Abstract
The two-dimensional Kondo lattice model with both nearest and next-nearest neighbor exchange interactions is studied within a mean-field approach and its phase diagram is determined. In particular, we allow for lattice translation symmetry breaking. We observe that the usual uniform intersite order parameter is never realized, being unstable towards other more complex types of order. When the nearest neighbor exchange ${J}_{1}$ is ferromagnetic the flux phase is always the most stable state, irrespective of the value of the next-nearest-neighbor interaction ${J}_{2}$. For antiferromagnetic ${J}_{1,}$, however, either a columnar or a flux phase is realized, depending on conduction electron filling and the value of ${J}_{2}$.
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