Competing magnetic interactions in quantum thin films

Abstract In this work we study the quantum spin-1/2 Heisenberg model in two dimensions, with a nearest-neighbor short-range antiferromagnetic exchange ( J ) and a long-range ferromagnetic dipole–dipole ( E d ) coupling. Using the double-time Green's function method within the random phase approximation (RPA) we obtain the magnon dispersion relation as function of frustration parameter δ ( δ being the ratio between exchange and dipolar interactions δ = J / E d ). We study the competition between long-range ferromagnetic dipole–dipole interaction and short-range antiferromagnetic exchange in stabilizing the magnetic long-range order in a two-dimensional system. We find that the ferromagnetic order is stable at small k up to critical value of frustration δ c = 0.04375 . For frustration higher than the critical value ( δ > δ c ) our magnetic system is disordered.