Exotic phases induced by RKKY interaction in the square lattice.

We study a model of Ising spins in which direct exchange interactions compete with the Ruderman-Kittel-Kasuya-Yosida (RKKY) coupling, which may arise effectively from itinerant electrons. We consider the model in the two-dimensional square lattice and focus on values of the RKKY coupling constant (JRKKY) and the Fermi momentum (kF) that induce strong frustration. We study the low-temperature magnetic field phase diagram using Monte Carlo simulations, considering several nearest neighbors in the RKKY interaction. Magnetic frustration yields a rich phase diagram with a variety of exotic phases. We compute the structure factors and define appropriate order parameters to describe the transitions. We also discuss the validity of the approximation made for long-range couplings and analytically demonstrate the change in the coexistence lines in the phase diagram by including up to the tenth nearest neighbors.