Group theoretical analysis of second order phase transitions in magnetic structures

1979 ◽  
Vol 20 (7) ◽  
pp. 1579-1592 ◽  
Author(s):  
P. Rudra ◽  
M. K. Sikdar
Keyword(s):  
Phase Transitions ◽  
Theoretical Analysis ◽  
Second Order ◽  
Magnetic Structures ◽  
Group Theoretical Analysis

scholarly journals Group-theoretical analysis of 1:3 A-site-ordered perovskite formation

2019 ◽  
Vol 75 (2) ◽  
pp. 379-397 ◽  
Author(s):  
Mikhail V. Talanov
Keyword(s):  
Phase Transitions ◽  
Theoretical Analysis ◽  
Perovskite Structure ◽  
Functional Materials ◽  
Order Parameters ◽  
Space Group ◽  
Symmetry Phase ◽  
Structural Mechanisms ◽  
Low Symmetry ◽  
Group Theoretical Analysis

The quadruple perovskites AA′3 B 4 X 12 are characterized by an extremely wide variety of intriguing physical properties, which makes them attractive candidates for various applications. Using group-theoretical analysis, possible 1:3 A-site-ordered low-symmetry phases have been found. They can be formed from a parent Pm{\bar 3}m perovskite structure (archetype) as a result of real or hypothetical (virtual) phase transitions due to different structural mechanisms (orderings and displacements of atoms, tilts of octahedra). For each type of low-symmetry phase, the full set of order parameters (proper and improper order parameters), the calculated structure, including the space group, the primitive cell multiplication, splitting of the Wyckoff positions and the structural formula were determined. All ordered phases were classified according to the irreducible representations of the space group of the parent phase (archetype) and systematized according to the types of structural mechanisms responsible for their formation. Special attention is paid to the structural mechanisms of formation of the low-symmetry phase of the compounds known from experimental data, such as: CaCu3Ti4O12, CaCu3Ga2Sn2O12, CaMn3Mn4O12, Ce1/2Cu3Ti4O12, LaMn3Mn4O12, BiMn3Mn4O12 and others. For the first time, the phenomenon of variability in the choice of the proper order parameters, which allows one to obtain the same structure by different group-theoretical paths, is established. This phenomenon emphasizes the fundamental importance of considering the full set of order parameters in describing phase transitions. Possible transition paths from the archetype with space group Pm{\bar 3}m to all 1:3 A-site-ordered perovskites are illustrated using the Bärnighausen tree formalism. These results may be used to identify new phases and interpret experimental results, determine the structural mechanisms responsible for the formation of low-symmetry phases as well as to understand the structural genesis of the perovskite-like phases. The obtained non-model group-theoretical results in combination with crystal chemical data and first-principles calculations may be a starting point for the design of new functional materials with a perovskite structure.

Group-theoretical analysis of octahedral tilting in ferroelectric perovskites

2002 ◽  
Vol 58 (6) ◽  
pp. 934-938 ◽  
Author(s):  
Harold T. Stokes ◽  
Erich H. Kisi ◽  
Dorian M. Hatch ◽  
Christopher J. Howard
Keyword(s):  
Phase Transitions ◽  
Theoretical Analysis ◽  
Landau Theory ◽  
Group Symmetry ◽  
Theoretical Methods ◽  
Space Group Symmetry ◽  
Space Group ◽  
First Order ◽  
Octahedral Tilting ◽  
Group Theoretical Analysis

Group-theoretical methods are used to analyze perovskite structures where both ferroelectric cation displacements and simple tilting of octahedral units are present. This results in a list of 40 different structures, each with a unique space-group symmetry. The list is compared with that of Aleksandrov & Bartolomé [Phase Transit. (2001), 74, 255–335] and a number of differences are found. The group–subgroup relationships between the structures are also determined, along with an indication of those phase transitions that must be first order by Landau theory.

scholarly journals Analysis of magnetic structures of iron nitrides by Landau's theory of second-order phase transitions

AIP Advances ◽  
2013 ◽  
Vol 3 (7) ◽  
pp. 072136 ◽  
Author(s):  
H. N. Fang ◽  
R. Zhang ◽  
B. Liu ◽  
Z. K. Tao ◽  
M. W. Xiao ◽  
...  
Keyword(s):  
Phase Transitions ◽  
Second Order ◽  
Iron Nitrides ◽  
Magnetic Structures

Ferromagnetoelectric phases of hexaferrites: a group-theoretical analysis

2021 ◽  
Vol 77 (5) ◽  
Author(s):  
Vladimir Borisovich Shirokov ◽  
Anna Grigoryevna Razumnaya ◽  
Alexey Sergeevich Mikheykin
Keyword(s):  
Phase Transitions ◽  
Theoretical Analysis ◽  
Magnetic Structure ◽  
Magnetic Moment ◽  
Thermodynamic Model ◽  
Theoretical Study ◽  
Magnetic Phase ◽  
Cation Substitution ◽  
Group Theoretical Analysis ◽  
Magnetic Sublattices

A symmetry-guided approach for designing and tailoring magnetoelectric and multiferroic hexaferrites is proposed. A group-theoretical study of the magnetoferroelectric structures of a hexagonal ferrite was carried out. The results were applied to M-, W- and Z-type hexaferrites. It is shown that the magnetic structure cannot be collinear in the main magnetic phase, with the direction of the magnetic moment along the hexagonal axis. Magnetic sublattices are shown in which cation substitution should lead to the formation of a multiferroic state. A thermodynamic model of a hexagonal ferroelectric ferrimagnet was constructed, in which isostructural phase transitions were observed.

SYMMODES: a software package for group-theoretical analysis of structural phase transitions

2003 ◽  
Vol 36 (3) ◽  
pp. 953-954 ◽  
Author(s):  
Cesar Capillas ◽  
Eli Kroumova ◽  
Mois I. Aroyo ◽  
J. Manuel Perez-Mato ◽  
Harold T. Stokes ◽  
...  
Keyword(s):  
Phase Transitions ◽  
Theoretical Analysis ◽  
Software Package ◽  
Structural Phase ◽  
Structural Phase Transitions ◽  
Group Theoretical Analysis
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