Silicene, a two-dimensional (2D) honeycomb arrangement of Si atoms, is expected to have better electronic properties than graphene and has been mostly synthesized on Ag surfaces. Although scanning tunneling microscopy (STM) has been used for visualizing its atomic structure in real space, the interpretation of STM contrast is not straightforward and only the topmost Si atoms were observed on the $(4\times 4)$ silicene/Ag(111) surface. Here, we demonstrate that high-resolution atomic force microscopy (AFM) can resolve all constituent Si atoms in the buckled honeycomb arrangement of the $(4\times 4)$ silicene. Site-specific force spectroscopy attributes the origin of the high-resolution AFM images to chemical bonds between the AFM probe apex and the individual Si atoms on the $(4\times 4)$ silicene. A detailed analysis of the geometric parameters suggests that the pulling up of lower-buckled Si atoms by the AFM tip could be a key for high-resolution AFM, implying a weakening of the Si-Ag interactions at the interface. We expect that high-resolution AFM will also unveil atomic structures of edges and defects of silicene, or other emerging 2D materials.

To study exotic excitations described by parafermions in the possible spin liquid states of $\mathrm{SU}\left(n\right)$ spin systems, we introduce a parafermion parton approach. The $\mathrm{SU}\left(n\right)$ spin operators can be represented by clock and shift matrices, which are shown to be the polynomials of parafermion operators in the parafermion representation. We find that $\mathrm{SU}\left(n\right)$ spins can be decomposed into $n$ parafermion matrices of degree one. In this decomposition, the spin has a ${\{⨂\mathrm{SU}\left(n\right)\}}^{n-1}$ gauge symmetry. As an application, we study the one-dimensional three-state clock model and generalized Kitaev model by a mean-field theory; both of them have been proved to be related to parafermion excitations. We find that with the symmetries of translations, sixfold rotation, and combination of parity and time reversal, there are 9 types and 102 solutions for two-dimensional ${\mathbb{Z}}_3$ parafermion spin liquids on the honeycomb lattice. By contrast, there are 9 types and 36 solutions if both parity and time-reversal symmetries are present. Our results provide a route for the systematic search of types of spin liquids with exotic anyon excitations.

Arrays of dopants in silicon are promising platforms for the quantum simulation of the Fermi-Hubbard model. We show that the simplest model with only on-site interaction is insufficient to describe the physics of an array of phosphorous donors in silicon due to the strong intersite interaction in the system. We also study the resonant tunneling transport in the array at low temperature as a mean of probing the features of the Hubbard physics, such as the Hubbard bands and the Mott gap. Two mechanisms of localization which suppresses transport in the array are investigated: The first arises from the electron-ion core attraction and is significant at low filling; the second is due to the sharp oscillation in the tunnel coupling caused by the intervalley interference of the donor electron's wave function. This disorder in the tunnel coupling leads to a steep exponential decay of conductance with channel length in one-dimensional arrays, but its effect is less prominent in two-dimensional ones. Hence, it is possible to observe resonant tunneling transport in a relatively large array in two dimensions.

We use a time-dependent density functional theory approach to study the optical response of a hybrid nanostructure where the junction between thin metallic films is functionalized with a quantum well (QW) structure. We show that an unoccupied QW-localized electronic state opens the possibility of the active electrical control of the photoassisted electron transport through the junction and of the absorption at optical frequencies. Control strategies based on an applied bias or an external THz field are demonstrated.

Scanning tunneling microscopy (STM) and spectroscopy (STS) in combination with density functional theory (DFT) calculations are employed to study the surface and subsurface properties of the metastable phase of the phase-change material ${\mathrm{Ge}}_2{\mathrm{Sb}}_2{\mathrm{Te}}_5$ as grown by molecular beam epitaxy. The (111) surface is covered by an intact Te layer, which nevertheless permits the detection of the more disordered subsurface layer made of Ge and Sb atoms. Centrally, we find that the subsurface layer is significantly more ordered than expected for metastable ${\mathrm{Ge}}_2{\mathrm{Sb}}_2{\mathrm{Te}}_5$. First, we show that vacancies are nearly absent within the subsurface layer. Secondly, the potential fluctuation, tracked by the spatial variation of the valence band onset, is significantly less than expected for a random distribution of atoms and vacancies in the subsurface layer. The strength of the fluctuation is compatible with the potential distribution of charged acceptors without being influenced by other types of defects. Thirdly, DFT calculations predict a partially tetrahedral Ge bonding within a disordered subsurface layer, exhibiting a clear fingerprint in the local density of states as a peak close to the conduction band onset. This peak is absent in the STS data implying the absence of tetrahedral Ge, which is likely due to the missing vacancies required for structural relaxation around the shorter tetrahedral Ge bonds. Finally, isolated defect configurations with a low density of ${10}^{-4}{\mathrm{nm}}^{-2}$ are identified by comparison of STM and DFT data, which corroborates the significantly improved order in the epitaxial films driven by the buildup of vacancy layers.

