$ was investigated. The effects of scattering controlled by the annealing of as-grown crystals was compared with the effects of artificial disorder introduced by 2.5 MeV electron irradiation. The low-temperature behavior of $\lambda \left(T\right)$ can be described by a power-law function $\Delta \lambda \left(T\right)=A{T}^n$, with the exponent $n$ close to one in pristine annealed samples, as expected for a superconducting gap with line nodes. Upon electron irradiation with a dose of $1.2\times {10}^{19}$ $e/{\mathrm{cm}}^2$, the exponent $n$ increases rapidly, exceeding a dirty limit value of $n=2$, implying that the nodes in the superconducting gap are accidental and can be lifted by the disorder. The variation of the exponent $n$ with $T_c$ is much stronger in the irradiated crystals compared to the crystals in which disorder was controlled by the annealing of the growth defects. We discuss the results in terms of different influence of different types of disorder on intraband and interband scattering.

By means of first-principles calculations coupled with the kinetic Monte Carlo simulations, we have systematically investigated the effects of dilute substitutional solutes on the behaviors of carbon in $\alpha$-Fe. Our results uncover the following. (i) Without the Fe vacancy the interactions between most solutes and carbon are repulsive due to the strain relief, whereas Mn has a weak attractive interaction with its nearest-neighbor carbon due to the local ferromagnetic coupling effect. (ii) The presence of the Fe vacancy results in attractive interactions of all the solutes with carbon. In particular, the Mn-vacancy pair shows an exceptionally large binding energy of $-$0.81 eV with carbon. (iii) The alloying addition significantly impacts the atomic-scale concentration distributions and chemical potential of carbon in the Fe matrix. Among them, Mn and Cr increase the carbon chemical potential, whereas Al and Si reduce it. (iv) Within the dilute scale of the alloying solution, the solute concentration- and temperature-dependent carbon diffusivities demonstrate that Mn has a little impact on the carbon diffusion, whereas Cr (Al or Si) remarkably retards the carbon diffusion. Our results provide a certain implication for better understanding the experimental observations related with the carbon solubility limit, carbon microsegregation, and carbide precipitations in the ferritic steels.

The magnetocaloric effect in bcc iron and hcp gadolinium is simulated on pico- and nanosecond time scales using Langevin spin dynamics on a discrete lattice, with parameters determined from ab initio calculations. It is found that transient external magnetic fields can drive thermodynamic cycles even in strongly nonequilibrium spin configurations, and that these are correlated with changes to the dynamic spin temperature. The theoretical predictions are found to agree closely with existing experimental measurements.

A spin reorientation transition (SRT) induced in a ferromagnetic nanolayer by the polarization switching in an adjoining ferroelectric film or bulk crystal is described theoretically. It is shown that such a polarization-controlled SRT can be realized in a narrow range of the nanolayer thicknesses only. Our calculations allowing for the polarization-dependent interfacial magnetic anisotropy predict that this “thickness window” is located between two threshold thicknesses, at which a size-induced SRT takes place in the ferromagnetic nanolayer at two different directions of the ferroelectric polarization. Importantly, the polarization-controlled SRT manifests itself in the resistance switching occurring in multiferroic tunnel junctions (MFTJs), where an ultrathin ferroelectric barrier is embedded between a ferromagnetic electrode with controllable magnetization and an electrode with a fixed magnetization. Using ${\mathrm{Fe}/\mathrm{BaTiO}}_3/\mathrm{Fe}$ junctions as a representative example, we demonstrate that such MFTJs can be employed as electric-write nanoscale memory cells with reliable nondestructive readout and high thermal stability of information storage.

We report measurements of spectral properties of spin-wave modes in permalloy/platinum (Py/Pt) bilayer wires magnetized along two principal in-plane axes. We find that the spin torque arising from the spin Hall current in Pt can significantly reduce the spectral linewidth of the bulk and edge spin-wave modes of the wire magnetized perpendicular to its long axis. The linewidth reduction is strongest for the quasiuniform mode and weakest for the edge mode. Our work demonstrates the importance of extrinsic contributions to spin-wave damping for tuning of magnetization dynamics by spin Hall current.

