Comment on ‘ ‘ Ultrathin Mn films on Cu „ 111 ... substrates : Frustrated antiferromagnetic order ’ ’

We have studied collinear and noncollinear magnetic structures of a Mn monolayer on Cu~111! by use of the generalized gradient approximation to the density-functional theory using the full-potential linearized augmented plane-wave method. We found that the inclusion of the gradient correction did not significantly modify earlier results obtained in the local-density approximation. Irrespective of the choice of the exchange correlation functional, among the magnetic structures investigated, the minimal energy was found for a collinear row-wise antiferromagnetic structure. Our findings are at clear variance with a recent first-principles study @Phys. Rev. B 61, 12 728 ~2000!#, which reported that Mn on Cu~111! exhibits a noncollinear ground state with magnetic moments forming 6120° angles between nearest neighbors, claiming that this is due to the generalized gradient approximation essential in these systems. We discuss this point in detail. From our investigation of the zero-temperature phase diagram of the Heisenberg model going beyond nearest-neighbor interaction, we argue that it is not possible to determine the magnetic ground state from an investigation of a limited set of three different magnetic states, but a full investigation of spiral spin-density waves is required.