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Jun. 20, 2008

Frustration yields results

Theoretical calculations elucidate the origin of unusual electronic behaviors recently observed in geometrically frustrated compounds

image of a classical example of geometrical frustration Figure 1:A classical example of geometrical frustration. Spins of neighboring atoms tend to point in opposite directions. This creates an ambiguity for the spin in the bottom right corner, which cannot point in the opposite direction of both its nearest neighbors.

A study by researchers at the RIKEN Advanced Science Institute in Wako, in collaboration with scientists at the Universities of Tokyo and Kyoto, provides insight into the effects of geometrical frustration in strongly correlated electron systems1.

Geometrical frustration occurs in materials in which the spatial arrangement of atoms creates ambiguity in the magnetic configuration that corresponds to the minimum energy, or ground state. For example, in a triangular lattice in which the magnetic moments, or dipoles, of the atoms are coupled antiferromagnetically—such that the spins of neighboring atoms point in opposite directions—there are two configurations that correspond to the same magnetic energy (Fig. 1).

Tsutomu Momoi of RIKEN and his colleagues focused on the effect of geometric frustration on the Mott transition, a phenomenon that occurs when metallic systems become insulators due to the strong repulsion between electrons. “Recent experiments on triangular lattice organic materials prompted us to consider the effect of magnetic frustration on this phase transition,” says Momoi. Indeed, the organic material κ-(BEDT-TTF)2Cu[N(CN)2]Cl, which has an anisotropic triangular lattice, has recently been found to exhibit a so-called re-entrant Mott transition. In other words, by lowering the temperature the system changes from an insulator to a metal (as in a usual Mott transition), but becomes an insulator again at a lower temperature.

The researchers studied a generic triangular lattice with a Hubbard model—one of the most standard models used to describe metal–insulator transitions. For their calculations, they used an extension of the dynamical mean-field theory, which has already been used to explain Mott insulator transitions, but did not allow for re-entrant behavior.

The team’s calculations have shown that a generic triangular lattice with a medium degree of anisotropy comparable to that of κ-(BEDT-TTF)2Cu[N(CN)2]Cl indeed exhibits re-entrant Mott insulator behavior.

The details of the theoretical study also suggest the mechanism behind the re-entrant behavior. “There are two energy scales in electron systems,” explains Momoi. One comes from the electrical repulsion between electrons and the other from ordering of spin correlations. “In the frustrated systems, the second energy scale becomes very low, which makes two energy scales well separated in temperature and the reentrant behavior visible.”

Because the results of the calculations are not specific to κ-(BEDT-TTF)2Cu[N(CN)2]Cl, it can be expected that the re-entrant behavior will also be observed in other geometrically frustrated systems.


  • 1. Ohashi, T., Momoi, T., Tsunetsugu, H. & Kawakami, N. Finite temperature Mott transition in Hubbard model on anisotropic triangular lattice. Physical Review Letters100, 076402 (2008). (Link)