Quantum oscillations of resistance and magnetization in the degenerate semiconductor n-HgCr2Se4

In the magnetic field range ΔH=8–60 kOe we observed and studied the anomalous oscillations in the magnetic field dependence of the resistance and magnetization of single crystals of n-HgCr₂Se₄. The absence of periodicity in 1/H in the ΔH=8–20 kOe range can be explained by the non-Fermi-liquid behavior of the electron subsystem and agrees with the theory of the de Haas-van Alphen in systems with intermediate valence. In stronger fields, ΔH=20–60 kOe, the amplitude of the fundamental harmonic decreases, with the number and amplitude of the higher-order harmonics increasing. As a result, noise is superimposed on the signal as magnetic field strength grows. The temperature dependence of the magnetization is the sum of the monotonic spin-wave contribution and the oscillating part. Zh. éksp. Teor. Fiz. 113, 1877–1882 (May 1998)     

Combined polaron states in magnetooptical effects in a quantum well

Combined polaron states in a rectangular quantum well in a strong magnetic field perpendicular to the well plane are discussed. These states are due to interaction between two discrete electron levels with different Landau quantum numbers (n and n ₁) and different size-quantization quantum numbers (m and m ₁) on the one hand and a confined LO phonon on the other under conditions of low temperature when the energy difference between the electronic levelsis equal or close to the energy of the confined LO phonon. The expression for the resonant magnetic field H _res at which a combined polaron is formed contains the energy difference between size-quantized levels, so it is a function of quantum well parameters. The separation ΔE _res between branches in the energy spectrum of a combined polaron and H _res has been calculated as a function of the quantum well width d. The resonant field H _res can be reduced dramatically in comparison with the case m=m ₁. The case of size-quantization with n=n ₁ has been analyzed. The energy difference ΔE _res is in the range (1–5)· 10⁻³ eV. The damping of combined polaron states due to the effect of anharmonicity on the LO phonon has been studied. Interband absorption and features in the reflection spectrum due to interband transitions have been calculated for an arbitrary ratio between the radiative and “phonon” lifetime of a combined polaron have been investigated. Zh. éksp. Teor. Fiz. 116, 1419–1439 (October 1999)     

Observation of diamagnetic domains in beryllium

We have observed diamagnetic domains (Condon domains) in a beryllium single crystal in magnetic fields H⩽3 T (H∥[0001]) at liquid-helium temperatures. The formation of the domain structure was determined according to magnetic-breakdown quantum oscillations of the resistance thermoelectric power as well as according to the splitting of the resonance peak of the free spin precession frequency of muons (μSR). The alternation of a uniform state (with one μSR peak) and a state with domain structure (with two peaks) is consistent as regards the periodicity with the de Haas-van Alphen effect, the period is ΔH≅78 Oe, and the range of existence of domains and the difference in their magnetizations are ΔB=4πΔM=B ₂−B ₁≅30 Oe. Fiz. Tverd. Tela (St. Petersburg) 40, 524–526 (March 1998)     

Submillimetric cyclotron resonance linewidths and electron relaxation time in copper

For the first time submillimetric microwaves (λ<1 mm) are used to observe Azbel' Kaner cyclotron resonance in metals. The very high frequency used (typicallyF≅400 GHz) gives a large value ofωτ (typically 500) and therefore very sharp peaks. The fundamental resonance fieldH _c=m ^* cω/e is rather high (typically 200 KG), so subharmonicsH _c/n can be observed at many values ofH in the field region 0–27 KG. If relatively few electrons participate in the resonance and ifω _cτ≧50 (ω _c=eH/m ^* c,τ relaxation time) thenChambers has shown that the line shapes are independent of relaxation time while the fractional linewidthΔH/H varies as l/ωτ. For the belly orbit in pure copper the conditions of Chambers' theory are satisfied forH≧20 KG parallel to [111] axis.m ^* is a minimum andτ=1.8×10⁻¹⁰ s.     

Dispersion of the Voigt effect in the magnetic semiconductors Cd1−x MnxTe

Spectral measurements of the Voigt birefringence Δn were performed for the cubic magnetic semiconductor Cd_1−x Mn _x Te (0≤x≤0.52) in order to investigate how the exchange interaction of Mn²⁺ ions with itinerant electrons depends on the electron wave vector. It was determined that Δn/x ² is independent of x and the magnetic field direction, i.e., the effect is due to the Mn²⁺ ions and is isotropic. Below the band gap edge the dispersion of the birefringence Δn can be described well in all samples by the unusual dependence Δn∼(E _g −ℏω) ^−3.5. This can be explained by a decrease of the exchange interaction of Mn²⁺ ions with itinerant electrons with increasing distance from the center of the Brillouin zone. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 8, 569–573 (25 April 1998)     

