Competition Between Two Ordering Processes in Two-Dimensional Doped Antiferromagnets

We provide a Landau theory of the coupled charge density wave and spin density wave order parameters to investigate the possibility of coexistence or competition between the two ordering processes occurring in the two-dimensional doped antiferromagnet. We find that the two ordering processes can coexist only in a certain region of coupling parameters, andthe one with lower transition temperature can only coexist together with the other one with higher transition temperature and can not be stabilized separately. Phase diagrams in different situations are given.