The dynamics in quantum magnets can often be described by effective models with bosonic excitations obeying a hard-core constraint. Such models can be systematically derived by renormalization schemes such as continuous unitary transformations or by variational approaches. Even in the absence of further interactions the hard-core constraint makes the dynamics of the hard-core bosons nontrivial. Here, we develop a systematic diagrammatic approach to the spectral properties of hard-core bosons at finite temperature. Starting from an expansion in the density of thermally excited bosons in a system with an energy gap, our approach leads to a summation of ladder diagrams. Conceptually, the approach is not restricted to one dimension, but the one-dimensional case offers the opportunity to gauge the method by comparison to exact results obtained via a mapping to Jordan-Wigner fermions. In particular, we present results for the thermal broadening of single-particle spectral functions at finite temperature. The line shape is found to be asymmetric at elevated temperatures and the bandwidth of the dispersion narrows with increasing temperature. Additionally, the total number of thermally excited bosons is calculated and compared to various approximations and analytic results. Thereby, a flexible approach is introduced that can also be applied to more sophisticated and higher dimensional models.

We report a study of the Ce doping effect on the thermal conductivity $\left(\kappa \right)$ of ${\mathrm{Nd}}_{2-x}$${\mathrm{Ce}}_x$${\mathrm{CuO}}_4$ (NCCO) at low temperatures down to 0.3 K and in magnetic fields up to 14 T. It is found that with Ce doping, the electronic thermal conductivity increases; at the same time, the $a$-axis field-induced changes in $\kappa \left(H\right)$, associated with the spin flop and spin polarization of the ${\mathrm{Nd}}^{3+}$ sublattice, and the spin flop of the ${\mathrm{Cu}}^{2+}$ sublattice, gradually disappear. These are clearly due to the electron doping and the destruction of the antiferromagnetic orders. In the superconducting NCCO with $x$ = 0.14 and 0.18, although the electronic thermal conductivity shows sizable field dependencies with $H\parallel c$, the paramagnetic scattering of phonons is still playing the dominant role in the heat transport, which is different from many other cuprates. In the lightly doped samples $(x$ = 0.03 and 0.06), the low-$T$ $\kappa \left(H\right)$ isotherms with $H\parallel c$ show a steplike anomaly and are likely related to the spin/charge stripes.

We report on the spectroscopic observation of a quantized electronic fine structure near the Fermi energy in thin Fe films grown on W(110). The quantum well states are detected down to binding energies of $\sim$10 meV by angle-resolved photoelectron spectroscopy. The band dispersion of these states is found to feature a pronounced anisotropy within the surface plane: It is free-electron-like along the $\overline{\Gamma H}$ direction while it becomes heavy along $\overline{\Gamma N}$. Density functional theory calculations identify the observed states to have both majority and minority spin character and indicate that the large anisotropy can be dependent on the number of Fe layers and coupling to the substrate.

We study the magnetic order and excitations in strong spin-orbit-coupled, Van Vleck–type, $d^4$ Mott insulators on a square lattice. Extending the previous work, we include the tetragonal crystal-field splitting and explore its effects on the magnetic phase diagram and magnon spectra. Two different ordered phases, with in-plane and out-of-plane orientations of the staggered moments, are found for the higher and lower values of the crystal-field splitting, respectively. The magnetic excitation spectra for paramagnetic and magnetically ordered phases are calculated and discussed in the context of a candidate spin-orbit $d^4$ Mott insulator, ${\mathrm{Ca}}_2$${\mathrm{RuO}}_4$.

