First-principles study of the conduction-electron-mediated interactions between nuclear spins in copper metal

Motivated by recent success in observing the ordering of copper nuclei at very low temperatures, we have used first-principles electronic structure calculations to evaluate the conduction-electron-mediated coupling strengths between the nuclear spins. Scalar-relativistic wave functions from a self-consistent linear augmented-plane-wave calculation were used to evaluate the contact, dipolar, and orbital electron-nuclear interactions. Besides the isotropic Ruderman-Kittel coupling between nuclei, the electron-nuclear dipolar and orbital interactions give rise to significant anisotropic coupling terms. The symmetry of the anisotropic coupling is not dipolar in form and the significance of this for analysis of NMR line broadening is pointed out. The coupling strengths are in good agreement with various NMR measurements. Using mean-field theory, the overall coupling predicts an ordering wave vector at (2{π}/a)(0.87,0,0) and a helical spin structure; however, this state is only 0.6% lower in energy than the state with ordering vector (2{π}/a)(1,0,0), which is the one recently observed in neutron scattering experiments. The numerical calculations are not precise enough to accurately determine the ordering vector because of this extremely small difference in energy for states near the zone boundary along the (1,0,0) direction.