Contribution to the theory of the ferromagnetism of metals with a hexagonal close-packed lattice

The possibility of the appearance of ferromagnetic instability in a hexagonal close-packed system is established on the basis of the idea of a strong interaction in the same unit cell. The conditions for the appearance of spin and orbital instability as a function of the degree of filling of the 2xy, x ²−y ² shell are obtained. The physical picture obtained has a direct relationship to ferromagnetism of hexagonal and cubic cobalt, which possesses the highest Curie temperature, 1396 K. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 7, 451–456 (10 October 1999)     

Influence of interatomic correlation effects on short-range order in hexagonal close-packed polycrystalline alloys

The first x-ray diffraction procedure suitable for the investigation of short-range order in polycrystalline alloys having a hexagonal close-packed (hcp) lattice is developed on the basis of the theory proposed by M. A. Krivoglaz for diffuse x-ray scattering by hcp single-crystal alloys. This procedure takes into account specific details of the crystal structure of the hcp lattice, in particular, the presence of two atoms in the unit cell and the close radii of the individual coordination spheres. The realistic character of the procedure is demonstrated experimentally in the example of hcp Mg-Dy and Mg-Tb alloys. The new procedure is used to calculate, for the first time, the modulating functions of linear and quadratic size effects in Mg-Dy and Mg-Tb alloys. It is shown that the size-effect modulating functions for coordination spheres with close radii have different characters, and their inclusion in diffuse scattering sets the stage for solving the problem of calculating the short-range order parameters on these spheres. Fiz. Tverd. Tela (St. Petersburg) 41, 2109–2115 (December 1999)     

Theory of ordered alloys with anisotropic interatomic interactions

The problem of an ordered binary alloy, in which the interatomic interaction energy depends on direction inside the crystal, is considered within the quasichemical approximation. Anisotropic correlation parameters and equilibrium values of pair number of atoms of various kinds in various directions are determined. Lattice constants are calculated as functions of the alloy compound, of long-range order, and of correlation parameters.     

Direct optical absorption selection rules for the hexagonal close-packed lattice

The direct electric dipole optical selection rules between Bloch electronic states at the symmetry points of the Brillouin zone of the hexagonal close-packed lattice are calculated. Bloch wave functions transforming according to the irreducible representations of both the single and double groups are considered.     

Effect of a third component on ordering of substitutional alloys with anisotropic interatomic interactions

The problem of third-component impurity effects on ordering processes in alloys with anisotropic interatomic interactions is treated in the quasichemical approximation. The case of low-impurity concentration is investigated in detail. It is shown that the presence of a third component leads to an anisotropic redistribution of atom pairs of different types over the various crystal directions even when it interacts isotropically with the main components. The nature of this redistribution depends on alloy composition. The magnetic anisotropy constant of a ternary alloy, induced by thermomagnetic processing, is calculated, and its concentration and temperature dependence are found.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No.7, pp.32–37, July, 1975.     

Effects of lattice dispersion and elastic anisotropy on the thermal properties of fcc metals

New parameters which separately take into account the effects of elastic anisotropy and phonon dispersion on the lattice specific heat in the case of fcc metals have been evaluated. A new graded mesh method which uses 162-direction approximation in (1/16) part of the Brillouin zone has been developed to evaluate the two new parameters.     

Effects of lattice dispersion and elastic anisotropy on the thermal properties of bcc metals

Two new parameters which take into account the effects of elastic anisotropy and phonon dispersion on lattice specific heat in the case of sodium and potassium have been evaluated. A new graded mesh method which uses a 162-direction approximation in (1/16) part of the Brillouin Zone (BZ) has been considered to evaluate the two parameters.     

The anisotropic effect of hexagonal warping on the transport

In the presence of hexagonal warping (HW), the surface state of a topological insulator (TI) exhibits anisotropic Fermi surface. In this work, we study the transport properties of a TI junction, focusing on the influence of anisotropic effect of the HW on the scattering. We establish general expressions for calculating the scattering with an arbitrary angle between TI surface and the potential step, and find that the transmission probability and conductance have a strong dependence on the angle, making TI junction a promising platform for studying the geometry control of transport. Remarkably, we find that the HW can induce a triple refraction, which gives rise to an anomalous increase of the transmission probability when varying incident angle. The general expressions here for calculating the scattering can be extended to the systems with trigonally and tetragonally warped Fermi surface.     

Charged particles on a two-dimensional lattice subject to anisotropic Jahn-Teller interactions

The properties of a system of charged particles on a 2D lattice, subject to an anisotropic Jahn-Teller-type interaction and 3D Coulomb repulsion, are investigated. In the mean-field approximation without Coulomb interaction, the system displays a phase transition of first order. When the long-range Coulomb interaction is included, Monte Carlo simulations show that the system displays very diverse mesoscopic textures, ranging from spatially disordered pairs to ordered arrays of stripes, or charged clusters, depending only on the ratio of the two interactions (and the particle density). Remarkably, charged objects with an even number of particles are more stable than with an odd number of particles. We suggest that the diverse functional behavior-including superconductivity-observed in oxides can be thought to arise from the self-organization of this type.     

