Ferromagnetic and spin-wave resonance in Co/Pd/CoNi multilayer films

It has been found that the magnitude and sign of exchange interaction between Co(5 nm) and CoNi(5 nm) ferromagnetic layers through Pd depend on magnetization orientation of ferromagnetic layers. If magnetization is oriented in a layer plane, exchange interaction can be both ferromagnetic and antiferromagnetic. If magnetization orientation is orthogonal to a layer plane, the exchange constant is always positive at d_Pd<d _c and equals zero at d_Pd>d _c (d _c is the characteristic length).     

Intersubband cyclotron resonance of holes in strained Ge/GeSi(111) heterostructures with germanium wide quantum wells and cyclotron resonance of 1<Emphasis Type="Italic">L</Emphasis> electrons in GeSi layers

The submillimeter (?ω=0.5–5 meV) magnetoabsorption spectra of strained Ge/Ge_1?xSi_x(111) multilayer heterostructures with thick Ge layers (d_Ge=300–850 Å, d_GeSi≈200 Å, x≈0.1) are investigated at T=4.2 K upon band-gap optical excitation. It is revealed that the absorption spectra contain cyclotron resonance lines of 1L electrons localized in GeSi solid solution layers (unlike the previously studied structures with thin Ge layers as quantum wells for 3L electrons). The absorption spectra of the samples with thick Ge layers (d_Ge=800–850 Å) exhibit cyclotron resonance lines of holes due to transitions from the lower Landau levels in the first quantum-well subband to the Landau levels belonging to the third and fifth higher subbands.     

Spectrum of calcium-like copper Cu X

A copper spectrum has been excited in a vacuum spark and recorded in the range from 80 to 200 Å on high-resolution vacuum spectrographs. The 3d ²?(3d4p + 3d4f + 4p ⁵4d ³) transitions in the spectrum of ninetimes ionized copper (Cu X) have been investigated. Atomic calculations by the Hartree-Fock method with semiempirical correction made it possible to identify 64 new spectral lines. The energies of the corresponding levels are determined.     

Elastic strain and coloration pattern in natural quartz crystals

Very small elastic strains (tilts of the order of 0.25 sec of arc and dilationsΔd/d?10^?6, whered is the spacing of net planes) have been observed in natural quartz crystals. According to their rocking curves which are of almost theoretical width, these crystals were commonly expected to be practically perfect crystals. On double crystal X-ray topographs a pattern was revealed of uniformly strained layers parallel to the rhombohedron faces (10¯11) and with thickness ranging between 20 and 200 microns. This fine structure strain pattern was correlated to the pattern of the optical coloration which could be produced by irradiating the originally transparent crystals with X-rays. A localincrease of coloration matched with a localcontraction of the lattice. Tilts occurred in transition zones between adjacent layers with slightly different lattice spacings. Strain and coloration patterns probably have as a common cause the deposition of layers with different impurity concentrations during the growth process of the crystals. Although no change of the strain as a result of the X irradiation could be detected in the colored layers in particular, experimental evidence has been found for anoverall expansion of the lattice of the order ofΔd/d?5×10^?7 due to X irradiation. This expansion seems to saturate at this low value and is probably caused by electronic processes connected with the coloration. Some aspects concerning the nature of the color centers have been discussed. It seems likely from the results of the strain measurements that both sets of layers, colored and transparent ones, play a combined role in coloration.     

Size Dependences of the Magnetic Properties of Superconducting Lead–Porous Glass Nanostructures

Superconducting structures Pb–PG formed by filling a porous glass matrix with the lead from melt under pressure have been investigated. Samples with characteristic pore structure diameters of d ≈ 7, 3, and 2 nm have been studied. It has been found that the critical temperature of the superconducting transition in the samples under study is similar to the corresponding value T_c ≈ 7.2 K for bulk lead. At the same time, it has been observed that the critical magnetic field of the nanocomposites, which attains H_c(T = 0 K) ≈ 165 kOe for Pb–PG (3 nm), exceeds several times the value H_c(0) = 803 Oe for bulk lead. The low-temperature magnetic- field dependences of magnetic moment M(H) contain quasi-periodic flux jumps, which vanish with a decrease in the lead nanostructure diameter. A qualitative model of the observed effects is considered.     

