Systematic {\it ab initio} study of the magnetic and electronic properties of all 3d transition metal linear and zigzag nanowires

It is found that all the zigzag chains except the nonmagnetic (NM) Ni and antiferromagnetic (AF) Fe chains which form a twisted two-legger ladder, look like a corner-sharing triangle ribbon, and have a lower total energy than the corresponding linear chains. All the 3d transition metals in both linear and zigzag structures have a stable or metastable ferromagnetic (FM) state. The electronic spin-polarization at the Fermi level in the FM Sc, V, Mn, Fe, Co and Ni linear chains is close to 90% or above. In the zigzag structure, the AF state is more stable than the FM state only in the Cr chain. It is found that the shape anisotropy energy may be comparable to the electronic one and always prefers the axial magnetization in both the linear and zigzag structures. In the zigzag chains, there is also a pronounced shape anisotropy in the plane perpendicular to the chain axis. Remarkably, the axial magnetic anisotropy in the FM Ni linear chain is gigantic, being ~12 meV/atom. Interestingly, there is a spin-reorientation transition in the FM Fe and Co linear chains when the chains are compressed or elongated. Large orbital magnetic moment is found in the FM Fe, Co and Ni linear chains

A non-variational approach to nonlinear stability in stellar dynamics applied to the King model

In previous work by Y. Guo and G. Rein, nonlinear stability of equilibria in stellar dynamics, i.e., of steady states of the Vlasov-Poisson system, was accessed by variational techniques. Here we propose a different, non-variational technique and use it to prove nonlinear stability of the King model against a class of spherically symmetric, dynamically accessible perturbations. This model is very important in astrophysics and was out of reach of the previous techniques

An {\it ab initio} study of the magnetic and electronic properties of Fe, Co, and Ni nanowires on Cu(001) surface

Magnetism at the nanoscale has been a very active research area in the past decades, because of its novel fundamental physics and exciting potential applications. We have recently performed an {\it ab intio} study of the structural, electronic and magnetic properties of all 3$d$ transition metal (TM) freestanding atomic chains and found that Fe and Ni nanowires have a giant magnetic anisotropy energy (MAE), indicating that these nanowires would have applications in high density magnetic data storages. In this paper, we perform density functional calculations for the Fe, Co and Ni linear atomic chains on Cu(001) surface within the generalized gradient approximation, in order to investigate how the substrates would affect the magnetic properties of the nanowires. We find that Fe, Co and Ni linear chains on Cu(001) surface still have a stable or metastable ferromagnetic state. When spin-orbit coupling (SOC) is included, the spin magnetic moments remain almost unchanged, due to the weakness of SOC in 3$d$ TM chains, whilst significant orbital magnetic moments appear and also are direction-dependent. Finally, we find that the MAE for Fe, and Co remains large, i.e., being not much affected by the presence of Cu substrate.Comment: 4 pages, 2 figure

Band structure of honeycomb photonic crystal slabs

Two-dimensional (2D) honeycomb photonic crystals with cylinders and connecting walls have the potential to have a large full band gap. In experiments, 2D photonic crystals do not have an infinite height, and therefore, we investigate the effects of the thickness of the walls, the height of the slabs and the type of the substrates on the photonic bands and gap maps of 2D honeycomb photonic crystal slabs. The band structures are calculated by the plane wave expansion method and the supercell approach. We find that the slab thickness is a key parameter affecting the band gap size while on the other hand the wall thickness hardly affact the gap size. For symmetric photonic crystal slabs with lower dielectric claddings, the height of the slabs needs to be sufficiently large to maintain a band gap. For asymmetric claddings, the projected band diagrams are similar to that of symmetric slabs as long as the dielectric constants of the claddings do not differ greatly.Comment: Accepted for publication in Journal of Applied Physic

A sharp stability criterion for the Vlasov-Maxwell system

We consider the linear stability problem for a 3D cylindrically symmetric equilibrium of the relativistic Vlasov-Maxwell system that describes a collisionless plasma. For an equilibrium whose distribution function decreases monotonically with the particle energy, we obtained a linear stability criterion in our previous paper. Here we prove that this criterion is sharp; that is, there would otherwise be an exponentially growing solution to the linearized system. Therefore for the class of symmetric Vlasov-Maxwell equilibria, we establish an energy principle for linear stability. We also treat the considerably simpler periodic 1.5D case. The new formulation introduced here is applicable as well to the nonrelativistic case, to other symmetries, and to general equilibria

Measurement-induced nonlocality over two-sided projective measurements

Measurement-induced nonlocality (MiN), introduced by Luo and Fu [Phys. Rev. Lett. 106(2011)120401], is a kind of quantum correlation that beyond entanglement and even beyond quantum discord. Recently, we extended MiN to infinite-dimensional bipartite system [arXiv:1107.0355]. MiN is defined over one-sided projective measurements. In this letter we introduce a measurement-induced nonlocality over two-sided projective measurements. The nullity of this two-sided MiN is characterized, a formula for calculating two-sided MiN for pure states is proposed, and a lower bound of (two-sided) MiN for maximally entangled mixed states is given. In addition, we find that (two-sided) MiN is not continuous. The two-sided geometric measure of quantum discord (GMQD) is introduced in [Phys. Lett. A 376(2012)320--324]. We extend it to infinite-dimensional system and then compare it with the two-sided MiN. Both finite- and infinite-dimensional cases are considered.Comment: 12 page

