The Kagome Lattice

The term, kagome, originates from a traditional Japanese basket weave pattern but in fact the motif is used widely in Japanese culture. Currently, kagome lattice materials also represent one of the most active research areas. This is due in part to the theoretical tractability of the two-dimensional kagome lattice and also to expectations that exotic ground states should be found, especially with quantum, S = V2 and S = 1 spins.  

We will refer to these materials as 2DKAF (two-dimensional kagome antiferr omagnets). 

Perhaps the most interesting iron jarosite is that for A = [H30] which is reported to show 98% coverage of the M sites, even in earlier work.  

Remarkably, dilution of the Fe site with Al results in long range order evidenced by resolution limited Bragg peaks. ° This was interpreted, originally, as an order by disorder process, based on the 

The crystal chemistry of jarosites does extend to other ions, especially Cr which is S = 3/2 compared with S = 5/2 for Fe. Unfortunately, there are apparently no detailed studies of any stoichiometric Cr jarosite. KCr3(S04)2(OH)g with 76% Cr sites occupied is reported to show AFLRO only below 1.8 K with an ordered Cr moment of only lpB which is 1/3 of the expected value.With Oq values ranging from -55 K to -70 K for this material, f 31 to 39, indicating high levels of frustration. It should be noted that the values for are much lower than those for Fe jarosites with similar site coverage, by more than an order of magnitude. More effort should be directed to the preparation and study of fully stoichiometric Cr jarosites. Unfortunately, jarosites with 5 = V2 or 5 = 1 ions, such as Ti or are unknown. 

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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. 

The intraplanar spin structure of the iron jarosites is described by the so-called k=(00) structure. Figure 2.16, left, rather than the k = (yi/3 yi/3) structure, right, in spite of both classical and quantum theories for the kagome lattice which predict the latter. ... 

Figure 2.16 Two possible magnetic structures for the kagome lattice, (a) k = (00). (b) k = (-y/3 X Reprinted with permission from Greedan, 2001 [4]. Copyright...

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