Geometrical Frustration

In condensed matter physics, the term geometrical frustration (or in short: frustration ) means a phenomenon in which the geometrical properties of the crystal lattice or the presence of conflicting atomic forces forbid simultaneous minimization of the interaction energies acting at a given site. This may lead to highly degenerate ground states with a nonzero entropy at zero temperature. Or in simple terms, the substance can never be completely frozen, because the structure it forms does not have a single minimal-energy state, so motion on a molecular scale continues even at absolute zero and even without input of energy.

The term frustration, in the context of magnetic systems, is due to Gerard Toulouse (1977) . Frustrated magnetic systems have been studied for many years. Early work includes a study of the Ising model on a triangular lattice with nearest-neighbor spins coupled antiferromagnetically by G. H. Wannier, published in 1950 . Related research on magnets with competing interactions, where different couplings, each favoring simple (e.g. ferro- and antiferromagnetic), but different structures, are present. In that case incommensurate, such as helical spin arrangements may result, as had been discussed originally by A. Yoshimori, T. A. Kaplan, R. J. Elliott, and others, starting in 1959. A renewed interest in such spin systems with competing or frustrated interactions arose about two decades later in the context of spin glasses and spatially modulated magnetic superstructures. In spin glasses, frustration is augmented by stochastic disorder in the interactions. Well-known spin models with competing or frustrated interactions include the Sherrington-Kirkpatrick model, describing spin glasses, and the ANNNI model, describing commensurate and incommensurate magnetic superstructures.

Read more about Geometrical Frustration:  Magnetic Ordering, Mathematical Definition, Water Ice, Spin Ice, Extension of Pauling’s Model: General Frustration, Artificial Geometrically Frustrated Ferromagnets, Geometric Frustration Without Lattice, Literature

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