Mean-field approach to magnetic ordering in highly frustrated pyrochlores

Journal Article · Tue Jan 01 04:00:00 EST 1991 · Physical Review, B: Condensed Matter; (USA)

DOI:https://doi.org/10.1103/PhysRevB.43.865· OSTI ID:6257355

Reimers, J N; Berlinsky, A J; Shi, A ^[1]

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1. Institute for Materials Research, McMaster University, Hamilton, Ontario, Canada L8S 4M1 (CA)

The metal atoms in the pyrochlore system of compounds ({ital A}{sub 2}{ital B2}O{sub 7}, where {ital A} and {ital B} are metals) form an infinite three-dimensional network of corner-sharing tetrahedra with cubic symmetry. For antiferromagnetic nearest-neighbor interactions and only {ital B} atoms magnetic, there is a very high degree of frustration, and no long-range order is predicted in the absence of further neighbor interactions. A general form of the mean-field theory is developed for dealing with {ital n}-component classical vector spins on any lattice. Calculations for the pyrochlore problem show that the Fourier modes of the system are completely degenerate for all wave vectors in the first Brillouin zone. In some cases further neighbor interactions will select the {bold q}={bold 0} or incommensurate modes. A comparison is made with long-range order known to exist in the pyrochlore form of FeF{sub 3}. The highly degenerate ordered phases of more complicated systems, where both {ital A} and {ital B} atoms are magnetic, will also be discussed. A comparison is made of the corner-sharing tetrahedral lattice and the more familiar stacked triangular antiferromagnets, with regard to the degree of frustration in both systems. Results for the Kagome lattice and the square lattice with crossings, which are the two-dimensional analogs of the corner-sharing tetrahedral lattice, are also briefly discussed.

• OSTI ID: 6257355
• Journal Information: Physical Review, B: Condensed Matter; (USA), Journal Name: Physical Review, B: Condensed Matter; (USA) Vol. 43:1; ISSN 0163-1829; ISSN PRBMD
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
360603* -- Materials-- Properties
ANTIFERROMAGNETISM
MAGNETISM
MEAN-FIELD THEORY
MINERALS
PYROCHLORE