Hard-mode Raman spectroscopy was applied to analyze the temperature-induced transformation processes in perovskite-type $\left({\mathrm{ABO}}_3\right)$ single crystals of $\left(1\text{−}x\right){\mathrm{Na}}_{0.5}{\mathrm{Bi}}_{0.5}{\mathrm{TiO}}_3\text{−}x{\mathrm{BaTiO}}_3$ (NBT-$x\mathrm{BT})$ in a wide temperature range between 100 and 1010 K and a composition range of $x=0–0.074$ across the morphotropic phase boundary (MPB). The results show abundant uncoupled ferroic structural distortions even at 1010 K and coexistence of two types of mesoscopic-scale ferroic order at lower temperatures. Octahedral ${\mathrm{BO}}_6$ tilting is typical of pure NBT, while the incorporation of A-site ${\mathrm{Ba}}^{2+}$ suppresses the tilting and promotes the off centering of ${\mathrm{BO}}_6$ octahedra. The temperature evolution of the phonon modes clearly reveals the two macroscopically observed critical temperatures $T_m$ and $T_d$ as well as, in the case of $x\ne 0$, two characteristic temperatures $T^{\prime }$ and $T^{\prime \prime }$ preceding the $T_m$ and $T_d$, respectively, which are attributed to mesoscopic-scale antiferroelectric and ferroelectric coupling processes within the A-site-cation subsystem. At $x<x_{\mathrm{MPB}}$ the two sublattices, off-centered A-site cations and off-centered B-site cations, remain incoherent in the entire temperature range. Only when the amount of Ba reaches $x_{\mathrm{MPB}}$ the two subsystems couple dynamically, which can explain the enhancement of properties at the MPB. The overall ferroic distortion, however, has a minimum at the MPB, probably because at $x_{\mathrm{MPB}}$ the ferroelectric coupling between B-site ${\mathrm{Ti}}^{4+}$ cations is reduced to a greater extent than the enhancement of ferroelectric coupling between A-site ${\mathrm{Bi}}^{3+}$ cations.

We present a detailed structure solution for the $16\text{−}\AA$ decagonal quasicrystal in the Al-Pd-Mn system by means of cluster decoration and ab initio energy minimization. It is based on structure models of the $\varepsilon$ and other approximant phases. The $\varepsilon$ phases can be represented as subsets of a hexagon-boat-star (HBS) tiling. The decagonal phase comprises further HBS tiles. We have constructed several fictitious HBS approximants and optimized their structures individually. All tiles are decorated by two types of atomic clusters: the pseudo-Mackay icosahedron (PMI) and the large bicapped pentagonal prism (LBPP). It turns out that, whereas the PMI clusters can be kept essentially unchanged, the LBPP clusters must be adjusted in occupancy with Al atoms depending on their positions in the various tiles. In this way we obtain cluster decorations for all tiles of the decagonal quasicrystal. The calculations were confirmed by evaluation of an effective tile Hamiltonian.

A spin-torque diode, which is a magnetic tunnel junction with magnetic layers softly pinned at some tilt to each other, is proposed. The resonance operating frequency of such a dual exchange-pinned spin-torque diode can be significantly higher (up to 9.5 GHz) than that of a traditional free layer spin-torque diode, and, at the same time, the sensitivity remains rather high. Using micromagnetic modeling we show that the maximum microwave sensitivity of the considered diode is reached at the bias current densities slightly below the self-sustained oscillations initiating. The dependence of the resonance frequency and the sensitivity on the angle between pinning exchange fields is presented. Thus, a way of designing spin-torque diode with a given resonance response frequency in the microwave region in the absence of an external magnetic field is proposed.