We propose a photoexcitation scheme for pure spin-current generation in graphene subject to a Rashba spin-orbit coupling. Although excitation using circularly polarized light does not result in optical orientation of spins in graphene unless an additional magnetic field is present, we show that excitation with linearly polarized light at normal incidence yields spin-current injection without magnetic field. Spins are polarized within the graphene plane and are displaced in opposite directions, with no net charge displacement. The direction of the spin current is determined by the linear polarization axis of the light, and the injection rate is proportional to the intensity. The technique is tunable via an applied bias voltage and is accessible over a wide frequency range. We predict a spin-current polarization as high as 75% for photon frequencies comparable to the Rashba frequency. Spin-current injection via optical methods removes the need for ferromagnetic contacts, which have been identified as a possible source of spin scattering in electrical spin injection in graphene.

This paper elaborates a comprehensive theory of the thermodynamics of light management in solar cells explicitly considering imperfect light trapping, parasitic absorption and nonradiative recombination losses. A quantitative description of the entropic losses that reduce the open-circuit voltage and the energy conversion efficiency from the radiative limit towards realistic situations is presented. The theory embraces the fundamental limits for idealized solar cell devices given by the Yablonovitch limit and the Shockley-Queisser limit. We discriminate between reversible and irreversible entropic loss processes for four fundamental light management concepts: (i) conventional light trapping as an integral part of the device, (ii) geometric concentration of incident light, (iii) angular restriction of incoming and outgoing light, and (iv) light concentration by luminescent solar collectors. Based on this discrimination, a comprehensive discussion of the interplay between the loss processes and light management is presented. As part of this analysis, a new figure of merit for efficient light trapping in solar cells is introduced as well as an example of a deterministic light trapping concept which induces almost optimal light trapping.

The scattering of two-dimensional massless Dirac fermions from local spin-orbit interactions with an origin in dilute concentrations of physisorbed atomic species on graphene is theoretically investigated. The hybridization between graphene and the adatoms' orbitals lifts spin and valley degeneracies of the pristine host material, giving rise to rich spin-orbit coupling mechanisms with features determined by the exact adsorption position on the honeycomb lattice—bridge, hollow, or top position—and the adatoms' outer-shell orbital type. Effective graphene-only Hamiltonians are derived from symmetry considerations, while a microscopic tight-binding approach connects effective low-energy couplings and graphene-adatom hybridization parameters. Within the $T$-matrix formalism, a theory for (spin-dependent) scattering events involving graphene's charge carriers, and the spin-orbit active adatoms is developed. Spin currents associated with intravalley and intervalley scattering are found to tend to oppose each other. We establish that under certain conditions, hollow-position adatoms give rise to the spin Hall effect, through skew scattering, while top-position adatoms induce transverse charge currents via trigonal potential scattering. We also identify the critical Fermi energy range where the spin Hall effect is dramatically enhanced, and the associated transverse spin currents can be reversed.

We present a real-space method for first-principles nanoscale electronic transport calculations. We use the nonequilibrium Green's function method with density functional theory and implement absorbing boundary conditions (ABCs, also known as complex absorbing potentials, or CAPs) to represent the effects of the semi-infinite leads. In real space, the Kohn-Sham Hamiltonian matrix is highly sparse. As a result, the transport problem parallelizes naturally and can scale favorably with system size, enabling the computation of conductance in relatively large molecular junction models. Our use of ABCs circumvents the demanding task of explicitly calculating the leads' self-energies from surface Green's functions, and is expected to be more accurate than the use of the jellium approximation. In addition, we take advantage of the sparsity in real space to solve efficiently for the Green's function over the entire energy range relevant to low-bias transport. We illustrate the advantages of our method with calculations on several challenging test systems and find good agreement with reference calculation results.

