  We predict the occurrence of a novel type of atomic-scale spin lattice in an
Fe monolayer on the Ir(001) surface. Based on density functional theory
calculations we parametrize a spin Hamiltonian and solve it numerically using
Monte-Carlo simulations. We find the stabilization of a three-dimensional spin
structure arranged on a 3x3 lattice. Despite an almost vanishing total
magnetization we predict the emergence of a large anomalous Hall effect, to
which there is a significant topological contribution purely due to the real
space spin texture at the surface.
