First-principles study of hyperfine fields in a Cd impurity in the Fe/Ag(100) interface

Monolayer-resolved hyperfine fields (HFF's) at the Fe/Ag(100) interface have recently been determined using ${}^{111}\mathrm{In}$ probe atoms, which decay to ${}^{111}$Cd, in perturbed $\ensuremath{\gamma}\ensuremath{\gamma}$ angular-correlation spectroscopy (PAC). Isolated radioactive probe atoms in PAC allow to sense the presence of HFF's at the Fe and induced HFF's at the Ag layers but, poses a complementary physical problem to that of the HFF's at the host Fe/Ag system: that of an impurity within the layers. Using density-functional theory (DFT) within the generalized gradient approximation (GGA) and a supercell approach, we investigate this problem. Similarly as experimentalists insert the probe atom on a layer-by-layer growth, preparing samples with radioactive probe atoms either in the Fe/Ag interface, or in the second (from the interface) Ag layer, or embedded within the bulk Fe, our supercell methodology can simulate each of these systems. The theoretical approach has the advantage of having the capability of distinguishing between two different cases at the interface: Cd in the Fe or Ag side. This allows us to make a clear assignment of the measured HFF's. We discuss: (i) the relation of the HFF in the Cd probe with that of the original host atom, (ii) the precision of state of the art DFT-GGA calculations to obtain quantitative predictions of HFF's in very complex systems such as interfaces and the effect of lattice relaxations (interlayer spacings, lateral displacements). The importance of including spin-orbit coupling and the influence of additionally considering orbital polarization are assessed.