The magnetic structure of exchange-coupled antiferromagnetic (AF) layers in epitaxial $\mathrm{L}{\mathrm{a}}_{0.7}\mathrm{S}{\mathrm{r}}_{0.3}\mathrm{Mn}{\mathrm{O}}_3$ (LSMO)/$\mathrm{L}{\mathrm{a}}_{0.7}\mathrm{S}{\mathrm{r}}_{0.3}\mathrm{Fe}{\mathrm{O}}_3$ (LSFO) superlattices grown on (111)-oriented $\mathrm{SrTi}{\mathrm{O}}_3$ substrates was studied using angle-dependent x-ray absorption spectroscopy utilizing linearly polarized x rays. We demonstrate the development of the measurement protocols needed to determine the orientation of the LSFO antiferromagnetic spin axis and how it responds to an applied magnetic field due to exchange interactions with an adjacent ferromagnetic layer. A small energy difference exists between two types of AF order: the majority of the AF moments cant out-of-the-plane of the film along the 110 or 100 directions depending on the LSFO layer thickness. In response to an applied magnetic field, these canted moments are aligned with a single 110 or 100 direction that maintains a nearly perpendicular orientation relative to the LSMO sublayer magnetization. The remaining AF moments lie within the $\left(111\right)$ plane and these in-plane moments can be reoriented to an arbitrary in-plane direction to lie parallel to the LSMO sublayer magnetization. These results demonstrate that the magnetic order of AF thin films and heterostructures is far more complex than in bulk LSFO and can be tuned with orientation, thickness, and applied magnetic field.

In antiferromagnetic materials the order parameter exhibits resonant modes at frequencies that can be in the terahertz range, making them interesting components for spintronic devices. Here, it is shown that antiferromagnetic resonance can be excited using the inverse spin-Hall effect in a system consisting of an antiferromagnetic insulator coupled to a normal-metal waveguide. The time-dependent interplay between spin torque, ac spin accumulation, and magnetic degrees of freedom is studied. It is found that the dynamics of the antiferromagnet affects the frequency-dependent conductivity of the normal metal. Further, a comparison is made between spin-current-induced and Oersted-field-induced excitation under the condition of constant power injection.

We investigate the stability of Néel skyrmions against tilted magnetic fields in polar magnets with uniaxial anisotropy ranging from easy-plane to easy-axis type. We construct the corresponding phase diagrams and investigate the internal structure of skewed skyrmions with displaced cores. We find that moderate easy-plane anisotropy increases the stability range of Néel skyrmions for fields along the symmetry axis, while moderate easy-axis anisotropy enhances their robustness against tilted magnetic fields. We stress that the direction along which the skyrmion cores are shifted depends on the symmetry of the underlying crystal lattice. The cores of Néel skyrmions, realized in polar magnets with ${\mathrm{C}}_{nv}$ symmetry, are displaced either along or opposite to the off-axis (in-plane) component of the magnetic field depending on the rotation sense of the magnetization, dictated by the sign of the Dzyaloshinskii constant. The core shift of antiskyrmions, present in noncentrosymmetric magnets with ${\mathrm{D}}_{2d}$ symmetry, depends on the in-plane orientation of the magnetic field and can be parallel, antiparallel, or perpendicular to it. We argue that the role of anisotropy in magnets with axially symmetric crystal structure is different from that in cubic helimagnets. Our results can be applied to address recent experiments on polar magnets with ${\mathrm{C}}_{3v}$ symmetry, ${\mathrm{GaV}}_4{\mathrm{S}}_8$ and ${\mathrm{GaV}}_4{\mathrm{Se}}_8$, and ${\mathrm{Mn}}_{1.4}{\mathrm{Pt}}_{0.9}{\mathrm{Pd}}_{0.1}\mathrm{Sn}$ with ${\mathrm{D}}_{2d}$ symmetry.

A Rb-NMR study has been performed on the quasi-one-dimensional competing spin chain $\mathrm{R}{\mathrm{b}}_2\mathrm{C}{\mathrm{u}}_2\mathrm{M}{\mathrm{o}}_3{\mathrm{O}}_{12}$ with ferromagnetic and antiferromagnetic exchange interactions on nearest-neighboring and next-nearest neighboring spins, respectively. The system changes from a gapped ground state at zero field to a gapless state at $H_{\mathrm{C}}\simeq 2\mathrm{T}$, where the existence of magnetic order below 1 K was demonstrated by a broadening of the NMR spectrum, associated with a critical divergence of $1/T_1$. In the higher-temperature region, $T_1^{-1}$ showed a power-law-type temperature dependence, from which the field dependence of the Luttinger parameter $K$ was obtained and compared with theoretical calculations based on the spin nematic Tomonaga-Luttinger liquid (TLL) state.

In this work we develop an atomistic spin dynamics model for the ideal ${\mathrm{Mn}}_{50}{\mathrm{Al}}_{50}\tau$-phase by means of first-principles calculations. The model is applied to study the domain wall and antiphase boundary phenomenology. In particular, it allows us to obtain the dependence on the interfacial exchange coupling of the nucleation and depinning fields, as well as the macroscopic magnetization profile across the antiphase boundary. We find that microscopic antiferromagnetic exchange coupling stronger than $10\mathrm{meV}$ could unavoidably lead to the formation of a domain wall at the antiphase boundary.

