The analysis of the knight shift in the μ+ SR technique

Abstract

We present an analysis and first-principles calculations of the Knight shifts of a positive muon (μ+) in normal and transition metals using a cellular multiple-scattering technique. The main conclusions are the following: (a) The μ+ induces the segregation of states (one of each spin) from the conduction band to lower energies. This cluster bonding state is occupied with two (antiparallel spin) electrons but in general it has less than 35% of μ+1s character. The screening is completed with the conduction electrons, (b) The observed Knight shift is the sum of a diamagnetic shielding (of the order —20 to —50 ppm arising in almost equal parts from the localized bonding cluster states and from the diamagnetic shielding of the conduction electrons) and a spin-enhanced paramagnetic shielding, large for all metals except for the divalent normal metals having a low density of states at the Fermi level which seats at the separation between the s- and the p-conduction bands. A spin-polarized calculation shows that the local spin density at the μ+ site is definitely smaller or even different in sign than the value computed from the local charge density enhancement. The ferromagnetic transition metals, because of the d-electron polarization, present a negative local magnetization at the μ+ site which gives a dominant negative contribution to the observed values.