The ground state problem in the infinite-U Hubbard model

The problem of the ground state of the electronic system in the Hubbard model for U=∞ is discussed. The author investigates the normal (singlet or nonmagnetic) N state of the electronic system over the entire range of electron densities n⩽1. It is shown that the energy of the N state ɛ ₀ ⁽¹⁾ (n) in a one-particle approximation, such as (e.g.) the extended Hartree-Fock approximation, is lower than the energy of the saturated ferromagnetic FM state ɛ _FM(n) for all n. The dynamic magnetic susceptibility is calculated in the random phase approximation, and it is shown that the N state is stable over the entire range of electron densities: The static susceptibility (ω=0) does not have a band singularity in the zero-wave vector limit q→0. A formally exact representation is obtained for the mass operator of the one-particle Green’s function, and an approximation of this operator is proposed: M _k(E)⋍λF(E), where λ=n(1−n)/(1−n/2)z is the kinematic interaction parameter, z is the number of nearest neighbors, and F(E) is the total single-site Green’s function. For an elliptical density of states the integral equation for F(E) is solved exactly, ad it is shown that the spectral intensity rigorously satisfies the sum rule. The calculated energy of the strongly correlated N state ɛ ₀(n)<ɛ _FM(n) for all n, and in light of this relationship the author discusses the hypothesis that the ground state of the system is the normal (singlet) state in the thermodynamic limit. The electron distribution function at T=0 differs significantly from the Fermi step; it is “smeared” along the entire energy spectrum, and discontinuities do not occur in the region of the chemical potential m. Fiz. Tverd. Tela (St. Petersburg) 39, 193–203 (February 1997)     

Defect-level analysis of semiconductors by a new differential evaluation ofn(1/T)-characteristics

A new method for the defect-level analysis of extrinsic semiconductors is described. Provided that the defect-level concentration is not too large and the temperature is not too low, the Fermi levelE _F is shifted with increasing temperature from a position near the conduction (or valence) band towards the middle of the forbidden gap monotonously. Thus majority carriers are emitted into the conduction (or valence) band from the defect levels successively. If for a small increment of the temperature the Fermi levelE _F is shifted by ΔE _F and the concentration of free majority carriers is increased by Δn, then the ratio Δn/ΔE _F is a measure of the defect-level concentration within ΔE _F . Furthermore we discuss how this analysis is influenced by additional defect levels outside the range over which the Fermi energy can be shifted by variation of the temperature.     

Dipolar Zeeman mixing in weak magnetic fields: An experiment with ice protons

The evolution of the longitudinal magnetization of nuclear spins in a cw high-frequency magnetic field has been measured using a SQUID magnetometer at liquid-helium temperatures in magnetic fields H ₀ of up to 57 Oe. The time T _m for thermal mixing of the Zeeman and dipolar systems has been found to range between 0.05 and 4×10² s. For T _m>1 s the function T _m(H ₀) is exponential. The proton NMR spectra near the fundamental and twice the Larmor frequency have been obtained. The shift in the resonance with respect to the Larmor frequency is close to the theoretical prediction. Zh. éksp. Teor. Fiz. 114, 1006–1017 (September 1998) Deceased.     

Study of the NMR spectra of hydrogen isotopic analogs and estimation of the magnetic moment of the triton

Nuclear magnetic resonance spectra of the hydrogen isotopic analogs TH and TD on the triton resonance and HT, HD, and H₂ on the proton resonance in the gas phase have been studied. The triton and proton spectra from a single sample have been recorded simultaneously by using the inductivity of a common receiver LC circuit. The energies of the interaction between the magnetic moments of the nuclei of the hydrogen isotopic analogs have been determined: J _tp = 299.3(1) Hz, J _td = 45.5(1) Hz, and J _pd = 43.3(1) Hz. The ratio of the resonance frequencies of the HT molecule nuclei: F _t (TH)/F _p (HT) = 1.066693898(2), which is equal to the ratio of the magnetic moments of the nuclei in the bound state, has been obtained. If the value Δσ(TH) = 2.04 × 10⁻⁸ calculated previously is used for the difference in the screening of nuclei in the HT molecule, then the ratio of the magnetic moment of the triton to the magnetic moment of the proton is μ _t /μ _p = 1.066693920(2), where the statistical standard deviation of the data is given in the parentheses in the units of the last digit.     

Holomorphic Factorization of Determinants of Laplacians using Quasi-Fuchsian Uniformization

For a quasi-Fuchsian group Γ with ordinary set Ω, and Δ _n the Laplacian on n-differentials on Γ\Ω, we define a notion of a Bers dual basis for ker Δ _n . We prove that det , is, up to an anomaly computed by Takhtajan and the second author in (Commun. Math Phys 239(1-2):183–240, 2003), the modulus squared of a holomorphic function F(n), where F(n) is a quasi-Fuchsian analogue of the Selberg zeta function Z(n). This generalizes the D’Hoker–Phong formula det , and is a quasi-Fuchsian counterpart of the result for Schottky groups proved by Takhtajan and the first author in Analysis 16, 1291–1323, 2006.      

