Competing magnetic interactions in quantum thin films

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 (Ed)(Ed) 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 δδ (δδ being the ratio between exchange and dipolar interactions δ=J/Edδ=J/Ed). 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 δc=0.04375δc=0.04375. For frustration higher than the critical value (δ>δc)(δ>δc) our magnetic system is disordered.

► Competition between interactions short-range (exchange J  ) and long-range dipole–dipole (Ed)(Ed) is studied.
► The quantum spin-1/2 Heisenberg model in two dimensions is used as example.
► The interactions are exchange (antiferromagnetic) and ferromagnetic dipole–dipole.
► The double-time Green's function method and RPA is used to obtain the dispersion relations of the acoustic branch.
► The system has ferromagnetic order stable for values less than critical of frustration (J/Ed)(J/Ed).