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 (3×3) lattice. Despite an almost vanishing total spin magnetization we predict the emergence of orbital magnetization and large anomalous Hall effect, to which there is a significant topological contribution purely due to the real space spin texture at the surface.