Lattices kagome

Figure 9.38 The simplest types of regular 2D lattices (A) the Bethe lattice (Z=3) (B) the honeycomb lattice (Z=3), The simple square lattice (Z=4), (C) the simple square lattice (Z=4), (D) Kagome lattice (Z=4), (E) the triangular lattice (Z=6).

Figure V l 4. Kagome lattice in the triangular lattice of cobalt ions, (a) Solid circles indicate the cohalt ions in Fig. 1(b). Gray triangles form a Kagome lattice which is made by a trace of the travel of an electron starting from zx,l> (see text), (b) Layout of the four (gray, black, hatched and white) Kagome lattices...

The dispersion relation Fig. 3(b) clearly shows that the upper lying band takes over the nature of the Kagome lattice structure hidden in the triangular lattice of cobalt ions (see Fig. 4) despite of the presence of tdd, l and t2. Therefore, it is of crucial importance to study the effect of the Kagome lattice structure to clarify the electronic state in the C0O2 layer. 

The Kagome lattice involves a triangle as a basic unit. On the triangle, the mechanism by Kumar and Shastry [18, 31] for the anomalous Hall effect will be available and explain the experiments by Wang et al. 

The Kagome lattice structure clearly explains the non-symmetric nature of the band structure of the C0O2 layer. When the effect of the Kagome lattice becomes dominant, the bottom band, i.e., the flat band as shown in Fig, 3(a) will play a crucial role on the electronic state. Mielke [32] has shown that the flat band with the Coulomb interaction has the ferromagnetic ground state at around half filling. A prospective system for the ferromagnet will be dl transition metal oxides, i.e., the layered titanates with iso-structure of the cobalt oxides. 

Layout of the four (gray, black, hatched and white) Kagome lattices.206... 

FIGURE 3.13 (a) A section of a Kagome lattice in which equilateral triangles (gray) are... 

Kagome lattice leads to Dzyaloshinsky-Moriya (DM) interactions, the in-plane components of which can give rise to magnetic polarizations in the out-of-plane directions with canted vectors of magnetic moments.16 It is interesting to... 

An organically templated iron(II) sulfate with a highly distorted Kagome lattice has been synthesized and character-... 

Incidentally, let us observe that the same exponents can be obtained with partially repulsive chains provided that the repulsive part is dominant. Thus, Watson21 showed that purely repulsive chains drawn on a honeycomb lattice can be transformed into chains drawn on the corresponding kagome lattice (see Fig. 4.2), in such a way that the interaction potentials for the new chains are... 

Fig. 4.2. Figure illustrating the correspondence between honeycomb lattice (dashed line) and kagome lattice (solid line). 

Six-vertex models have been solved by E. Lieb and followers55-56 but the six-vertex model considered by Nienhuis is defined on a kagome lattice. ... 

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