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Frustrated systems

 

In an isolated frustrated triangular unit, for example, three spins can minimize energy by aligning at 120° angles between neighboring spins. When many triangles assemble together in a crystal, this can give rise to many different degenerate configurations.This occurs, for example, when the triangular lattice is diluted, giving rise to the Kagome lattice. In three dimensions, a similar situation obtains in the pyrochlores, tetrahedron-based structures. Thermal and/or quantum fluctuations can lead to phenomena, such as order-by-disorder, or new types of nonmagnetic states.

 

Kagome lattice showing spin degrees of freedom An example of such a spin system studied in our laboratory is the mineral Herbertsmithite ZnCu3(OH)6Cl2.

 

Model (green bonds are antiferromagnetic. The addition of the red bonds leads to frustration) SrCu2(BO3)2 is a compound whose spin-spin interactions are well approximated in terms of the Shastry-Sutherland model.

 

Materials such as Ho2Ti2O7 (« spin ice « ) have corner-sharing tetrahedra. The spin degrees of freedom in this compound are Ising-like, and their ferromagnetic couplings lead to frustration.

 

Ising spin representation of a two dimensional spin ice.

 

Many recent experimental and theoretical studies on some of the systems illustrated above are aimed at understanding the low temperature properties of such materials.