Exchange Coupling of Magnetic Multilayers in Spin-Polarized Jellium

The bilinear and biquadratic coupling between two metallic layers separated by a nonmagnetic metal spacer are studied. The paper contains analytical formulae for the coupling which are obtained from the energy potential of the spin-polarized electron gas. The formulae for the coupling are obtained in the framework of the Hohenberg-Kohn formalism of the density functional theory and variables of the coupling are the electron density and the spin polarization of the magnetic multilayer.