Polar Jahn-Teller centers and the anomalous isotope effect in copper-oxygen high-T c superconductors

We examine the isotope effect in copper-oxygen high-T _c superconductors using the model of polar Jahn-Teller centers, a variant of the local-boson model. The isotope-effect exponents for oxygen and copper depend on the structure of Jahn-Teller centers and its variation due to boson motion. A number of YBa₂Cu₃O_7−δ -based compounds are used to illustrate the feasibility of quantitatively describing the experimentally observed values of α _Cu and α _O and their relationship to T _c. Zh. éksp. Teor. Fiz. 111, 644–653 (February 1997)     

Focal switch of cosine-Gaussian beams

The focal switch of cosine-Gaussian (CsG) beams passing through a system with the aperture and lens separated is studied analytically and numerically. It is shown that the focal switch of CsG beams can appear not only for the apertured case, but also for the unapertured case. The necessary condition for the focal switch is that truncation parameter α > α_c and the beam parameter β > β_c, α_c, β_c being the corresponding critical values. There exists a maximum of the relative transition height Δz _sw as α varies, and Δz _sw increases with increasing β and decreasing N _w. The normalized axial intensity minimum I _min / I _max decreases with an increase of α and β, and I _min / I _max remains unchanged as N _w varies.     

Special magnetic phenomena in heavily doped La<Subscript>0.7−<Emphasis Type="Italic">x</Emphasis></Subscript>Dy<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Sr<Subscript>0.3</Subscript>MnO<Subscript>3</Subscript> system

The magnetism in heavily Dy doped La_0.7−x Dy _x Sr_0.3MnO₃ (0.40⩽x⩽0.70) system is studied in this paper. The M-T relation seems to be complicated with the increase of x. For sample with x = 0.40, AFM behavior exists at T⩽T _N and M-T curves under zero field cooling (ZFC) and field cooling (FC) exhibit typical behavior of spincluster glass state above T _N. For the sample with x = 0.50, the M-T curve under ZFC exhibits a valley at a low temperature while the M-T curve under FC exhibits the negative magnetization below T _N. For samples with x = 0.60, 0.70, their ZFC M-T curves are similar to that of x = 0.50, but the FC M-T curves do not exhibit negative values any more. All the peculiar phenomena above are well explained by Néel double-lattice model combined with M-H relation at typical temperatures. The molecular field theory fits well the negative magnetization for x = 0.50. Supported by the State Key Project of Fundamental Research of China (Grant No. 2007CB925001), the State Key Development Program for Basic Research of China (Grant No. 001CB610604), the Natural Science Foundation of Anhui Higher Education Institutions of China (Grant Nos. 2006KJ266B and ZD2007003-1), Anhui Key Laboratory of Spin Electron and Nanomaterials (Cultivating Base)     

Weak chaos and metastability in a symplectic system of many long-range-coupled standard maps

We introduce, and numerically study, a system of N symplectically and globally coupled standard maps localized in a d=1 lattice array. The global coupling is modulated through a factor r^-α, being r the distance between maps. Thus, interactions are long-range (nonintegrable) when 0≤α≤1, and short-range (integrable) when α>1. We verify that the largest Lyapunov exponent λ_M scales as λ_M ∝ N^-κ(α), where κ(α) is positive when interactions are long-range, yielding weak chaos in the thermodynamic limit N↦∞ (hence λ_M→0). In the short-range case, κ(α) appears to vanish, and the behaviour corresponds to strong chaos. We show that, for certain values of the control parameters of the system, long-lasting metastable states can be present. Their duration t_c scales as t_c ∝N^β(α), where β(α) appears to be numerically in agreement with the following behavior: β>0 for 0 ≤α< 1, and zero for α≥1. These results are consistent with features typically found in nonextensive statistical mechanics. Moreover, they exhibit strong similarity between the present discrete-time system, and the α-XY Hamiltonian ferromagnetic model.     

