Electronic structures of Cr1−δ_{1-\delta}X (X=S, Te) studied by Cr 2p soft x-ray magnetic circular dichroism

Cr 2p core excited XAS and XMCD spectra of ferromagnetic Cr$_{1-\delta}$Te with several concentrations of $\delta$=0.11-0.33 and ferrimagnetic Cr$_{5}$S$_{6}$ have been measured. The observed XMCD lineshapes are found to very weakly depend on $\delta$ for Cr$_{1-\delta}$Te. The experimental results are analyzed by means of a configuration-interaction cluster model calculation with consideration of hybridization and electron correlation effects. The obtained values of the spin magnetic moment by the cluster model analyses are in agreement with the results of the band structure calculation.The calculated result shows that the doped holes created by the Cr deficiency exist mainly in the Te 5porbital of Cr$_{1-\delta}$Te, whereas the holes are likely to be in Cr 3d state for Cr$_{5}$S$_{6}$.Comment: 8 pages, 6 figures, accepted for publication in Physical Review

Hill's equation with quasi-periodic forcing: resonance tongues, instability pockets and global phenomena

A simple example is considered of Hill's equation x" + (a^2 + bp(t))x = 0, where the forcing term p, instead of periodic, is quasi periodic with two frequencies. A geometric exploration is carried out of certain resonance tongues, containing instability pockets. This phenomenon in the perturbative case of small |b|, can be explained by averaging. Next a numerical exploration is given for the global case of arbitrary b, where some interesting phenomena occur. Regarding these, a detailed numerical investigation and tentative explanations are presented.

Electronic Structure of Charge- and Spin-controlled Sr_{1-(x+y)}La_{x+y}Ti_{1-x}Cr_{x}O_{3}

We present the electronic structure of Sr_{1-(x+y)}La_{x+y}Ti_{1-x}Cr_{x}O_{3} investigated by high-resolution photoemission spectroscopy. In the vicinity of Fermi level, it was found that the electronic structure were composed of a Cr 3d local state with the t_{2g}^{3} configuration and a Ti 3d itinerant state. The energy levels of these Cr and Ti 3d states are well interpreted by the difference of the charge-transfer energy of both ions. The spectral weight of the Cr 3d state is completely proportional to the spin concentration x irrespective of the carrier concentration y, indicating that the spin density can be controlled by x as desired. In contrast, the spectral weight of the Ti 3d state is not proportional to y, depending on the amount of Cr doping.Comment: 4 pages, 3 figures. Accepted for publication in Phys. Rev. Let

Global Branch of Solutions for Non-Linear Schrödinger Equations with Deepening Potential Well

We consider the stationary non-linear Schrödinger equation Δu+{ 1+λg(x) }u=f(u)with u∈H1RN,u ≠0 where λ > 0 and the functions f and g are such that lims→0f(s)s=0and1<α+1=lim| s |→∞f(s)s<∞d and g(x)≡0on Ω&macr;,g(x)∈(0,1]on RN\Ω&macr;and lim| x |→+∞g(x)=1 for some bounded open set Ω ∈ RN. We use topological methods to establish the existence of two connected sets D± of positive/negative solutions in R × W2, p RN where $p \in [2, \infty) \cap (\frac{N}{2},\infty)$ that cover the interval (α, Λ(α)) in the sense that PD±=(α,Λ(α))where P(λ,u)=λ, and furthermore, limλ→Λ(α)-‖ uλ ‖L∞(RN)=limλ→Λ(α)-‖ uλ ‖W2,p(RN)=∞,for (λ,uλ)∈D± The number Λ(α) is characterized as the unique value of λ in the interval (α, ∞) for which the asymptotic linearization has a positive eigenfunction. Our work uses a degree for Fredholm maps of index zero. 2000 Mathematics Subject Classification 35J60, 35B32, 58J5

Chebyshev's bias for composite numbers with restricted prime divisors

Let P(x,d,a) denote the number of primes p<=x with p=a(mod d). Chebyshev's bias is the phenomenon that `more often' P(x;d,n)>P(x;d,r) than the other way around, where n is a quadratic non-residue mod d and r is a quadratic residue mod d. If P(x;d,n)>=P(x;d,r) for every x up to some large number, then one expects that N(x;d,n)>=N(x;d,r) for every x. Here N(x;d,a) denotes the number of integers n<=x such that every prime divisor p of n satisfies p=a(mod d). In this paper we develop some tools to deal with this type of problem and apply them to show that, for example, N(x;4,3)>=N(x;4,1) for every x. In the process we express the so called second order Landau-Ramanujan constant as an infinite series and show that the same type of formula holds true for a much larger class of constants. In a sequel to this paper the methods developed here will be used and somewhat refined to resolve a conjecture from P. Schmutz Schaller to the extent that the hexagonal lattice is `better' than the square lattice (see p. 201 of Bull. Amer. Math. Soc. 35 (1998), 193-214).Comment: 26 page

Training Induced Positive Exchange Bias in NiFe/IrMn Bilayers

Positive exchange bias has been observed in the Ni$_{81}$Fe$_{19}$/Ir$_{20}$Mn$_{80}$ bilayer system via soft x-ray resonant magnetic scattering. After field cooling of the system through the blocking temperature of the antiferromagnet, an initial conventional negative exchange bias is removed after training i. e. successive magnetization reversals, resulting in a positive exchange bias for a temperature range down to 30 K below the blocking temperature (450 K). This new manifestation of magnetic training is discussed in terms of metastable magnetic disorder at the magnetically frustrated interface during magnetization reversal.Comment: 4 pages, 3 figure

Extreme values for Benedicks-Carleson quadratic maps

We consider the quadratic family of maps given by $f_{a}(x)=1-a x^2$ with $x\in [-1,1]$, where $a$ is a Benedicks-Carleson parameter. For each of these chaotic dynamical systems we study the extreme value distribution of the stationary stochastic processes $X_0,X_1,...$, given by $X_{n}=f_a^n$, for every integer $n\geq0$, where each random variable $X_n$ is distributed according to the unique absolutely continuous, invariant probability of $f_a$. Using techniques developed by Benedicks and Carleson, we show that the limiting distribution of $M_n=\max\{X_0,...,X_{n-1}\}$ is the same as that which would apply if the sequence $X_0,X_1,...$ was independent and identically distributed. This result allows us to conclude that the asymptotic distribution of $M_n$ is of Type III (Weibull).Comment: 18 page

Decay of semilinear damped wave equations:cases without geometric control condition

We consider the semilinear damped wave equation $\partial_{tt}^2 u(x,t)+\gamma(x)\partial_t u(x,t)=\Delta u(x,t)-\alpha u(x,t)-f(x,u(x,t))$. In this article, we obtain the first results concerning the stabilization of this semilinear equation in cases where $\gamma$ does not satisfy the geometric control condition. When some of the geodesic rays are trapped, the stabilization of the linear semigroup is semi-uniform in the sense that $\|e^{At}A^{-1}\|\leq h(t)$ for some function $h$ with $h(t)\rightarrow 0$ when $t\rightarrow +\infty$. We provide general tools to deal with the semilinear stabilization problem in the case where $h(t)$ has a sufficiently fast decay