Vibronic interaction as main reason of magnetic ordering in insulating manganites R 1-x A x MnO 3

The model of orbitally dependent magnetic structure of charge ordered insulated manganites is proposed. The model is semi-phenomenological. It allows using a few parameters to describe possible magnetic structures of compounds. The experimental crystal structure of compounds also could be taken into account. The compounds LaMnO 3 , La 1/2 Ca 1/2 MnO 3 , La 1/3 Ca 2/3 MnO 3 , BiMnO 3 are considered. © 2018 The Authors, published by EDP Sciences

Crucial role of orbital structure in formation of frustrated magnetic structure in BiMnO3

The paper presents an investigation in the field of orbital physics of strongly correlated oxides. The theoretical study of vibronic mechanism of orbital and magnetic structures forming in BiMnO3 crystal is carried out. An effect of orbital structure upon superexchange interaction is described. Nonlinear and second-neighbor terms in vibronic interaction on manganese ions play an important role in magnetic ordering of frustrated BiMnO3. It is shown that the linear vibronic interaction is insufficient to describe the experimentally detected ferromagnetic structure of bismuth manganite. The new approach to orbital structure formation, presented in the paper, could be used not only in manganite physics but also in other Jahn-Teller compounds. © 2013 American Physical Society

Meromorphic Approximants to Complex Cauchy Transforms with Polar Singularities

We study AAK-type meromorphic approximants to functions $F$, where $F$ is a sum of a rational function $R$ and a Cauchy transform of a complex measure $\lambda$ with compact regular support included in $(-1,1)$, whose argument has bounded variation on the support. The approximation is understood in $L^p$-norm of the unit circle, $p\geq2$. We obtain that the counting measures of poles of the approximants converge to the Green equilibrium distribution on the support of $\lambda$ relative to the unit disk, that the approximants themselves converge in capacity to $F$, and that the poles of $R$ attract at least as many poles of the approximants as their multiplicity and not much more.Comment: 39 pages, 4 figure

Specific features of magnetic structure formation in orbitally degenerate BiMnO3 manganite

The orbital structure and magnetic ordering of the Jahn-Teller multiferroic BiMnO3 manganite have been theoretically studied. It is shown that the orbital structure depends not only on the nearest-neighbor oxygen environment of manganese ions, but also on their next-to-nearest neighbors. The orbital structure significantly influences the magnetic order that forms as a result of competition between ferromagnetic and antiferromagnetic exchange interactions. © 2013 Pleiades Publishing, Ltd

Some Peculiarities of Functioning of Self-Evaluative Utterances in the Context of Inter-Cultural Communication

Статтю присвячено аналізу особливостей функціонування висловлень самооцінки в контексті між¬культурної комунікації. The article deals with the analysis of some peculiarities of functioning of self-evaluative utterances in the context of inter-cultural communication

A family of Nikishin systems with periodic recurrence coefficients

Suppose we have a Nikishin system of $p$ measures with the $k$th generating measure of the Nikishin system supported on an interval \Delta_k\subset\er with $\Delta_k\cap\Delta_{k+1}=\emptyset$ for all $k$. It is well known that the corresponding staircase sequence of multiple orthogonal polynomials satisfies a $(p+2)$-term recurrence relation whose recurrence coefficients, under appropriate assumptions on the generating measures, have periodic limits of period $p$. (The limit values depend only on the positions of the intervals $\Delta_k$.) Taking these periodic limit values as the coefficients of a new $(p+2)$-term recurrence relation, we construct a canonical sequence of monic polynomials $\{P_{n}\}_{n=0}^{\infty}$, the so-called \emph{Chebyshev-Nikishin polynomials}. We show that the polynomials $P_{n}$ themselves form a sequence of multiple orthogonal polynomials with respect to some Nikishin system of measures, with the $k$th generating measure being absolutely continuous on $\Delta_{k}$. In this way we generalize a result of the third author and Rocha \cite{LopRoc} for the case $p=2$. The proof uses the connection with block Toeplitz matrices, and with a certain Riemann surface of genus zero. We also obtain strong asymptotics and an exact Widom-type formula for the second kind functions of the Nikishin system for $\{P_{n}\}_{n=0}^{\infty}$.Comment: 30 pages, minor change

Theoretical Investigation of NMR Spectra in Rare-Earth Manganites

The work is aimed to theoretical investigation of orbital and magnetic structure of manganites. The orbitally-dependent exchange interaction model was used in order to describe the superexchange interaction in all range of RMnO3 (R=La, Pr, Nd, Tb, Dy, Ho) orfhorhombic compounds. The model of nearest-neighbour and next-nearest neighbour exchange was used to describe the magnetic structures of manganites with small rare-earth ion sublattice (R=Dy, Tb, Ho). We investigate different types -A, E, non-collinear - of magnetic structures. The models of NMR spectra calculation of Mn3+ ion in RMnO3 compounds are proposed. The theoretical study of the magnetic structure could distinguish The NMR-spectra of antiferromagnetic (A or E) or strongly non-collinear ordering type