Spin-orbit coupling,spin-lattice relaxation,and spin-memory studies ofF-center-molecular-ion pairs in alkali halides

Summary The spin-orbit parameter Δ, spin-lattice relaxation timeT ₁, and spin-mixing parameter ɛ ofF _H(OH⁻) andF _H(CN⁻) centers in several alkali halides have been studied with magnetic circular dichroism at ∼2 K. A close comparison of the experimental results before and after optically induced association of theF center with the molecular ion has been made. In crystals of NaCl structure the negative spin-orbit parameter Δ changes little betweenF andF _H centers in the same host. For CsCl and CsBr two values of Δ have been derived forF _H(CN⁻) centers with axis parallel or perpendicular to the magnetic field. In all studied systems, the spin-lattice relaxation timeT ₁ is already shorter before aggregation compared toF formation. The spin-mixing parameter ɛ decreases slightly forF _H(OH⁻) compared toF centers, while it increases drastically forF _H(CN⁻) defects and reaches its maximum possible value ɛ=0.5 in cesium halides. First attempts to interpret these magneto-optical results will be presented. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

Baryon asymmetry at the weak phase transition in the presence of arbitrary CP violation

The interactions of fermions with the domain-wall bubbles produced during a first-order phase transition are considered. An exact solution of the Dirac equation’s fermion propagation is obtained for a wall profile incorporating a position-dependent CP-violating phase. The reflection coefficients through the wall are computed for particles and antiparticles. The asymmetry in the reflection coefficients is especially high (a resonance effect) when the energy and mass of the incident particles are E/m=Δθ/2, where Δθ is the phase variation across the wall width. We compute the chiral-charge flux through the wall surface and the corresponding baryon asymmetry of the Universe. It agrees in sign and magnitude with the observed baryonic excess ϱB/s ≈ 10^-10 for a larnge of parameters and CP violation. As a function of Δθ, the ratio ϱb/s reaches a maximum for large values of Δθ (m ≈ m _top). The text was submitted by the author in English.     

Width of the ferromagnetic resonance line in highly dispersed powders of crystalline and amorphous Co-P alloys

The resonance characteristics (inhomogeneous FMR linewidth ΔH) in highly dispersed (d=0.1–3 μm) powders of crystalline and amorphous Co-P alloys are investigated as a function of the composition, particle size, and atomic structure. It is established that ΔH for powders of amorphous Co-P alloys is two to three times larger than ΔH for crystalline Co-P powders. According to the investigations performed, this is caused by thermodynamically stimulated segregation of nonmagnetic Co₂P inclusions, apparently an effective relaxation channel, in the amorphous state of Co-P powders. Fiz. Tverd. Tela (St. Petersburg) 41, 464–467 (March 1999)     

Phase-sensitive reentrance into the normal state of mesoscopic SNS structures

Normal (N) metallic (Ag) mesoscopic conductors with two superconducting (S) faces (Al), arranged mirror-symmetrically relative to the streamlines of the current, periodically switch into the normal state as the superconducting phase difference Δϕ between the NS boundaries approaches the values Δϕ =(2n+1)π, n=0,1,2,..., irrespective of temperature and applied voltage. For Δϕ =2nπ and low applied voltages the conductance passes through a maximum and approaches the normal value as temperature decreases (reentrance). As the voltage subsequently increases, the conductance increases and passes through a maximum. As the phase difference moves away from the values Δϕ=2nπ, the maxima shift in the direction of low temperatures and voltages. The latter result shows unequivocally that in our metal structures it is necessary to take into account the next-order corrections to the “weak” proximity effect approximation. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 7, 489–494 (10 April 1998)     

An anomalous Zeeman effect in methane at 3.39 μm

The present paper reports on the first observation of an anomalous Zeeman effect on the hyperfine components of theF ₂ ⁽²⁾ line in methane (λ=3.39 μm), on an asymmetry of a nonlinear resonance in the magnetic field due to the influence of recoid, and on measurements of shifts of individual hyperfine components in weak magnetic fields.     

Magnetic circular dichroism in the absorption of theF A centre in KCl doped with Li and Na

Summary The spin-orbit structure ofF _A centres in KCl:Li and KCl:Na have been studied by means of the magnetic circular dichroism. Due to theirC _4V symmetry theF _A centres have two different spin-orbit parameters, Δ^‖ and Δ^⊥, which only in the KCl:Li case follow the relation: Δ^‖ < Δ_F < Δ^⊥ as expected from the theory. For a close comparison we have also reported our measurement of the spin-orbit coupling ofF centre in KCl. The spin-orbit parameters of theF andF _A centres have been determined using the method of moment.     

