Electronic spectrum of a two-dimensional Fibonacci lattice

The electronic spectrum and wave functions of a new quasicrystal structure—a two-dimensional Fibonacci lattice—are investigated in the tight-binding approximation using the method of the level statistics. This is a self-similar structure consisting of three elementary structural units. The “central” and “nodal” decoration of this structure are examined. It is shown that the electronic energy spectrum of a two-dimensional Fibonacci lattice contains a singular part, but in contrast to a one-dimensional Fibonacci lattice the spectrum does not contain a hierarchical gap structure. The measure of allowed states (Lebesgue measure) of the spectrum is different from zero, and for “central” decoration it is close to 1. The character of the localization of the wave functions is investigated, and it is found that the wave functions are “critical.” Zh. éksp. Teor. Fiz. 116, 1834–1842 (November 1999)     

Exchange mechanism for localization of phonons near the surface of a magnetically ordered crystal

It is shown that first-principles inclusion of nonuniform exchange interaction leads to the creation of a new type of generalized shear acoustic wave propagating near the mechanically free surface of a magnet. Criteria are formulated that can be used to specify conditions under which an “exchange” type of surface acoustic wave can exist at the boundary between a magnetic and a nonmagnetic medium once the spectrum of magnetoelastic oscillations of the unbounded magnetic crystal is known. Fiz. Tverd. Tela (St. Petersburg) 40, 299–304 (February 1998)     

Anisotropic momentum transfer in low-dimensional electron systems in a magnetic field

In low-dimensional systems with an asymmetric quantizing potential, an asymmetric electron energy spectrum ε(p)≠ε(−p), where p is the electron momentum, arises in the presence of a magnetic field. A consequence of such an energy spectrum is that momentum transfer to the electron system in mutually opposite directions in the presence of an external perturbation is different. Therefore, in the presence of a standing electromagnetic wave momentum is transferred from the wave to the electrons, which gives rise to a new type of electromotive force. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 8, 551–555 (25 October 1997)     

Electron spectrum and wave functions of icosahedral quasicrystals

Electron spectra and wave functions of icosahedral quasicrystals have been investigated in the tight-binding approximation using the two-fragment structural model (the Amman-MacKay network) with “central” decoration. A quasicrystal has been considered as a limiting structure in a set of optimal cubic approximants with increasing lattice constants. The method of level statistics indicates that the energy spectrum of an icosahedral quasicrystal contains a singular (nonsmooth) component. The density of electron states has been calculated for the first four optimal cubic approximants of the icosahedral quasicrystal, and the respective Lebesgue measures of energy spectra of these approximants have been obtained. Unlike the case of a one-dimensional quasiperiodic structure, the energy spectrum of an icosahedral quasicrystal does not contain a hierarchical gap structure typical of the Cantor set of measure zero in a one-dimensional quasicrystal. Localization of wave functions in an icosahedral quasicrystal has been studied, and their “critical” behavior has been detected. The effect of disorder due to substitutional impurities on electron properties of icosahedral quasicrystals has been investigated. This disorder makes the electron spectrum “smoother” and leads to a tendency to localization of wave functions. Zh. éksp. Teor. Fiz. 113, 1009–1025 (March 1998)     

Characteristic features of the energy spectrum of icosahedral quasicrystals

The character of the energy spectrum of an icosahedral quasicrystal is investigated in the tight-binding approximation. It is found that the spectrum does not contain the hierarchical gap structure characteristic for a Cantor set. Investigation of the smoothness of the energy spectrum by the method of level statistics showed that the spectrum contains a singular part. Suggestions are made concerning the form of the wave functions. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 2, 101–105 (25 January 1996)     

Reflection and refraction of spin waves in uniaxial magnets in the geometrical-optics approximation

The laws governing the propagation of magnetization waves are investigated in the geometricaloptics approximation, in which a spin wave can be treated as a ray. The refractive index for a spin wave on the interface between two magnets with different exchange coupling constants and magnetic anisotropy constants is determined. The dependences of the intensity of the reflected wave and the refractive index on the spin-wave frequency and the strength of the external uniform magnetic field are calculated. Estimates of the dimensions of inhomogeneous inclusions that perform functions analogous to the functions of lenses and mirrors in optics are presented. The possibility of using the same inhomogeneities both as lenses and as mirrors, depending on the magnetic field strength, is pointed out. Zh. Tekh. Fiz. 68, 60–63 (February 1998)     

Energy spectra and quantum crystallization in two-electron quantum dots in a magnetic field

Quantum crystallization of electrons in a quantum dot (QD) subjected to an external magnetic field is considered. Two-electron QDs with two-dimensional (2D) parabolic confining potential in an external transverse magnetic field are calculated. The Hamiltonian is numerically diagonalized in the basis of one-particle functions to find the energy spectra and wave functions for the relative motion of electrons with inclusion of electron-electron interaction for a broad range of the confining-potential steepness (α) and external magnetic fields (B). The region of the external parameters (α, B) within which a gradual transition to quantum crystalline order occurs is numerically determined. In contrast to a 2D unbounded system, a magnetic field acts nonmonotonically on “crystallization” in a quantum dot with several electrons because of a competition between two effects taking place with increasing B, namely, decreasing spread of the electron wave functions and increasing effective steepness of the confining potential, which reduces the average separation between electrons. Fiz. Tverd. Tela (St. Petersburg) 40, 1753–1759 (September 1998)     

