Abstract: within the Kubo formalism. We show that the anisotropic Rashba effect caused by an external field significantly changes the magnitude of the spin splitting. Furthermore, we obtain an analytical expression for the longitudinal optical conductivity associated with interband transitions as a function of the frequency for arbitrary polarization angle. We find that the diagonal components of the optical conductivity tensor are direction dependent and the optical absorption spectrum exhibits a strongly anisotropic absorption window. The height and width of this absorption window are very sensitive to the anisotropy of the system. While the height of absorption peak increases with increasing effective mass anisotropy ratio, the peak intensity is larger when the light polarization is along the armchair direction. Moreover, the absorption peak width becomes broader as the density-of-states mass or Rashba interaction is enhanced. These features in the optical absorption spectrum can be used to determine parameters relevant for spintronics.

Abstract: The anomalous Hall effect (AHE) is studied on the surface of a 3D magnetic topological insulator. By applying a modified semiclassical framework, all three contributions to the AHE, the Berry curvature effect, the side jump effect and the skew scattering effects are systematically treated, and analytical expressions for the conductivities are obtained in terms of the Fermi level, the spatial orientation of the surface magnetization and the concentration of magnetic and nonmagnetic impurities. We demonstrate that the AHE can change sign by altering the orientation of the surface magnetization, the concentration of the impurities and also the position of the Fermi level, in agreement with recent experimental observations. We show how each contribution to the AHE, or even the whole AHE, can be turned off by properly adjusting the given parameters. For example, one can turn off the anomalous hall conductivity in a system with in-plane magnetization by pushing the system into the fully metallic regime.

Abstract: In the Comment, the authors state that the separation of the relative and center of mass variables in our work is not correct. Here we point out that there is a typographical error, i.e., qi instead of -e, in two of our equations which, when corrected, makes the Comment redundant. Within the ansatzes mentioned in our paper all our results are correct, in contrast to the claims of the Comment.

Abstract: Using first-principle calculations, we systematically study strain tuning of the electronic properties of two- dimensional graphitic carbon nitride nanosheets with empirical formula CnNm. We found the following: (i) the ferromagnetic ordered state in the metal-free systems (n, m) = (4,3), (10,9), and (14,12) remains stable in the presence of strain of about 6%. However, the system (9,7) loses its ferromagnetic ordering when increasing strain. This is due to the presence of topological defects in the (9,7) system, which eliminates the asymmetry between spin up and spin down of the p(z) orbitals when strain is applied. (ii) By applying uniaxial strain, a band gap opens in systems which are initially gapless. (iii) In semiconducting systems which have an initial gap of about 1 eV, the band gap is closed with applying uniaxial strain.

Abstract: We present a detailed analysis of the point-defect clustering in strained Si/Si(1-x)Ge(x)/(001)Si structures, including the interaction of the point defects with the strained interfaces and the sample surface during 400 kV electron irradiation at room temperature. Point-defect cluster formation is very sensitive to the type and magnitude of the strain in the Si and Si(1-x)Ge(x) layers. A small compressive strain (-0.3%) in the SiGe alloy causes an aggregation of vacancies in the form of metastable [110]-oriented chains. They are located on {113} planes and further recombine with interstitials. Tensile strain in the Si layer causes an aggregation of interstitial atoms in the forms of additional [110] rows which are inserted on {113} planes with [001]-split configurations. The chainlike configurations are characterized by a large outward lattice relaxation for interstitial rows (0.13 +/-0.01 nm) and a very small inward relaxation for vacancy chains (0.02+/-0.01 nm). A compressive strain higher than -0.5% strongly decreases point-defect generation inside the strained SiGe alloy due to the large positive value of the formation volume of a Frenkel pair. This leads to the suppression of point-defect clustering in a strained SiGe alloy so that SiGe relaxes via a diffusion of vacancies from the Si layer, giving rise to an intermixing at the Si/SiGe interface. In material with a 0.9% misfit a strongly increased flow of vacancies from the Si layer to the SiGe layer and an increased biaxial strain in SiGe bath promote the preferential aggregation of vacancies in the (001) plane, which relaxes to form intrinsic 60 degrees dislocation loops.

Abstract: The role of dielectric screening of electron-hole interaction in van der Waals heterostructures is theoretically investigated. A comparison between models available in the literature for describing these interactions is made and the limitations of these approaches are discussed. A simple numerical solution of Poisson's equation for a stack of dielectric slabs based on a transfer matrix method is developed, enabling the calculation of the electron-hole interaction potential at very low computational cost and with reasonable accuracy. Using different potential models, direct and indirect exciton binding energies in these systems are calculated within Wannier-Mott theory, and a comparison of theoretical results with recent experiments on excitons in two-dimensional materials is discussed.

Abstract: We report extensive measurements on a new compound (Yb0.24Sn0.76)Ru that crystallizes in the cubic CsCl structure. Valence-band photoemission (PES) and L3 x-ray absorption show no divalent component in the 4f configuration of Yb. Inelastic neutron scattering (INS) indicates that the eight-fold degenerate J-multiplet of Yb3+ is split by the crystalline electric field (CEF) into a Γ7-doublet ground state and a Γ8 quartet at an excitation energy 20 meV. The magnetic susceptibility can be fit very well by this CEF scheme under the assumption that a Γ6-excited state resides at 32 meV; however, the Γ8/Γ6 transition expected at 12 meV was not observed in the INS. The resistivity follows a Bloch-Grüneisen law shunted by a parallel resistor, as is typical of systems subject to phonon scattering with no apparent magnetic scattering. All of these properties can be understood as representing simple local moment behavior of the trivalent Yb ion. At 1 K there is a peak in specific heat that is too broad to represent a magnetic-phase transition, consistent with absence of magnetic reflections in neutron diffraction. On the other hand this peak also is too narrow to represent the Kondo effect in the Γ7-doublet ground state. On the basis of the field dependence of the specific heat, we argue that antiferromagnetic (AF) short-range order (SRO) (possibly coexisting with Kondo physics) occurs at low temperatures. The long-range magnetic order is suppressed because the Yb site occupancy is below the percolation threshold for this disordered compound.

