Internal magnetic fields in submicron particles of barium hexaferrite detected by 57Fe NMR

⁵⁷Fe nuclear magnetic resonance (NMR) spectra of hexaferrite BaFe₁₂O₁₉ powder samples prepared by glass crystallization method were measured at 4.2 K and analyzed in comparison to spectra of single crystals. Samples with various mean particle dimensions were tested. NMR spectral lines corresponding to individual iron sublattices showed pronounced frequency shifts of their positions and a significant line broadening compared to single crystals. The significant contribution to the line shifts and line shape had a uniform macroscopic origin giving identical absolute value of shifts and the same line shapes for all measured lines of a particular sample. Estimations of demagnetization fields based on mean particle dimensions reasonably corresponded to the observed frequency shifts for particle mean diameter 67 nm, or had a higher value for a sample with mean diameter of 340 nm, for which a presence of domain walls was detected by NMR. In the spectrum of a sample with the smallest particles (～16 nm), an additional contribution having broader lines and faster spin-spin relaxations was found. It could be assigned to weaker exchange interactions or deviations of magnetic moment directions from the hexagonal axis in a surface layer.     

Code loops in both parities

We present equivalent definitions of code loops in any characteristic p≠0. The most natural definition is via combinatorial polarization, but we also show how to realize code loops by linear codes and as a class of symplectic conjugacy closed loops. For p odd, it is possible to define code loops via characteristic trilinear forms. Related concepts are discussed.     

On induced Ramsey numbers for k‐uniform hypergraphs

Let denote the complete k‐uniform k‐partite hypergraph with classes of size t and the complete k‐uniform hypergraph of order s. One can show that the Ramsey number for and satisfies when t = s^o(1) as s →∞. The main part of this paper gives an analogous result for induced Ramsey numbers: Let be an arbitrary k‐partite k‐uniform hypergraph with classes of size t and an arbitrary k‐graph of order s. We use the probabilistic method to show that the induced Ramsey number (i.e. the smallest n for which there exists a hypergraph such that any red/blue coloring of yields either an induced red copy of or an induced blue copy of ) satisfies . © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 48, 5–20, 2016     

A semi-empirical dim calculation of the resonant energy and autoionization width of the He(23S)—H2 system

The DIM method is used to compute the resonant energy and the autoionization width for a wide range of configurations of the He(2³S)—H₂ syste     

Infrared optical constants of n-type silicon

The infrared optical constants of n-type Si are determined from reflectance and transmittance spectra. The Drude formula with empirically adjusted, concentration dependent, parameters is used. Its low-wavelength limit is in agreement with recent mobility results. A pronounced difference between As-, P-, and Sb-doped Si is found for the free electron concentration above 10¹⁹ cm^–3. Simple empirical formulae are given for the optical constants as functions of both wavenumber and concentration.     

Crystal structures of lanthanide(III) complexes with cyclen derivative bearing three acetate and one methylphosphonate pendants

A series of lanthanide(III) complexes formulated as M[Ln(Hdo3ap)].xH(2)O (M = Li or H and Ln = Tb, Dy, Er, Lu, and Y) with the monophosphonate analogue of H(4)dota, 1,4,7,10-tetraazacyclododecane-1,4,7-triacetic-10-methylphosphonic acid (H(5)do3ap), was prepared in the solid state and studied using X-ray crystallography. All of the structures show that the (Hdo3ap)(4-) anion is octadentate coordinated to a lanthanide(III) ion similarly to the other H(4)dota-like ligands, i.e., forming O(4) and N(4) planes that are parallel and have mutual angle smaller than 3 degrees . The lanthanide(III) ions lie between these planes, closer to the O(4) base than to the N(4) plane. All of the structures present the lanthanide(III) complexes in their twisted-square-antiprismatic (TSA) configuration. Twist angles of the pendants vary in the range between -24 and -30 degrees, and for each complex, they lie in a very narrow region of 1 degree. The coordinated phosphonate oxygen is located slightly above (0.02-0.19 Angstroms) the O(3) plane formed with the coordinated acetates. A water molecule was found to be coordinated only in the terbium(III) and neodymium(III) complexes. The bond distance Tb-O(w) is unusually long (2.678 Angstroms). The O-Ln-O angles decrease from 140 degrees [Nd(III)] to 121 degrees [Lu(III)], thus confirming the increasing steric crowding around the water binding site. A comparison of a number of structures of Ln(III) complexes with DOTA-like ligands shows that the TSA arrangement is flexible. On the other hand, the SA arrangement is rigid, and the derived structural parameters are almost identical for different ligands and lanthanide(III) ions.