The Asymptotic Limits of Zero Modes of Massless Dirac Operators

Asymptotic behaviors of zero modes of the massless Dirac operator H = α · D + Q(x) are discussed, where α = (α₁, α₂, α₃) is the triple of 4 × 4 Dirac matrices, , and Q(x) = (q _jk (x)) is a 4 × 4 Hermitian matrix-valued function with | q _jk (x) | ≤ C 〈x〉^−ρ, ρ > 1. We shall show that for every zero mode f, the asymptotic limit of |x|² f (x) as |x| → + ∞ exists. The limit is expressed in terms of the Dirac matrices and an integral of Q(x) f (x).      

Effects of low-level La doping and ageing on TlPb-1223 high Tc superconductors

Bulk samples of the nominal composition of (Tl_0.6Pb_0.5)(Sr_0.8Ba_0.2)₂Ca₂Cu₃O_8+δ−xLaO_1.5 (x = 0–0.1) were prepared by using two-step process and their microstructure, T _c values, and magnetization were studied. The samples consist of the Tl-1223 dominant phase with small Tl-1212 admixture, which increases with a rise of La content. Five years ageing and following oxygen annealing at 450°C and subsequently at 750°C have only a modest effect on T _c values of the studied samples. Low-level La doping (x = 0:04) leads to an increase of T _c values by about 2 K in comparison with undoped samples. Oxygen annealing at 750°C results in an increase in the volume magnetization hysteresis in low applied magnetic fields and rise of critical current density at zero magnetic field and 77 K. This effect is most pronounced for the low La doped sample with x = 0.04. Changes of the induced voltage, U originating in the Meissner effect and of its harmonics in dependence on temperature were measured and used for characterization of the temperature distribution of inter-grain junctions.     

Magnetically two-phase state in Eu1−x AxMnO3 (A=Ca, Sr)

It is observed that low-temperature magnetic properties (dependence of the magnetization on the cooling conditions and the presence of a maximum in the initial magnetic susceptibility) of Eu_{1− x} A_xMnO₃ (A=Ca, Sr; x=0,0.3) samples are similar to those of spin glasses. However, there are also substantial differences: The magnetization depends on the cooling conditions right up to the maximum measurement fields H=45 kOe, and the temperature of T _N of the maximum of the initial magnetic susceptibility is independent of the frequency of the ac magnetic field in which the susceptibility is measured. The magnetization isotherms for T<T _N are a superposition of a linear part, characteristic for an antiferromagnet, and a small spontaneous part. For compositions containing Sr a maximum of the resistivity ρ (ρ_max∼10⁸ Ω ·cm) is observed near T _N; in a 120 kOe magnetic field this maximum is lowered by four orders of magnitude and the temperature of the maximum is two times higher. In compositions with x=0.3 the paramagnetic Curie point is much higher than for the composition with x=0: θ=110 K (A=Ca), 175 K (A=Sr), and −100 K (x=0). These characteristic features of the magnetic and electric properties are explained by the existence of a magnetically two-phase state in this system, consisting of ferromagnetic clusters, in which the charge carriers are concentrated, embedded in an insulating antiferromagnetic matrix. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 5, 375–380 (10 March 1999)     

Temporal correlations and persistence in the kinetic Ising model: the role of temperature

We study the statistical properties of the sum S _t = dt'σ _t', that is the difference of time spent positive or negative by the spin σ _t, located at a given site of a D-dimensional Ising model evolving under Glauber dynamics from a random initial configuration. We investigate the distribution of S_t and the first-passage statistics (persistence) of this quantity. We discuss successively the three regimes of high temperature ( T > T _c), criticality ( T = T _c), and low temperature ( T < T _c). We discuss in particular the question of the temperature dependence of the persistence exponent , as well as that of the spectrum of exponents (x), in the low temperature phase. The probability that the temporal mean S _t/t was always larger than the equilibrium magnetization is found to decay as t ^{- - ?}. This yields a numerical determination of the persistence exponent in the whole low temperature phase, in two dimensions, and above the roughening transition, in the low-temperature phase of the three-dimensional Ising model. Received 4 December 2000     

The Hopfield Model on a Sparse Erdös-Renyi Graph

We analyze the storage capacity of the Hopfield model on a sparse G(N,p) random graph. We show that it is proportional to αpN in the entire regime where the corresponding random graph is asymptotically connected and for all value of α≤α _c =0.03.     