Phase transitions of ann-vector model on an elastic anisotropic lattice

Wegner's model for magnetic phase transitions on elastic isotropic lattices is generalized to elastic anisotropy and the general spin-lattice coupling linear in lattice distortion. Cyclic boundary conditions are employed. The elimination of the elastic degrees of freedom gives rise to an effective spin Hamiltonian which consists of a shortrange and a long-range part. Renormalization group analysis yields the following result: If the lattice couples to a relevant operator with an exponenty >d/2, the long-range part contains a relevant contribution with exponent 2y—d leading away from any fixed pointH ^* associated with the short-range interactions. In particular,H ^* is unstable for positive specific heat exponent, and, in most cases, if a spin-anisotropy is involved.     

A two—dimensional photonic crystal with six large bandgaps formed by a hexagonal lattice of anisotropic cylinders

The plane-wave expansion method is used to calculate the band structure of a two-dimensional photonic crystal formed by a hexagonal structure of anisotropic cylinders. Two cylindrical inclusions in the unit cell have two different radii, R₁ and R₂ (R₁2). By reducing the symmetry of the structure and choosing appropriately parameters R₂ and s=R₁/R₂ (s<1), we obtain six large complete bandgaps, among which three are over 0.05 ω_e (where ω_e=\frac{2πc}{a}) in the high region of the normalized frequency (however, one of these over 0.065 ω_e is not stable). There are two other stable complete bandgaps in the low-frequency region.     

A model for lattice dynamics of hexagonal close packed metals

The point ion axially symmetric model of Lehman et al. has been modified for h.c.p. metals to include the electron-ion interaction on the formalism of Krebs. The calculated phonon frequencies of magnesium have almost reproduced the experimental ones within the limit of experimental error.     

The effect of a Pt impurity layer on the magnetocrystalline anisotropy of hexagonal close-packed Co: a first-principles study

On the basis of the fully relativistic screened Korringa-Kohn-Rostoker method we investigate the variation in the magnetocrystalline anisotropy energy (MAE) of hexagonal close-packed cobalt with the addition of platinum impurities. In particular, we perform calculations on a bulk cobalt system in which one of the atomic layers contains a fractional, substitutional platinum impurity. Our calculations show that at small concentrations of platinum the MAE is reduced, while at larger concentrations the MAE is enhanced. This change in the MAE can be attributed to an interplay between on-site Pt MAE contributions and induced MAE contributions on the Co sites. The latter are subject to pronounced, long-ranged Friedel oscillations that can lead to significant size effects in the experimental determination of the MAE of nanosized samples.     

Description of the geometry of crystals with a hexagonal close-packed structure based on pair interaction potentials

The pair force interaction potential that allows one to describe a deviation from spherical symmetry, which is typical for hexagonal close-packed structures, is constructed using the ??spherically symmetric?? Mie potential that depends only on the interatomic distance. The parameters of the considered potential, which ensure the stability of hexagonal close-packed lattices, are obtained for a wide range of metals, namely, beryllium, gadolinium, hafnium, holmium, dysprosium, yttrium, cobalt, lutetium, magnesium, osmium, rhenium, ruthenium, scandium, thallium, terbium, technetium, titanium, thulium, cerium, zirconium, and erbium. It is shown that for this pair interaction potential the hexagonal close-packed structure is energetically more favorable than the face-centered cubic structure. The proposed potential can be used to perform computational experiments and analytical investigations.     

Critical properties of the anisotropic Ising model with competing interactions

The critical properties of the anisotropic Ising model with competing interactions have been investigated by Monte Carlo methods. The region of localization of the Lifshitz point on the phase diagram has been computed. Relations of the finite-size scaling theory are used to calculate the critical exponents of the heat capacity, susceptibility, and magnetization at various values of the competing interaction parameter J ₁. A crossover to a critical behavior characteristic of a multicritical point with increasing parameter J ₁ is shown to be present in the system.     

Discretons: Discrete compactons on a hexagonal lattice

We study the formation and interaction of discretons, solitary waves with an almost compact support (tails decaying at a super-exponential rate), on a hexagonal lattice and its spatial extension. Discretons are shown to be robust and their interaction though not entirely, is quite clean.     

Critical properties of the antiferromagnetic layered Ising model on a cubic lattice with competing interactions

The critical properties of the antiferromagnetic layered Ising model on a cubic lattice with regard to the nearest-neighbor and next-nearest-neighbor interactions are investigated by the Monte Carlo method using the replica algorithm. The investigations are carried out for the ratios of exchange nearest-neighbor and next-nearest-neighbor interactions r = J ₂/J ₁ in the range of 0 ≤ r ≤ 1.0. Using the finite-size scaling theory, the static critical indices of specific heat α, order parameter β, susceptibility γ, correlation radius ν, and Fisher index η are calculated. It is shown that the universality class of the critical behavior of this model is retained in the range of 0 ≤ r ≤ 0.4. It is established that the change in the next-nearest-neighbor interaction value in this model in the range of r > 0.8 leads to the same universality class as the three-dimensional fully frustrated Ising model on the cubic lattice.

     

Self-avoiding random walks on the hexagonal lattice

We use the algorithm recently introduce by A. Berretti and A. D. Sokal to compute numerically the critical exponents for the self-avoiding random walk on the hexagonal lattice. We find=1.3509±0.0057±0.0023v=0.7580±0.0049±0.0046=0.519±0.082±0.077 where the first error is the systematic one due to corrections to scaling and the second is the statistical error. For the effective coordination number we find=1.84779±0.00006±0.0017 The results support the Nienhuis conjecture=43/32 and provide a rough numerical check of the hyperscaling relationdv=2–. An additional analysis, taking the Nienhuis value of=(2+2^1/2)^1/2 for granted, gives=1.3459±0.0040±0.0008