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

Spin Wave Spectra in Pseudoperovskite Manganites with Superexchange Interaction Competition

In compounds La1/3Ca2/3MnO3 and BiMnO3, a calculation of spin-wave dispersion dependences along pseudoperovskite directions of reciprocal space is made. The model includes orbitally dependent superexchange interaction and single-ion anisotropy. Considered compounds present competing exchange interactions within magnetic unit cell because of orbital or charge-orbital ordering. The nearest neighbor superexchange interaction is taken into account. The magnetic structure and dispersion dependences of spin waves frequencies are calculated within the framework of regular multi-sublattice model. The peculiarities of frustrated magnetic spin-wave spectra are found. It is shown, that crossing and splitting of spin-waves branches in non-symmetric points of magnetic Brillouin zone is a common feature of the spectra due to exchange competition. The band structure of Г-point spectra for both compounds are predicted. © 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature

Orbital dependence of superexchange interaction in charge-ordered manganites

The current investigation is devoted to the theoretical study of orbital structure influence upon magnetic subsystem in half-doped charge-ordered manganites. The main interaction of magnetic subsystem is superexchange interaction. It forms spin-wave dispersion dependencies. Because of charge and orbital ordering, there are a lot of superexchange parameters in these compounds. That makes the dispersion rather complicated. This work clarifies some features of dispersion in terms of orbitally-dependent superexchange interactions. © Published under licence by IOP Publishing Ltd

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

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

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

Origin of Jahn-Teller distortion and orbital-order in LaMnO3

The origin of the cooperative Jahn-Teller distortion and orbital-order in LaMnO3 is central to the physics of the manganites. The question is complicated by the simultaneous presence of tetragonal and GdFeO3-type distortions and the strong Hund's rule coupling between e_g and t_2g electrons. To clarify the situation we calculate the transition temperature for the Kugel-Khomskii superexchange mechanism by using the local density approximation+dynamical mean-field method, and disentangle the effects of super-exchange from those of lattice distortions. We find that super-exchange alone would yield T_KK=650 K. The tetragonal and GdFeO3-type distortions, however, reduce T_KK to 550 K. Thus electron-phonon coupling is essential to explain the persistence of local Jahn-Teller distortions to at least 1150 K and to reproduce the occupied orbital deduced from neutron scattering.Comment: 4 pages, 3 figures; published version (minor changes

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

Kramers escape driven by fractional Brownian motion

We investigate the Kramers escape from a potential well of a test particle driven by fractional Gaussian noise with Hurst exponent 0<H<1. From a numerical analysis we demonstrate the exponential distribution of escape times from the well and analyze in detail the dependence of the mean escape time as function of H and the particle diffusivity D. We observe different behavior for the subdiffusive (antipersistent) and superdiffusive (persistent) domains. In particular we find that the escape becomes increasingly faster for decreasing values of H, consistent with previous findings on the first passage behavior. Approximate analytical calculations are shown to support the numerically observed dependencies.Comment: 14 pages, 16 figures, RevTeX