The proximity effect in an Fe-Cr-V-Cr-Fe system

The proximity effect was studied in a thin-film Fe-Cr-V-Cr-Fe layered system. As the chromium layer thickness (d_Cr) increases at a fixed thickness of iron layers (d_Fe), the dependence of the superconducting transition temperature (T_c) on d_Cr exhibits a maximum at d_Cr ? 40 Å followed by a sharp decrease. Investigation of the dependence of T_c on d_Fe at a fixed d_Cr showed that the depth of penetration of the Cooper pairs into a chromium layer does not exceed 40 Å. Analysis of the results obtained suggests that, at d_Cr ? 40 Å, chromium layers exhibit the transition from a nonmagnetic state to an incommensurate spin density wave state.     

Ground State Energy of the Low Density Hubbard Model

We derive a lower bound on the ground state energy of the Hubbard model for given value of the total spin. In combination with the upper bound derived previously by Giuliani (J. Math. Phys. 48:023302, [2007]), our result proves that in the low density limit the leading order correction compared to the ground state energy of a non-interacting lattice Fermi gas is given by 8π a ? _u ? _d , where ? _u(d) denotes the density of the spin-up (down) particles, and a is the scattering length of the contact interaction potential. This result extends previous work on the corresponding continuum model to the lattice case.     

Magnetic anisotropy of Co/Cu/Co films with indirect exchange coupling

The effect of isothermal annealing on the magnetic anisotropy, bilinear and biquadratic exchange coupling energies, and domain structure of Co/Cu/Co trilayer fiilms with d_Co=6 nm and d_Cu=1.0 and 2.1 nm prepared by magnetron sputtering has been studied. It is shown that, under isothermal annealing, the biquadratic coupling energy decreases by more than an order of magnitude in films with d_Cu=1.0 nm and increases in films with d_Cu=2.1 nm. The fourth-order magnetic anisotropy is shown to be related to the existence of biquadratic exchange energy.     

Structure and physical properties of titanium diselenide intercalated with nickel

The structure, electrical resistivity, thermopower, and magnetic susceptibility of titanium diselenide intercalated with nickel (N_xTiSe₂) are studied systematically in the nickel concentration range x=0–0.5. In accordance with a model proposed earlier, strong hybridization of the Ni3d/Ti3d states is observed, giving rise to suppression of the magnetic moment because of delocalization of the nickel d electrons. It is shown that the strain caused by the Ni3d/Ti3d hybridization does not change the local coordination of a titanium atom.     

Effect of spin crossovers on the Mott-Hubbard transition at high pressures

The effect of spin crossovers in d _n terms on the effective Hubbard parameter (U _eff) determining the gap between the lower and upper Hubbard bands is analyzed using a many-electron approach to describe the electron structure of Mott insulators. A new mechanism of the insulator-metal transition is established for d ⁵ ions, which is related to a decrease in U _eff caused by spin crossover. For other ions, the U _eff value is either independent of pressure (d ², d ⁴, d ⁷) or it exhibits nonmonotonic growth (d ³, d ⁶, d ⁸).     

Stabilizer of a function in the gage group

It is proved that, for the dimension d of the stabilizer of an analytic function z(x, y) in the gage pseudogroup G = {z(x, y) → c(z(a(x), b(y))}, there are precisely four possibilities: (1) d = ∞ and the complexity of z is zero, (2) d = 3 and the complexity of z is equal to one, (3) d = 1 and z is equivalent the function r(x + y) ? x of complexity two, (4) d = 0 in all remaining cases.     

