We present first-principles calculations of the magnetic hyperfine fields H hf of 5sp impurities on the (001), (111), and (110) surfaces of Ni. We examine the dependence of H hf on the coordination number by placing the impurity in the surfaces, on top of them at the adatom positions, and in the bulk. We find a strong coordination dependence of H hf , different and characteristic for each impurity. The behavior is explained in terms of the on-site s-p hybridization as the symmetry is reduced at the surface. Our results are in agreement with recent experimental findings. PACS numbers: 73.20.Hb,75.75.+a,73.20.Hb,76.60.Jx The understanding of the magnetic properties of solids on the atomic level is a challenge for experiment and theory. The magnetic hyperfine interaction of the electronic magnetization with the nuclear magnetic moment of an atom is such a property, and it is known to depend in turn on the properties of the atom as well as on the neighboring atomic environment. In particular, for impurities in the bulk of the ferromagnetic materials Fe, Co, Ni, the trends of magnetic hyperfine field H hf have been well understood and the experimental and theoretical results extend practically over the whole periodic table [1,2]. The relation of H hf to the local magnetic moment and to the atomic environment is not trivial. Therefore, for the interpretation of the trends, first-principles, all-electron methods have been extremely useful [2], since they can describe the charge density and magnetization near the atomic nucleus self-consistently. H hf measurements for probe atoms at interfaces or surfaces can also provide unique information on the local structure [3], especially in combination with relevant calculations [4,5,6].One of the modern powerful experimental techniques allowing the study of the hyperfine interaction of impurities at surfaces or interfaces is the perturbed angular correlation spectroscopy [7]. It has a high enough sensitivity that allows accurate measurements from highly diluted probe atoms (10 −4 − 10 −5 of a monolayer), so that these form practically isolated impurities. In a recent experimental publication [8], the coordination number dependence of H hf of Cd impurities in Ni host was studied, by comparing data from Cd positioned on several Ni surfaces. The conclusion was that the H hf of Cd strongly depends on the coordination number. Although this might be expected, since the magnetic moment of the Cd impurity is not intrinsic but rather induced by the environment, the data show neither a linear dependence nor an increase with the number N of Ni neighbors. On the contrary, H hf is measured to be strongest for N = 3, while as N is progressively increased H hf seems to change sign and has a parabolic behavior.In order to interpret this puzzling behavior, we have performed first-principles calculations for all 5sp and the early 6s impurities (Ag to Ba) on various Ni surfaces and in bulk Ni in a substitutional position. The impurity positions studied are given in Table I together with the co...