Antiferromagnetic Ground States in Some Commonly Known Lattices

Authors: Ali BAYRI

Abstract: Antiferromagnetism is a very interesting behaviours in some real materials and their alloys. It is important in high T_c materials as well. The main reasons for antiferromagnetism are the kinetic exchange[1,2]. In this study, I will consider commonly known lattices in two or three dimensions. Using the Heisenberg model I will show that there are two systems: Frustrated and unfrustrated. In unfrustrated case the spin structure is unique and it involves ferromagnetism as well. However, in frustrated case the spin structure is not unique and it gives more than one spin orderings. This behaviours is very interesting since it causes a first order magnetic phase transition[3,4]. Finally, I will summarize that the simplier lattice (the square, the S.C. and B.C.C.) are unfrustrated and the complicated lattices (triangular, F.C.C. and H.C.P.) are frustrated.

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