Electron gas induced in SrTiO<Subscript>3</Subscript>

This mini-review is dedicated to the 85th birthday of Prof. L.V. Keldysh, from whom we have learned so much. In this paper, we study the potential and electron density depth profiles in surface accumulation layers in crystals with a large and nonlinear dielectric response such as SrTiO₃ (STO) in the cases of planar, spherical, and cylindrical geometries. The electron gas can be created by applying an induction D₀ to the STO surface. We describe the lattice dielectric response of STO using the Landau–Ginzburg free energy expansion and employ the Thomas–Fermi (TF) approximation for the electron gas. For the planar geometry, we arrive at the electron density profile n(x) ∝ (x + d)^–12/7, where d ∝ D₀^–12/7. We extend our results to overlapping electron gases in GTO/STO/GTO heterojunctions and electron gases created by spill-out from NSTO (heavily n-type doped STO) layers into STO. Generalization of our approach to a spherical donor cluster creating a big TF atom with electrons in STO brings us to the problem of supercharged nuclei. It is known that for an atom with a nuclear charge Ze where Z > 170, electrons collapse onto the nucleus, resulting in a net charge Zn < Z. Here, instead of relativistic physics, the collapse is caused by the nonlinear dielectric response. Electrons collapse into the charged spherical donor cluster with radius R when its total charge number Z exceeds the critical value Z_c ≈ R/a, where a is the lattice constant. The net charge eZ_n grows with Z until Z exceeds Z* ≈ (R/a)^9/7. After this point, the charge number of the compact core Z_n remains ≈ Z*, with the rest Z* electrons forming a sparse TF atom with it. We extend our studies of collapse to the case of long cylindrical clusters as well.     

Size effect of the thermal expansion of nanostructural copper oxide

The temperature dependence of the thermal expansion ΔL/L of samples of high-density nanostructural CuO ceramics with a crystallite size of 20, 70, and 90 nm was measured. The nanoceramics were obtained from coarse-grained CuO powders under converging spherical shock waves. It is found that, at temperatures T > 50 K, the thermal expansion coefficient α(T) of the nanoceramic samples increases with decreasing crystallite sizes and exceeds the value of α(T) of the CuO single crystal by a factor of 3.5 to 4.5. At temperatures T < 50 K, regions with zero and negative values of α(T) were revealed. The possible reasons for the increase in the thermal expansion coefficient of nanoceramics based on 3d-metal oxides are discussed.     

Magnetic Resonance in Gadolinium Nanoparticles near the Curie Point

The Influence of temperature in the range from 275 to 320 K on ESR spectra and magnetization m of ensembles of spherical gadolinium nanoparticles with the diameter from 89 to 18 nm was studied. The particles with d = 18 nm had a cubic face centered structure and no magnetic transition. At T > T_C all particles were paramagnetic, and their g factors were g = 1.98 ± 0.02 irrespective of their size and structure. At T = T_C the particles having 28 to 89 nm in size experienced a magnetic and orientation transition; at T < T_C their m(H) dependences were described by the Langevin function, and the FMR lines broadened and shifted towards H = 0. FMR lines of the Gd particle ensembles showed a hysteresis behavior during magnetization reversal, which did not correlate with the coercivity of the particles. Dependences of the Gd nanoparticles FMR linewidth ΔH(T) changed proportionally to |T–T_C|.     

A New Family of Solvable Pearson-Dirichlet Random Walks

An n-step Pearson-Gamma random walk in ? ^d starts at the origin and consists of n independent steps with gamma distributed lengths and uniform orientations. The gamma distribution of each step length has a shape parameter q>0. Constrained random walks of n steps in ? ^d are obtained from the latter walks by imposing that the sum of the step lengths is equal to a fixed value. Simple closed-form expressions were obtained in particular for the distribution of the endpoint of such constrained walks for any d≥d ₀ and any n≥2 when q is either \(q = \frac{d}{2} - 1 \) (d ₀=3) or q=d?1 (d ₀=2) (Le Caër in J. Stat. Phys. 140:728–751, 2010). When the total walk length is chosen, without loss of generality, to be equal to 1, then the constrained step lengths have a Dirichlet distribution whose parameters are all equal to q and the associated walk is thus named a Pearson-Dirichlet random walk. The density of the endpoint position of a n-step planar walk of this type (n≥2), with q=d=2, was shown recently to be a weighted mixture of 1+floor(n/2) endpoint densities of planar Pearson-Dirichlet walks with q=1 (Beghin and Orsingher in Stochastics 82:201–229, 2010). The previous result is generalized to any walk space dimension and any number of steps n≥2 when the parameter of the Pearson-Dirichlet random walk is q=d>1. We rely on the connection between an unconstrained random walk and a constrained one, which have both the same n and the same q=d, to obtain a closed-form expression of the endpoint density. The latter is a weighted mixture of 1+floor(n/2) densities with simple forms, equivalently expressed as a product of a power and a Gauss hypergeometric function. The weights are products of factors which depends both on d and n and Bessel numbers independent of d.     