Superconductivity and magnetism in HoNi2B2C

The effect of magnetic ordering on superconductivity in HoNi₂B₂C is studied. It is concluded that the abrupt suppression of superconductivity in the region of incommensurate antiferromagnetic ordering is due to a modification of the wave functions of the conduction electrons by the long-range magnetic order. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 9, 702–707 (10 May 1996)     

Tamm states of carbon nanotubes

The fine structure of the π-electron spectrum of semi-infinite carbotubulenes (cylindrical graphene tubes) is investigated. Together with closed short-diameter tubelenes, open nanotubes whose terminal fragments contain heteroatoms are studied. Algebraic equations are obtained for the one-electron energy levels corresponding to wave functions localized on a terminal fragment. It is shown that Tamm energy levels, lying in either the band gaps or the continuous spectrum (resonance states), can exist in the systems studied. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 8, 588–593 (25 April 1996)     

Electronic state confinement in a Hubbard chain

Electron redistribution over a 1D sublattice resulting from Hubbard repulsion leads to an effective two-particle interaction with a potential linear in coordinate difference. Two-particle wave functions and a narrow-band electron spectrum have been found. Fiz. Tverd. Tela (St. Petersburg) 40, 761–763 (April 1998)     

Electron states in quantum-dot and antidot arrays placed in a strong magnetic field

Quantum electronic states in a dot (antidot) array in the presence of a dc magnetic field are studied. A new method of numerical calculation of the electron spectrum and wave functions in a two-dimensional periodic potential and perpendicular magnetic field is proposed. The magnetic-subband energies, density of electron states, and electron density |ψ(x,y)|², as well as the amplitude of the potential, and lattice period and degree of anisotropy for different magnetic fields have been found. The calculations were performed for quantum dots in the In_0.2Ga_0.8As-GaAs and GaAs-Al_0.3Ga_0,7As systems. The rearrangement of the spectrum with variation of magnetic field and with transition from the tight-binding to weak-binding approximation is studied (ω _c is the cyclotron frequency, and V ₀ is the periodic-potential amplitude). The calculations show that the two-dimensional lattices epitaxially grown presently on semiconductor surfaces permit observation of quantum effects associated with rearrangement of the spectrum (electron transport and optical absorption) in magnetic fields H⩽1 MG. Fiz. Tverd. Tela (St. Petersburg) 40, 1134–1139 (June 1998)     

A quantitative determination of magnetic fluctuations in CuGeO3

A polarised neutron scattering investigation has been carried out on a powder sample of CuGeO₃ within the temperature range of 1.5 K to 600 K. The magnetic scattering has been separated from all other contributions by using polarised neutrons and polarisation analysis and placed onto an absolute scale. At low temperatures the long wavelength components of the paramagnetic response are suppressed consistent with the formation of Cu dimers in which the magnetic moments are correlated antiferromagnetically. This form of the scattering persists to temperatures well above the dimerisation temperature T _sp ∼ 14 K. However as the temperature is raised the intensity of the long wavelength spin fluctuations increases and above ∼150 K they are the dominant feature in the wave vector dependence of the response. At all temperatures the observed scattering extrapolates smoothly to the Q = 0 value given by the uniform susceptibility. Consequently the thermal variation of the uniform susceptibility arises from the evolution of the long wavelength magnetic fluctuations. At large wave vectors the energy dependence of the scattering revealed that the response occurs below 16 meV in agreement with the reported maximum magnetic excitation energy at the zone boundary in the ground state. However the total magnetic scattering is significantly less than that expected for a local moment system suggesting that the spectrum of thermal and quantum fluctuations overlap. Received 30 May 2000 and Received in final form 22 March 2001     

High-order perturbation theory for the hydrogen atom in a magnetic field

The states of a hydrogen atom with principal quantum numbers n⩽3 in a constant uniform magnetic field ℋ are studied. Coefficients in the expansion of the energy of these states in powers of ℋ² up to the 75th order are obtained. Series for the energies of the states and the wave functions are summed to values of ℋ on the order of the atomic magnetic field. A generalization of the moment method upon which these calculations are based can be used in other cases in which a hydrogen atom is perturbed by a potential with a polynomial dependence on the coordinates. Zh. éksp. Teor. Fiz. 113, 550–562 (February 1998)     

Ferromagnetic resonance in multilayer [Fe/Cr]n structures with noncollinear magnetic ordering