Mass spectrum in SQCD and problems with the Seiberg duality. Another scenario

The N = 1 SQCD with SU(N _c ) colors and N _F flavors of light quarks is considered within the dynamical scenario that assumes that quarks can be in the two different phases only: the heavy-quark phase, where they are confined, and the phase of higgsed quarks, at the appropriate values of the Lagrangian parameters. The mass spectra of this (direct) theory and its Seiberg dual are obtained and compared for quarks of small equal or unequal masses. It is shown that in those regions of the parameter space where an additional small parameter exists (it is < [`(b)]₀ /N_F = (3N_c - N_F )/N_F << 1< \bar b_0 /N_F = (3N_c - N_F )/N_F \ll 1 at the right end of the conformal window, where the direct theory is weakly coupled in the vicinity of its IR fixed point, or its analog 0 < b ₀/N _F = (2N _F − 3N _c )/N _F ≪ 1 for the dual theory at the left end of the conformal window), the mass spectra of the direct and dual theories are parametrically different. A number of other regimes are also considered.     

A frustrated heisenberg antiferromagnet on a triangular lattice with next-nearest neighbor interactions

Using the Monte Carlo method, we study the critical properties of the three-dimensional frustrated Heisenberg model on a triangular lattice with allowance for next-nearest neighbor interactions. Using the theory of finite-size scaling, we calculate the static magnetic and chiral critical exponents of heat capacity α, susceptibility γ, γ _k , magnetization β, β _k , and correlation length ν.     

Universal behavior of CePd<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Rh<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> ferromagnet at the quantum critical point

The heavy-fermion metal CePd_1−x Rh _x can be tuned from ferromagnetism at x = 0 to the nonmagnetic state at some critical concentration x _c . The non-Fermi liquid behavior (NFL) at x ≃ x _c is recognized by the power-law dependence of the specific heat C(T) given by the electronic contribution susceptibility X(T) and volume expansion coefficient α(T) at low temperatures: C/T ∝ X(T) ∝ α(T)/T∝ 1/ √T. We also demonstrate that the behavior of the normalized effective mass M _N ^* observed in CePd_1−x Rh _x at x ≃ 0.8 agrees with that of M _N ^* observed in paramagnetic CeRu₂Si₂ and conclude that these alloys exhibit the universal NFL thermodynamic behavior at their quantum critical points. We show that the NFL behavior of CePd_1−x Rh _x can be accounted for within the frameworks of the quasiparticle picture and fermion condensation quantum phase transition, while this alloy exhibits a universal thermodynamic NFL behavior that is independent of the characteristic features of the given alloy such as its lattice structure, magnetic ground state, dimension, etc. The text was submitted by the authors in English.     

Magnetic-Field-Controlled Quantum Critical Points in the Triangular Antiferromagnetic Cs2CuCl4-xBrx Mixed System

The triangular antiferromagnetic Cs₂CuCl_4-xBr_x mixed system is studied by neutron single-crystal diffraction in magnetic field. It shows a rich magnetic phase diagram consisting of four regimes depending on the Br concentration and is characterized by different exchange coupling mechanisms. For the investigated compositions from regime I (0 < x ≤ 1.5), a critical magnetic field B_c is found for a Br concentration x = 0.8 at B_c = 8.10(1) T and for x = 1.1 at B_c = 7.73(1) T and from regime IV (3.2 < x < 4) for x = 3.3 at B_c = 0.99(3) T. For magnetic fields larger than the respective B_c, magnetic superlattice reflections of these compounds are not found. The incommensurate magnetic wave vector q = (0, 0.470, 0) appears below the ordering temperature T_N = 0.51(1) K for Cs₂CuCl_3.2Br_0.8, and q = (0, 0.418, 0) below T_N = 1.00(6) K for Cs₂CuCl_0.3Br_3.7. Neutron diffraction experiments at around 60 mK for x = 3.7 in a magnetic field show the critical magnetic field at B_c = 7.94(16) T and the formation of the second magnetic phase at around 8.5 T depending on the temperature. Inelastic neutron scattering experiments for the compound from regime III (2 < x ≤ 3.2) with x = 2.2 show dynamical correlations at a temperature around 50 mK giving evidence for a spin liquid phase.     