In this paper, we have performed the first-principles density functional theory calculations to predict the magnetic properties of the CoPt and FePt nanoparticles in cuboctahedral, decahedral, and icosahedral shapes. The modeled alloy nanoparticles have a diameter of 1.1 nm and consist of 31 $5d$ Pt atoms and 24 $3d$ Co (or Fe) atoms. For both CoPt and FePt, we found that the decahedral nanoparticles had appreciably lower surface magnetic moments than the cuboctahedral and icosahedral nanoparticles. Our analysis indicated that this reduction in the surface magnetism was related to a large contraction of atomic spacing and high local Co (or Fe) concentration in the surface of the decahedral nanoparticles. More interestingly, we predicted that the CoPt and FePt cuboctahedral nanoparticles exhibited dramatically different surface spin structures when noncollinear magnetism was taken into account. Our calculation results revealed that surface anisotropy energy decided the fashion of surface spin canting in the CoPt and FePt nanoparticles, confirming previous predictions from atomistic Monte Carlo simulations.

First-principles electronic calculations show how the adsorption morphology, orbital magnetism, and magnetic anisotropy energy (MAE) of small ${\mathrm{Co}}_N$ and ${\mathrm{Fe}}_N$ clusters ($N\le 3$) on graphene (G) can be reversibly controlled under the action of an external electric field (EF). A variety of cluster-specific and EF-induced effects are revealed, including (i) perpendicular or canted adsorption configurations of the dimers and trimers, (ii) significant morphology-dependent permanent dipole moments and electric susceptibilities, (iii) EF-induced reversible transitions among the different metastable adsorption morphologies of ${\mathrm{Fe}}_3$ and ${\mathrm{Co}}_3$ on graphene, (iv) qualitative changes in the MAE landscape driven by structural changes, (v) colossal values of the magnetic anisotropy $\mathrm{\Delta }E\simeq 45$ meV per atom in ${\mathrm{Co}}_2/\mathrm{G}$, (vi) EF-induced spin-reorientation transitions in ${\mathrm{Co}}_3/\mathrm{G}$, and (vii) reversibly tunable coercive field and blocking temperatures, which in some cases allow a barrierless magnetization reversal of the cluster. These remarkable electric and magnetic fingerprints open new possibilities of characterizing and exploiting the size- and structural-dependent properties of magnetic nanostructures at surfaces.

We investigate the impurity-scattering-induced quasiparticle interference in the ($\pi ,0$) spin-density wave phase of the iron pnictides. We use a five-orbital tight-binding model and our mean-field theory in the clean limit captures key features of the Fermi surface observed in angle-resolved photoemission. We use a $t$-matrix formalism to incorporate the effect of doping-induced impurities on this state. The impurities lead to a spatial modulation of the local density of states about the impurity site, with a periodicity of $\sim 8a_{\mathrm{Fe}-\mathrm{Fe}}$ along the antiferromagnetic direction. The associated momentum space quasiparticle interference pattern is anisotropic, with major peaks located at $\sim (\pm \pi /4,0)$, consistent with spectroscopic imaging scanning tunneling microscopy. We trace the origin of this pattern to an elliptical contour of constant energy around momentum (0,0), with major axis oriented along the (0,1) direction, in the mean-field electronic structure.

We explore the Floquet band structure and electronic transport in laser-illuminated bilayer graphene ribbons. By using a bias voltage perpendicular to the graphene bilayer we show how to get one-way charge and valley transport among two unbiased leads. In contrast to quantum pumping, our proposal uses a different mechanism based on generating a nonreciprocal band structure with a built-in directionality. The Floquet states at one edge of a graphene layer become hybridized with the continuum on the other layer, so the resulting band structure allows for one-way transport as in an isolator. Our proof of concept may serve as a building block for devices exploiting one-way states.

Annealing of a monolayer of hexagonal boron nitride destroyed by Xe ion irradiation gives rise to rich structural phenomena investigated here through a combination of scanning tunneling microscopy, low-energy electron diffraction, x-ray photoelectron spectroscopy, and density functional theory calculations. We find selective pinning of vacancy clusters at a single specific location within the moiré formed by hexagonal boron nitride (h-BN) and the Ir substrate, crystalline Xe at room temperature of monolayer and bilayer thickness sealed inside h-BN blisters, standalone blisters only bound to the metal at temperatures where boron nitride on Ir(111) decomposes, and finally a pronounced threefold symmetry of all morphological features due to the preferential formation of boron-terminated zigzag edges that firmly bind to the substrate. The investigations give clear insight into the relevance of the substrate for the damage creation and annealing in a two-dimensional layer material.