Abstract: Electron-energy-loss spectroscopy (EELS) is used to investigate single layers of LaAlO3 grown on SrTiO3 having an n-type interface as well as multilayers of LaAlO3 and SrTiO3 in which both n- and p-type interfaces occur. Only minor changes in Ti valence at the n-type interface are observed. This finding seems to contradict earlier experiments for other SrTiO3/LaAlO3 systems where large deviations in Ti valency were assumed to be responsible for the conductivity of these interfaces. Ab initio calculations have been carried out in order to interpret our EELS results. Using the concept of Bader charges, it is demonstrated that the so-called polar discontinuity is mainly resolved by lattice distortions and to a far lesser extent by changes in valency for both single layer and multilayer geometries.

Abstract: The morphological evolution in La(0.5)Ca(0.5)MnO(3)/SrTiO(3)(100) ultrathin films has been revealed by atomic force microscopy. It was found that ordered linear defects, which are in 1-2 unit cells high and oriented along the cubic [110] and [100] directions, first appear on the smooth surface of films with a thickness of 10 nm. As the epitaxial growth proceeds, these lines on surface develop into a crosshatch pattern for films with a thickness of 25 nm. Using the results of transmission electron microscopy and electrical measurements, we discuss the interplay between the surface pattern formation, the internal dislocation structure, and the variations in the electrical properties.

Abstract: The Dzyaloshinskii-Moriya interaction (DMI) is a chiral interaction that favors formation of domain walls. Recent experiments and ab initio calculations show that there are multiple ways to modify the strength of the interfacially induced DMI in thin ferromagnetic films with perpendicular magnetic anisotropy. In this paper we reveal theoretically the effects of spatially varied DMI on the magnetic state in thin films. In such heterochiral 2D structures we report several emergent phenomena, ranging from the equilibrium spin canting at the interface between regions with different DMI, over particularly strong confinement of domain walls and skyrmions within high-DMI tracks, to advanced applications such as domain tailoring nearly at will, design of magnonic waveguides, and much improved skyrmion racetrack memory.

Abstract: After the discovery of magnetism in monolayer CrI3, the magnetic properties of different 2D materials from the chromium-trihalide family are intuitively assumed to be similar, yielding magnetic anisotropy from the spin-orbit coupling on halide ligands. Here we reveal significant differences between the CrI3 and CrBr3 magnetic monolayers in their magnetic anisotropy, resulting Curie temperature, hysteresis in external magnetic field, and evolution of magnetism with strain, all predominantly attributed to distinctly different interplay of atomic contributions to spin-orbit coupling in two materials.

Abstract: The magnetization of luminescent Er3+-doped PbF2 nanoparticles (formula Er0.3Pb0.7F2.3) has been studied. Despite the high concentration of the doping Er3+ ions and relatively large size (8 nm) of these nanoparticles we have found no deviation between field-cooled and zero-field-cooled magnetization curves down to T=0.35 K, which points out an ultralow blocking temperature for the reversal of magnetization. We also have found strongly deviating magnetization curves M(H/T) for different temperatures T. These results altogether show that the investigated nanoparticles are not superparamagnetic, but rather each Er3+ ion in these nanoparticles is found in a paramagnetic state down to very low temperatures, which implies the breakdown of the Néel-Brown giant spin model in the case of these nanoparticles. Calculations of magnetization within a paramagnetic model of noninteracting Er3+ ions completely support this conclusion. Due to the ultralow blocking temperature, these nanoparticles have a potential for magnetic field-induced nanoscale refrigeration with an option of their optical localization and temperature control.

Abstract: We report a method to reliably count the number of atoms from high-angle annular dark field scanning transmission electron microscopy images. A model-based analysis of the experimental images is used to measure scattering cross sections at the atomic level. The high sensitivity of these measurements in combination with a thorough statistical analysis enables us to count atoms with single-atom sensitivity. The validity of the results is confirmed by means of detailed image simulations. We will show that the method can be applied to nanocrystals of arbitrary shape, size, and atom type without the need for a priori knowledge about the atomic structure.

Abstract: The magnetic properties of manganite bilayers composed of G-type antiferromagnetic (AFM) SrMnO3 and double-exchange ferromagnetic (FM) La0.7Sr0.3MnO3 are studied. A spin-glass state is observed as a result of competing magnetic orders and spin frustration at the La0.7Sr0.3MnO3/SrMnO3 interface. The dependence of the irreversible temperature on the cooling magnetic field follows the Almeida-Thouless line. Although an ideal G-type AFM SrMnO3 is featured with a compensated spin configuration, the bilayers exhibit exchange bias below the spin glass freezing temperature, which is much lower than the Néel temperature of SMO, indicating that the exchange bias is strongly correlated with the spin glass state. The results indicate that the spin frustration that originates from the competition between the AFM super-exchange and the FM double-exchange interactions can induce a strong magnetic anisotropy at the La0.7Sr0.3MnO3/SrMnO3 interface.