The hexagonal reconstruction of Au(001) has been a model system for the understanding of complex metal surface reconstructions, and it has been intensively studied over almost five decades. Nevertheless, details of the reconstruction regarding the top layer to substrate matching and alignment are not unambiguously identified due to restricted resolution of previously available analytical tools as well as nonuniform sample quality. We therefore quantitatively reinvestigated the system by applying high-resolution real-space and reciprocal-space inspection using scanning tunneling microscopy and spot profile analysis low-energy electron diffraction in analyzing a high-quality Au(001) sample. We show that the Au(001) reconstruction consists of two rotational domains of a commensurate $c(28\times 48)$ superstructure. It results from a Moiré-like buckling of a quasihexagonal top layer which is characterized by lattice vectors having a length of $0.9655a$ and $0.9581a$, respectively, where $a$ is the interatomic distance of Au(001). The former vector runs exactly along [110] or [−110], whereas the latter one deviates by 59.75° from those directions. ${\mathrm{Ar}}^{+}$ ion bombardment at elevated temperatures induces a rotation of the top layers up to angles of ±0.83°. Sample annealing yields a turning back into the initial top layer alignment. Rotation and reorientation proceeds continuously, i.e. all angles between 0 and ±0.83° are observed. Using simple hard sphere models, the main characteristics of the reconstruction are explained. This includes even structural details of the reconstruction at step edges for nonrotated and rotated quasihexagonal top layers.

A graphenelike two-dimensional boron honeycomb is inherently prohibited due to its empty π valence band. Based on chemical intuition and first-principles calculations, we design a two-dimensional crystal ${\mathrm{MoB}}_4$ with two graphenelike boron honeycombs sandwiching a triangular molybdenum layer. It has the attractive electronic structure of double Dirac cones near Fermi level with high Fermi velocity, which are contributed by the coupling of Mo $d$ orbitals and B $p_z$ orbitals. Such a metal stabilized boron honeycomb system could even have both superconductivity and ferromagnetism through appropriate selection of the metal layer, such as manganese. The unique electronic properties of these two-dimensional systems inspire broad interest in nanoelectronics.

The growth of the $\sqrt{3}\times \sqrt{3}$ reconstructed silicene on Ag substrate has been frequently observed in experiments while its atomic structure and formation mechanism is poorly understood. Here, by first-principles calculations, we show that $\sqrt{3}\times \sqrt{3}$ reconstructed silicene is constituted by dumbbell units of Si atoms arranged in a honeycomb pattern. Our model shows excellent agreement with the experimentally reported lattice constant and STM image. We propose a new mechanism for explaining the spontaneous and consequential formation of $\sqrt{3}\times \sqrt{3}$ structures from $3\times 3$ structures on Ag substrate. We show that the $\sqrt{3}\times \sqrt{3}$ reconstruction is mainly determined by the interaction between Si atoms and have weak influence from Ag substrate. The proposed mechanism opens the path to understanding of multilayer silicon.

A topological insulator is a state of matter which does not break any symmetry and is characterized by topological invariants, the integer expectation values of nonlocal operators. Antiferromagnetism, on the other hand, is a broken symmetry state in which the translation symmetry is reduced and time reversal symmetry is broken. Can these two phenomena coexist in the same material? A proposal by Mong et al. [Phys. Rev. B 81, 245209 (2010)] asserts that the answer is yes. Moreover, it is theoretically possible that the onset of antiferromagnetism enables the nontrivial topology since it may create spin-orbit coupling effects which are absent in the nonmagnetic phase. The current work examines a real system, half-Heusler GdBiPt, as a candidate for topological antiferromagnetism. We find that the magnetic moments of the gadolinium atoms form ferromagnetic sheets which are stacked antiferromagnetically along the body diagonal. This magnetic structure may induce spin-orbit coupling on band electrons as they hop perpendicular to the ferromagnetic sheets.

Cluster dynamical mean-field calculations are used to construct the superconducting gap function of the two-dimensional Hubbard model. The frequency dependence of the imaginary part of the gap function indicates that the pairing is dominated by fluctuations at two characteristic frequencies: one at the scale of the hopping matrix element $t$ and one at a much lower scale. The lower-frequency component becomes more important as the doping is reduced into the pseudogap regime. Comparison to information on the spin-fluctuation spectrum of the model suggests that superconductivity arises from exchange of spin fluctuations. The inferred pairing glue function is in remarkable qualitative consistency with the pairing function inferred from optical conductivity data.