The excitation spectrum in an [Fe/Cr]n multilayer structure with non-collinear magnetic ordering was studied by the ferromagnetic resonance (FMR) method in the frequency interval 9.5–37 GHz at room temperature. Besides an acoustic branch, several additional modes were observed under parallel excitation of resonance. The FMR spectrum was calculated analytically in a biquadratic exchange model, neglecting in-plane anisotropy, for an infinite number of layers in the structure and numerically for a finite number of layers contained in real samples. It was shown that the observed modes correspond to excitation of standing spin waves with wave vectors perpendicular to the film plane. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 9, 690–695 (10 May 1998)     

Magnetic structure of Ce<Subscript>2</Subscript>Fe<Subscript>17 − <Emphasis Type="Italic">x</Emphasis></Subscript>Mn<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> intermetallic compounds

The magnetic structure of intermetallic compounds Ce₂Fe_{17 − x} Mn _x (0 ≤ x ≤ 3) was studied using neutron diffraction. The neutron diffraction patterns measured at 4.2 K contain satellites indicating a modulated structure with the wave vector k = [0, 0, τ]. As the concentration x increases, the value of τ increases, while the average magnetic moment of Fe/Mn atoms decreases. A change in the magnitudes of the average magnetic moment and wave vector k is explained by competition between exchange interactions at distances of nearest neighbor transition element atoms.     

Donors in a strong magnetic field and elastic magnetic-impurity resonance in diamondlike semiconductors

The possibility of resonance during elastic intravalley scattering in n-type semiconductors is investigated in connection with the crossing (due to anisotropy of the effective mass) of the energy levels of excited states of a shallow donor as functions of the magnetic field. The hybridization of states of different frequencies in the vicinity of a crossing is attributed to the emergence of a nonzero dipole moment of the excited impurity atom and, accordingly, a long-range potential, which creates carrier-transport anomalies. The lower part of the donor spectrum is calculated as a function of the magnetic field in Si with B∥〈001〉 and in Ge with B∥〈111〉 or B∥〈110〉. A crossing occurs in Ge in the field range 9.9 T<B<16.7 T and in Si in the field range 10.5 T<B<37.7 T. The characteristic longitudinal relaxation time and the transverse conductivity, which are determined by scattering at excited donors in the presence of the hybridization of states, are calculated. Zh. éksp. Teor. Fiz. 112, 975–1010 (September 1997)     

Nonlinear surface magnetic polaritons in a nonuniform magnetic field

High-frequency surface magnetic polaritons of finite amplitude propagating along the interface between a ferrite and a nonlinear insulator in a weakly nonuniform, shaft-shaped external magnetic field are investigated theoretically. The analysis is based on employment of the variational method together with bilinear relations having the form of Lorentz’s lemma. It is shown that the wave dispersion and the transverse profile of a wave along the field nonuniformity depend significantly on the amplitude of the wave. Zh. Tekh. Fiz. 68, 92–95 (September 1998)     

Quasiclassical approximation with the centrifugal potential excluded

We develop a modification of the WKB method (the modified quantization method, or MQM) for finding the radial wave functions. The method is based on excluding the centrifugal potential from the quasiclassical momentum and changing correspondingly the phase in the Bohr-Sommerfeld quantization condition. MQM is used to calculate the asymptotic coefficients at zero and at infinity. We use the examples of power-law and funnel potentials to show that MQM not only dramatically broadens the possibilities of studying the energy spectrum and the wave functions analytically but also ensures accuracy to within a few percent even when one calculates states with a radial quantum number n _r ∼1, provided that the angular momentum l is not too large. We also briefly discuss the possibility of generalizing MQM to the relativistic case (the spinless Salpeter equation). Zh. éksp. Teor. Fiz. 116, 511–525 (August 1999)     

Critical behavior of the wave functions of icosahedral quasicrystals

The character of the localization of the wave functions of an icosahedral quasicrystal is investigated in the tight-binding approximation. It is found that the wave functions exhibit “critical behavior”: they are neither localized, as in the case of Anderson localization, nor delocalized, as in the case of Bloch states. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 8, 559–563 (25 October 1996)     

Eigenmode scattering relations for plane-stratified gyrotropic media

We consider the 4×4 scattering matrixS for a plane wave incident on a plane-stratified gyrotropic multilayer slab, which is assumed to have a single symmetry axis (the magnetisation vector in a ferrite sheet, or the external magnetic field direction in a plane-stratified magnetoplasma). In the given (original) problem the plane of incidence is at an azimuthal angle ϕ with respect to the magnetic meridian plane (the plane containing the normal to the stratification, and the gyrotropic symmetry axis), and there is a corresponding “conjugate” set of wave fields, in which the plane of incidence is at an azimuthal angle (π−ϕ), with a corresponding conjugate scattering matrixS′. Adjoint wave fields, obtained by reversing the magnetic symmetry vector, are used to yield the eigenmode amplitudes required in the definition of the scattering matrices. At an interface between two adjacent layers the scattering matrices are shown to be uniquely determined by the characteristic wave polarisations, and this is used to prove that the given and conjugate scattering matrices,S andS′, for the overall multilayer system are mutually transposed, i.e. .