Geometries for Possible Kinematics

The algebras for all possible Lorentzian and Euclidean kinematics with $\frak{so}(3)$ isotropy except static ones are re-classified. The geometries for algebras are presented by contraction approach. The relations among the geometries are revealed. Almost all geometries fall into pairs. There exists $t \leftrightarrow 1/(\nu^2t)$ correspondence in each pair. In the viewpoint of differential geometry, there are only 9 geometries, which have right signature and geometrical spatial isotropy. They are 3 relativistic geometries, 3 absolute-time geometries, and 3 absolute-space geometries.Comment: 40 pages, 7 figure

Anomalous Nernst and Hall effects in magnetized platinum and palladium

We study the anomalous Nernst effect (ANE) and anomalous Hall effect (AHE) in proximity-induced ferromagnetic palladium and platinum which is widely used in spintronics, within the Berry phase formalism based on the relativistic band structure calculations. We find that both the anomalous Hall ($\sigma_{xy}^A$) and Nernst ($\alpha_{xy}^A$) conductivities can be related to the spin Hall conductivity ($\sigma_{xy}^S$) and band exchange-splitting ($\Delta_{ex}$) by relations $\sigma_{xy}^A =\Delta_{ex}\frac{e}{\hbar}\sigma_{xy}^S(E_F)'$ and $\alpha_{xy}^A = -\frac{\pi^2}{3}\frac{k_B^2T\Delta_{ex}}{\hbar}\sigma_{xy}^s(\mu)"$, respectively. In particular, these relations would predict that the $\sigma_{xy}^A$ in the magnetized Pt (Pd) would be positive (negative) since the $\sigma_{xy}^S(E_F)'$ is positive (negative). Furthermore, both $\sigma_{xy}^A$ and $\alpha_{xy}^A$ are approximately proportional to the induced spin magnetic moment ($m_s$) because the $\Delta_{ex}$ is a linear function of $m_s$. Using the reported $m_s$ in the magnetized Pt and Pd, we predict that the intrinsic anomalous Nernst conductivity (ANC) in the magnetic platinum and palladium would be gigantic, being up to ten times larger than, e.g., iron, while the intrinsic anomalous Hall conductivity (AHC) would also be significant.Comment: Accepted for publication in the Physical Review

Magnetic moment and magnetic anisotropy of linear and zigzag 4{\it d} and 5{\it d} transition metal nanowires: First-principles calculations

An extensive {\it ab initio} study of the physical properties of both linear and zigzag atomic chains of all 4$d$ and 5$d$ transition metals (TM) within the GGA by using the accurate PAW method, has been carried out. All the TM linear chains are found to be unstable against the corresponding zigzag structures. All the TM chains, except Nb, Ag and La, have a stable (or metastable) magnetic state in either the linear or zigzag or both structures. Magnetic states appear also in the sufficiently stretched Nb and La linear chains and in the largely compressed Y and La chains. The spin magnetic moments in the Mo, Tc, Ru, Rh, W, Re chains could be large ($\geq$1.0 $\mu_B$/atom). Structural transformation from the linear to zigzag chains could suppress the magnetism already in the linear chain, induce the magnetism in the zigzag structure, and also cause a change of the magnetic state (ferromagnetic to antiferroamgetic or vice verse). The calculations including the spin-orbit coupling reveal that the orbital moments in the Zr, Tc, Ru, Rh, Pd, Hf, Ta, W, Re, Os, Ir and Pt chains could be rather large ($\geq$0.1 $\mu_B$/atom). Importantly, large magnetic anisotropy energy ($\geq$1.0 meV/atom) is found in most of the magnetic TM chains, suggesting that these nanowires could have fascinating applications in ultrahigh density magnetic memories and hard disks. In particular, giant magnetic anisotropy energy ($\geq$10.0 meV/atom) could appear in the Ru, Re, Rh, and Ir chains. Furthermore, the magnetic anisotropy energy in several elongated linear chains could be as large as 40.0 meV/atom. A spin-reorientation transition occurs in the Ru, Ir, Ta, Zr, La and Zr, Ru, La, Ta and Ir linear chains when they are elongated. Remarkably, all the 5$d$ as well as Tc and Pd chains show the colossal magnetic anisotropy (i.e., it is impossible to rotate magnetization into certain directions). Finally, the electronic band structure and density of states of the nanowires have also been calculated in order to understand the electronic origin of the large magnetic anisotropy and orbital magnetic moment as well as to estimate the conduction electron spin polarization.Comment: To appear in Phys. Rev.