Hi all,
In the lattice I am working on, there are N (N>2) equivalent sites in primitive unit cell. All the bonds are equivalent, but have different orientation. e.g. kagome lattice, the three bonds have different directions. Now I need to write down the Dzyloshiski-Moriya interaction for this lattice, the D vector depends on the direction of the bond, or more specifically, D vector depends on the relative coordinates of the two sites. My question is how to specify the bond operator for different bonds, or, how to specify the coordinate-dependence of the bond operators?
The second question is about how to specify unit cell of the lattice. Here are two concrete examples from the library. I think if i can understand them, i won't have trouble with my lattice.
1. triangular,
<UNITCELL name="triangular" dimension="2"> <VERTEX/> <EDGE><SOURCE vertex="1" offset="0 0"/><TARGET vertex="1" offset="0 1"/></EDGE> <EDGE><SOURCE vertex="1" offset="0 0"/><TARGET vertex="1" offset="1 0"/></EDGE> <EDGE><SOURCE vertex="1" offset="0 0"/><TARGET vertex="1" offset="-1 1"/></EDGE> </UNITCELL>
I am confused about this. I don't why it is specified as this. It doesn't seem natural to me. Just from the offset, it will form a right triangle, rather than an equilateral triangle. Also, does the length of the offset matter?
2, kagome,
<UNITCELL name="Kagome" dimension="2"> <VERTEX><COORDINATE>0 0</COORDINATE></VERTEX> <VERTEX><COORDINATE>0.5 0</COORDINATE></VERTEX> <VERTEX><COORDINATE>0 0.5</COORDINATE></VERTEX>
<EDGE><SOURCE vertex="1"/><TARGET vertex="2"/></EDGE> <EDGE><SOURCE vertex="1"/><TARGET vertex="3"/></EDGE> <EDGE><SOURCE vertex="2"/><TARGET vertex="3"/></EDGE> <EDGE><SOURCE vertex="1"/><TARGET vertex="2" offset="-1 0"/></EDGE> <EDGE><SOURCE vertex="2"/><TARGET vertex="3" offset="1 -1"/></EDGE> <EDGE><SOURCE vertex="1"/><TARGET vertex="3" offset="0 -1"/></EDGE> </UNITCELL>
Why specify the coordinates as this? Why rewrite the <EDGE> once more with offset? I cannot draw a unit cell from just looking this. Could some one explain this for me?
THanks very much!
Gang Chen