The Spin Polarized Band Structure of Strained Thin Films of Gadolinium

The magnetic properties of strained thin films of gadolinium are characterized by a wave vector and thickness dependence of the exchange splitting. The spin-resolved band structure has been mapped by spin polarized photoemission, and provides considerable insight into the relationship between magnetism of local moment systems, and band structure. For more than 30 years theorists [l] have predicted that the magnetic coupling and exchange splitting of elemental local moment magnetic systems is wave vector dependent and strongly affected by the band structure. We have now the fmt direct experimental evidence of wave vector dependent exchange splitting in an elemental local moment system. The spin-polarized band structure of strained thin films of gadolinium is found to exhibit a compelling wave vector and thickness dependence of the magnetic exchange splitting [2]. Repeatedly there has been a tendency to assume that both, magnetic coupling and the correlation energy U, are wave vector independent. The possibility that the magnetic coupling or the correlation energy is anything other than a scalar is often ignored. Some recent studies [3] even suggest a wave vector independent exchange splitting of gadolinium. There is no a priori reason for this [l]. Magnetic anisotropy along distinct crystallographic directions is a consequence of spin-spin interactions (or so called dipole-dipole interactions) and spin-orbit interactions. The spin-orbit interactions make the spin sensitive to the crystal lattice and are generally the dominant effect [4,5]. Gadolinium is a ferromagnet where coupling to the crystal lattice is traditionally expected through spin-spin coupling (crystal field effects dominate) while spin-orbit coupling is expected to be weak because of the half filled 4f shell. The strong dipole coupling will also manifest in an anisotropy relative to specific crystal directions (magneto-crystalline anisotropy), and in 191 Mat. Res. Soc. Symp. Proc.Voi. 524 01998 Materials Research Society conjunction with some spin-orbit contributions can result in a wave vector dependence of the magnetic coupling. This also implies that the magnetic coupling of an elemental local moment system is expected to not only depend upon lattice spacing and bond angles but, as we will discuss in this paper, may also be strongly affected by the valence electron localization and the spin-polarized band structure. It is important to understand the significance of wave vector dependent magnetic behavior.