Role of interband mixing in exchange coupling and conduction-electron polarization in metals

The effect of interband mixing on the actual form of the exchange interaction J(k,k′) between a local moment and conduction electrons in a metal, and in turn on the induced conduction-electron spin density polarization, is investigated. Results of detailed calculations are reported which employ a realistic local moment (Hartree-Fock Gd3+ ion) and orthogonalized plane waves for the conduction electrons. As is well known, interband mixing induces a net negative conduction-electron spin moment, reducing and even reversing the positive moment induced by electrostatic exchange in the s-d or s-f interaction model. The main peak of the interband spin distribution is very diffuse, and the phase of the associated Friedel oscillations is shifted outwards. For the case of rare-earth interband mixing, these oscillations serve to enhance those already due to electrostatic exchange. In other words, while it is often assumed that the amplitude of the s-f Friedel oscillations faithfully reflects the net induced spin, this is not the case if s-f interband mixing occurs.