Kramers–Kronig Relations in Representation of Modulation Polarimetry by an Example of the Transmission Spectra of GaAs Crystal

The increments of the real and imaginary components of the complex refractive index ΔN = Δn–iΔk of a lightly doped GaAs crystal with a donor concentration of ~10¹⁶ cm^–3 have been measured using modulation polarimetry. It is shown that, within this representation, the birefringence and dichroism spectra (Δn(ω) and Δk(ω), respectively) obtained in the transparency window of a sample subjected to probe strain are derivatives of the corresponding functions: Δn(ω) ≈ dn/dω and Δk(ω) ≈ dk/dω. The experimental characteristics and primary dependences n(ω) and k(ω) derived from them by graphical integration are in agreement with the results of other researchers and measurements carried out by independent methods. The results obtained are compared (taking into account the integral (Kramers–Kronig) relations) with the resonance parameters: amplitude and phase in the Drude–Lorenz model. Agreement between the experimental characteristics and theoretical model predictions can be obtained by choosing an appropriate value of resonance damping parameter.     

Excitation of even levels of erbium atoms without a change in the number of 4<Emphasis Type="Italic">f</Emphasis> electrons

The excitation of even levels of erbium atoms by slow electrons that occurs without a change in the number of electrons in the 4f shell is experimentally studied. The levels investigated belong to the 4f ¹²6s7s, 4f ¹²5d6s, 4f ¹²6s6d configurations. The cross sections measured at an electron energy of 30 eV lie within the range (0.2–18) × 10^?18 cm².     

Periodic Striped Ground States in Ising Models with Competing Interactions

We consider Ising models in two and three dimensions, with short range ferromagnetic and long range, power-law decaying, antiferromagnetic interactions. We let J be the ratio between the strength of the ferromagnetic to antiferromagnetic interactions. The competition between these two kinds of interactions induces the system to form domains of minus spins in a background of plus spins, or vice versa. If the decay exponent p of the long range interaction is larger than d + 1, with d the space dimension, this happens for all values of J smaller than a critical value J_c(p), beyond which the ground state is homogeneous. In this paper, we give a characterization of the infinite volume ground states of the system, for p > 2d and J in a left neighborhood of J_c(p). In particular, we prove that the quasi-one-dimensional states consisting of infinite stripes (d = 2) or slabs (d = 3), all of the same optimal width and orientation, and alternating magnetization, are infinite volume ground states. Our proof is based on localization bounds combined with reflection positivity.     

Effect of bias voltage polarity of a substrate on the texture,microstructure, and magnetic properties of Ni films prepared by magnetron sputtering

The influence of the bias voltage polarity U_s on microstructure, crystallographic texture and magnetic properties has been investigated for Ni films with a thickness of ≈15–420 nm, which are obtained via magnetron sputtering at a working gas pressure P corresponding to the collision-deficient flight mode of atoms of the sputtered target between the target and the substrate. The Ni(111)-textured films have been shown to form at U_s ≈–100 V, whose microstructure and magnetic parameters are almost unchanged with a thickness. In contrast, the Ni(200) films are formed at U_s ≈ +100 V, whose magnetic properties and micro-structure depend significantly on the thickness d that manifests in a critical thickness d* ≈ 150 nm, when the structure of the film becomes inhomogeneous in the thickness, the remagnetization loops are changed from rectangular to supercritical with the formation of the band domain structure.