Electronic structure and magnetic properties of Gd-doped and Eu-rich EuO

The effects of Gd doping and O vacancies on the magnetic interaction and Curie temperature of EuO are studied using first-principles calculations. Linear response calculations in the virtual crystal approximation show a broad maximum in the Curie temperature as a function of doping, which results from the combination of the saturating contribution from indirect exchange and a decreasing contribution from the f-d hopping mechanism. Non-Heisenberg interaction at low doping levels and its effect on the Curie temperature are examined. The electronic structure of a substitutional Gd and of an O vacancy in EuO are evaluated. When the 4f spins are disordered, the impurity state goes from single to double occupation, but correlated bound magnetic polarons are not ruled out. At higher vacancy concentrations typical for Eu-rich EuO films, the impurity states broaden into bands and remain partially filled. To go beyond the homogeneous doping picture, magnetostructural cluster expansions are constructed, which describe the modified exchange parameters near Gd dopants or O vacancies. Thermodynamic properties are studied using Monte Carlo simulations. The Curie temperature for Gd-doped EuO agrees with the results of the virtual crystal approximation and shows a maximum of about 150 K. At 3.125% vacancy concentration the Curie temperature increases to 120 K, consistent with experimental data for Eu-rich film samples.Comment: 15 pages, 13 figures, under review in Physical Review

Enhanced relativistic harmonics by electron nanobunching

It is shown that when an few-cycle, relativistically intense, p-polarized laser pulse is obliquely incident on overdense plasma, the surface electrons may form ultra-thin, highly compressed layers, with a width of a few nanometers. These electron "nanobunches" emit synchrotron radiation coherently. We calculate the one-dimensional synchrotron spectrum analytically and obtain a slowly decaying power-law with an exponent of 4/3 or 6/5. This is much flatter than the 8/3 power of the BGP (Baeva-Gordienko-Pukhov) spectrum, produced by a relativistically oscillating bulk skin layer. The synchrotron spectrum cut-off frequency is defined either by the electron relativistic $\gamma$-factor, or by the thickness of the emitting layer. In the numerically demonstrated, locally optimal case, the radiation is emitted in the form of a single attosecond pulse, which contains almost the entire energy of the full optical cycle.Comment: to appear in Physics of Plasma

GRB 060218/SN 2006aj: A Gamma-Ray Burst and Prompt Supernova at z=0.0335

We report the imaging and spectroscopic localization of GRB 060218 to a low-metallicity dwarf starburst galaxy at z = 0.03345 +/- 0.00006. In addition to making it the second nearest gamma-ray burst known, optical spectroscopy reveals the earliest detection of weak, supernova-like Si II near 5720 Angstroms (0.1c), starting 1.95 days after the burst trigger. UBVRI photometry obtained between 1 and 26 days post-burst confirms the early rise of supernova light, and suggests a short time delay between the gamma-ray burst and the onset of SN 2006aj if the early appearance of a soft component in the X-ray spectrum is understood as a ``shock breakout''. Together, these results verify the long-hypothesized origin of soft gamma-ray bursts in the deaths of massive stars.Comment: 5 pages, 2 figure

Large deviations for solutions to stochastic recurrence equations under Kesten's condition

In this paper we prove large deviations results for partial sums constructed from the solution to a stochastic recurrence equation. We assume Kesten's condition [Acta Math. 131 (1973) 207-248] under which the solution of the stochastic recurrence equation has a marginal distribution with power law tails, while the noise sequence of the equations can have light tails. The results of the paper are analogs to those obtained by A. V. Nagaev [Theory Probab. Appl. 14 (1969) 51-64; 193-208] and S. V. Nagaev [Ann. Probab. 7 (1979) 745-789] in the case of partial sums of i.i.d. random variables. In the latter case, the large deviation probabilities of the partial sums are essentially determined by the largest step size of the partial sum. For the solution to a stochastic recurrence equation, the magnitude of the large deviation probabilities is again given by the tail of the maximum summand, but the exact asymptotic tail behavior is also influenced by clusters of extreme values, due to dependencies in the sequence. We apply the large deviation results to study the asymptotic behavior of the ruin probabilities in the model.Comment: Published in at http://dx.doi.org/10.1214/12-AOP782 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Electronic structure and Magnetism in BaMn2_2As2_2 and BaMn2_2Sb2_2

We study the properties of ThCr$_2$Si$_2$ structure BaMn$_2$As$_2$ and BaMn$_2$Sb$_2$ using density functional calculations of the electronic and magnetic as well experimental measurements on single crystal samples of BaMn$_2$As$_2$. These materials are local moment magnets with moderate band gap antiferromagnetic semiconducting ground states. The electronic structures show substantial Mn - pnictogen hybridization, which stabilizes an intermediate spin configuration for the nominally $d^5$ Mn. The results are discussed in the context of possible thermoelectric applications and the relationship with the corresponding iron / cobalt / nickel compounds Ba(Fe,Co,Ni)$_2$As$_2$

Universal subspaces for compact Lie groups

For a representation of a connected compact Lie group G in a finite dimensional real vector space U and a subspace V of U, invariant under a maximal torus of G, we obtain a sufficient condition for V to meet all G-orbits in U, which is also necessary in certain cases. The proof makes use of the cohomology of flag manifolds and the invariant theory of Weyl groups. Then we apply our condition to the conjugation representations of U(n), Sp(n), and SO(n) in the space of $n\times n$ matrices over C, H, and R, respectively. In particular, we obtain an interesting generalization of Schur's triangularization theorem.Comment: 20 page