Field dependence of spin-lattice relaxation of Nd3+ ions in Y3Al5O12 crystals

Our studies involve measuring spin-lattice relaxation times for Nd³⁺ ions in yttrium-aluminum garnets over the temperature range 4–50 K at 9.25 and 36.4 GHz for different orientations of the external magnetic field in relation to the crystallographic axes. The temperature dependence of the relaxation rate is described by T ₁ ⁻¹ =AT ⁿ+b exp(−Δ/kT), where n varies from sample to sample, with n=1 for “perfect” samples (i.e., with the longest relaxation times). Here Δ is approximately 130 cm⁻¹, which is the energy of the excited Kramers doublet of the neodymium ion closest to the ground state, and this makes it possible to interpret the second term in T ₁ ⁻¹ as the contribution of two-stage relaxation proceeding through the intermediate level Δ. A strong field dependence of these processes has been discovered: when the frequency was increased fourfold, the relaxation rate increased by a factor of 10. The effect is a specific manifestation of the degeneracy of the excited level, breaking of the symmetry of the crystalline field due to lattice defects, and the prevalence of deformations of a certain type in the spin-lattice interaction. Zh. éksp. Teor. Fiz. 111, 332–343 (January 1997)     

The estimates of periodic potentials in terms of effective masses

LetG _n=(A _n ⁻ , A _n ⁺ ),n≧1, denote the gaps,M _n ^± be the effective masses and Σn=[A _n−1 ⁺ ,A _n ^- ],A ₀ ⁺ =0, be the spectral bands of the Hill operatorT=−d ²/dx ²+V(x) inL ² (R), whereV is a 1-periodic real potential fromL ²(0,1). Let the length gapL _n=|G_n|, h_n be the height of the corresponding slit on the quasimomentum domain and Δ_n=π²(2n−1)−∣Σ_n∣>0 be the band reduction. Let ,n≧1, denote the gap length for the operator . Introduce the sequencesL={L_n}, h={h_n}, l={l_n}, Δ={Δ_n},M ^±={M _n ^± } and the norms ,m≧0. The following results are obtained: i) The estimates of‖V‖, ‖L‖, ‖h‖ ₁, ‖l‖₁, ‖δ‖ in terms of ‖M^±‖₂, ii) identities for the Dirichlet integral of quasimomentum and integral of potentials and so on, iii) the generation of i), ii) for more general potentials. The research described in this publication was made possible in part by grant from the Russian Fund of Fundamental Research and INTAS.     

Relation between the reduced and unreduced hardness in nanomicroindentation tests

Hooke’s law is generalized to the case of arbitrary elastic or plastic indentation , where ɛ=q/E _r is the elastic strain, q is the average pressure over the contact area, E _r is the reduced elastic (Young’s) modulus, A is the projected area of the contact, w ₁ is the deformation in elastic indentation by a flat punch. On this basis a relation is obtained between the reduced hardness H and unreduced hardness H _h, which depends on the ratio w _s/w₁=m _s; w _s is the elastic deformation along the perimeter of the indent, and m _s≅0.78. It is shown that the correction ΔE _r to the elastic modulus E _r determined from the condition of linearity of the initial part of the unloading diagram, is ΔE _r=0.27(ΔP/P _m), where ΔP is the value used in the calculation of E _r for the length of the linear part of the diagram, reckoned from the maximum load P _m. It is shown that for metallic construction materials of medium hardness one has q=HM, where HM is the Meyer hardness. With increasing HM and increasing angle ϕ at the tip of the indenter, the ratio HM/q grows by an exponential law. Zh. Tekh. Fiz. 69, 42–48 (July 1999)     

Thermal boundary layer for non-Newtonian fluid

Summary Analytical and numerical solutions for the momentum and thermal boundary layer equations of a non-Newtonian power law fluid are presented. The flow is assumed to be under the influence of an external magnetic fieldB (x) applied perpendicular to the surface and an electric fieldE(x) perpendicular toB(x) and the direction of the longitudinal velocity in the boundary layer. For the power law fluid it is assumed that the shear stress is proportional to then-th power of the velocity gradient andn is called the flow index. The variations of the velocity fieldf′, the temperature field θ, the shear stress on the surfaceτ _W , the displacement thicknessδ ₁ and the momentum thicknessδ ₂ with the magnetic-field parameter γ, the flow indexn, the heat transfer indexS and the Prandtl number Pr are studied. It is found that, if the outer flow velocityU(x) (potential flow) is proportional to the arc lengthx raised to a powerm, then the similarity solution for the thermal boundary layer equation is possible only whenm=1/3, which represents flow past a wedge of included angle π/2. It is established that the temperature of the wedge increases with the increase of γ, Pr,S and the decrease ofn. In general the magnetic field can be used as a heater for the surface of the wedge.