#
2009 APS March Meeting

## Volume 54, Number 1

##
Monday–Friday, March 16–20, 2009;
Pittsburgh, Pennsylvania

### Session S1: Poster Session III (1-4:00pm): Polymer Physics II; Phase Transitions; General Theory; Insulators and Dieletrics; Semiconductors; Supplementary Abstracts; Post-Deadline Abstracts

1:00 PM,
Wednesday, March 18, 2009

Room: Exhibit Hall A

Abstract ID: BAPS.2009.MAR.S1.77

### Abstract: S1.00077 : Antisymmetric Exchange in Antiferromagnetic Materials of Rhombohedral Structures

Preview Abstract
Abstract

####
Author:

Alexander Bazhan

(P.L.Kapitza Institute for Physical Problems, RAS, Moscow, Russia.)

Carriers transferrings, determined by wave functions and energy levels of i
j magnetic and oxygen ions, which are determined by rhombohedral oxygen
crystal fields and their particularities, are in discussions for
identification of antisymmetric, Dzyloshinskii-Moria exchange,
\textbf{D}$_{z}${\{}\textbf{S}$_{ix}$\textbf{S}$_{jy}-$\textbf{S}$_{iy}$\textbf{S}$_{jx
}${\}}, taking into account Hubbard Hamiltonians, including spin-orbit
interactions. Wave functions symmetry dependence are described by, depending
on trigonal symmetry $\alpha $, $\beta $ coefficients in wave functions of
energy levels of magnetic ions. Particularities of i j oxygen crystal fields
are concerned with rotations of j fields at angles 60 degrees with respect
to i fields. Taking spin-orbit, transferrings as perturbations, exchange
symmetric,$_{ }$antisymmetric parts of spin Hamiltonians are
H$_{ex}=\Sigma _{i,j}$J$_{i,j}$(\textbf{S}$_{i}\cdot
$\textbf{S}$_{j})+\Sigma
_{i,j}$\textbf{D}$_{i,j}$[\textbf{S}$_{i}\times $\textbf{S}$_{j}$],
where J$_{i,j}$ and \textbf{D}$_{i,j}$ are determined by carriers
transferrings, kinetic energies, Coulomb interactions, magnetic and oxygen
energy levels. As examples, after some assumptions \textbf{D}$_{ij }$=
J$\cdot (-\lambda )\cdot $i$\cdot ${\{}$\Sigma _{m}\langle \psi
_{im }$/\textbf{L}$_{i}$/$\psi _{i0}\rangle ^{\ast }$/($\varepsilon
_{im}-\varepsilon _{i0})\cdot $(t$_{im,kn}$/t$_{i0,kn})$ -
$\Sigma _{m}\langle \psi _{jm}$/\textbf{L}$_{j}$/$\psi
_{j0}\rangle ^{\ast }$/($\varepsilon _{jm}-\varepsilon
_{j0})\cdot $(t$_{kn,jm}$/t$_{kn,j0})${\}}, \textbf{D}$_{z}\sim
$J$\cdot \alpha \beta \cdot ${\{}$\lambda $/($\varepsilon
_{m}-\varepsilon _{0})${\}}$\cdot
${\{}(t$_{im,kn}$/t$_{i0,kn}-$t$_{kn,jm}$/t$_{kn,j0})${\}}. Energy levels
and Pauli requirements, determine depending on spin-orbit interactions,
carriers transferrings between magnetic -oxygen -magnetic ions, which
determine vectors \textbf{D}$_{z}$, oriented, according to trigonal
symmetry, along trigonal - z axis.

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2009.MAR.S1.77