Mao2002.htm

Ming Mao, B.D. Gaulin, R.B. Rogge, and Z. Tun

*Physical Review B* 66,
184432 (2002)

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Abstract

Introduction

Notes by Dr. Zin Tun

The combination of antiferromagnetic (AF) interactions and certain
lattice geometries based on triangles and tetrahedra are known to result in
phenomena known broadly as geometric frustration.^{1} AF interactions
between near neighbor spins on such local geometries cannot be simultaneously
satisfied, leading to novel ground states in which the frustrated spins try to
compromise the conflicting demands of their pairwise interactions. If the
interactions are frustrated in all three dimensions, the magnetic system may
have difficulties finding any ordered ground state. Such a situation is known to
arise in a subset of pyrochlore antiferromagnets, for example, for which
AF-coupled magnetic moments reside on a network of corner-sharing tetrahedra.^{2}
(Mao2002intro01.gif)

The ABX_{3} AF insulators occupy interesting territory
within this subject area.^{3} While these materials are
quasi-one-dimensional antiferromagnets, their three-dimensional crystalline
lattice is simple hexagonal. The crystal structure of CsCoBr_{3} is
shown in Fig. 1. As can be seen, a triad of Br^{-} ions mediates a
strong intiferromagnetic exchange interaction between neighboring Co^{2+}
ions along **c**. However, their magnetically ordered phases at low
temperatures are determined by relatively weak interactions with the **a-b**,
basal plane. As such they are thought of, and referred to, as stacked triangular
lattice (STL) antiferromagnets. (Mao2002intro02.gif)

In the *AB*X_{3} STL antiferromagnets, the
interactions along **c** are not frustrated, and these systems do undergo phase
transitions at low temperatures to long-range ordered states. However, the
geometrical frustration can manifest itself in novel critical phenomena at these
phase transitions, as occurs in the case for the *XY* STL antiferromagnet
CsMnBr_{3}. This novel critical phenomena has been experimentally
observed,^{4} and explained in terms of a chiral-XY universality class^{5}
which reflects both the *XY* symmetry of the Mn^{2+} spins and the
Ising-like chiral symmetry of the local ordering of the spins into the 120°
structure. (Mao2002intro03.gif)

Antiferromagnetically coupled Ising spins on the STL have stronger
manifestations of geometrical frustration than do continuous spins, as there is
analog of the 120° spin structure with which a triad of neighbor *XY* spins
may compromise. Theoretically, such classical, Ising STL systems have been
studied,^{6-10} and are known to display at least two phase transitions
as the temperature is lowered. At relatively high temperatures, the system
undergoes a phase transition from a paramagnetic state to a novel three-sublattice
AF structure, wherein one of the three long-range ordered sub-lattices remains
paramagnetic. The three sublattice structure consists of up, down and
paramagnetic sublattices. At lower temperatures the paramagnetic sublattice
orders, either up or down, so as to form a ferrimagnetic sheet with the **a-b**
plane. The ferrimagnetic sheets stack antiferromagnetically, so that there is no
net moment for the overall structure.
(Mao2002intro04.gif)

There are more in the introduction.

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