Fabrication and magnetic characterization of Co<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Pt<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript> nanowire arrays

Co _x Pt_1−x (x≥0.7) alloy nanowires are grown into self-synthesized anodic alumina templates by electrodeposition. Magnetic and magnetization properties of Co _x Pt_1−x alloy nanowires are measured as functions of wire length, temperature, and field orientation. X-ray diffraction shows that as-prepared CoPt nanowires are of fcc polycrystalline structure. A crossover of easy axis of magnetization is observed from parallel to perpendicular of the nanowire axis as a function of length. The coercivity (H _c) and remanent squareness (SQ) of Co _x Pt_1−x nanowire arrays are derived from hysteresis loops measured at various angles (θ) between the field and wire axis. H _c(θ) and SQ(θ) curves show bell-shaped or otherwise bell-shaped behavior corresponding to the easy axis of their magnetization.     

Monte Carlo investigation of phase transitions in the frustrated Heisenberg model on a triangular lattice

The critical properties and phase transitions of the three-dimensional frustrated antiferromagnetic Heisenberg model on a triangular lattice have been investigated using the Monte Carlo method with a replica algorithm. The critical temperature has been determined and the character of the phase transitions has been analyzed using the method of fourth-order Binder cumulants. A second-order phase transition has been found in the three-dimensional frustrated Heisenberg model on a triangular lattice. The static magnetic and chiral critical exponents of the heat capacity α, the susceptibility γ and γ _k , the magnetization β and β _k , the correlation length ν and ν _k , as well as the Fisher exponents η and η _k , have been calculated in terms of the finite-size scaling theory. It has been demonstrated that the three-dimensional frustrated antiferromagnetic Heisenberg model on a triangular lattice forms a new universality class of the critical behavior.     

A Tomography of the GREM: Beyond the REM Conjecture

In a companion paper we proved that in a large class of Gaussian disordered spin systems the local statistics of energy values near levels N^1/2+α with α<1/2 are described by a simple Poisson process. In this paper we address the issue as to whether this is optimal, and what will happen if α=1/2. We do this by analysing completely the Gaussian Generalised Random Energy Models (GREM). We show that the REM behaviour persists up to the level β_cN, where β_c denotes the critical temperature. We show that, beyond this value, the simple Poisson process must be replaced by more and more complex mixed Poisson point processes. Research supported in part by the DFG in the Dutch-German Bilateral Research Group ``Mathematics of Random Spatial Models from Physics and Biology' and by the European Science Foundation in the Programme RDSES.     

A dual resonance model for high energy electroweak reactions

We derive a dual resonance model for two body electroweak reactions at a few TeV. This model depends on one non standard free parameter, the “weak interaction Regge slope”α _w ^′ , and implies towers of resonances in all non-exotic channels at massesm _n=√n/α _w ^′ . Whenα _w ^′ goes to zero, we require, by explicit matching, consistency of our model at the tree level with the standard model with Higgs boson graphs removed. To derive this model, we have transposed in the electroweak domain an equivalent model suited to hadronic interactions at a few GeV which gives a good agreement with experimental data. This article was processed by the author using the LAT_EX style filepljour2 from Springer-Verlag.     

Effect of Fe substitution on the thermal expansion of the highT c superconductor Y1Ba2Cu3O y

Thermal expansion measurements have been carried out on Fe substituted superconducting compounds Y₁Ba₂(Cu_1−x Fe _x )₃O _y (0<x<4%) using a high resolution dilatometer employing the three terminal capacitance technique. The experimental set up is sensitive enough to detect changes in α of less than 10⁻⁸K⁻¹. Results show that the jump Δα in the coefficient of linear thermal expansion at the superconducting transition temperature,T _c, increases almost linearly with Fe concentration. The normal state thermal expansion coefficient α first decreases, attains a minimum value aroundx=1% and then increases for higher Fe concentrations. The oxygen content per unit formula is almost constant up tox=1% and then increases rapidly withx. It has also been observed that the anomalous behaviour of α around 260 K observed by Meingastet al [22] for Fe concentrationx=5% is due to inadequate annealing of the sample.