RKKY-like Biquadratic Exchange in Magnetic Superlattices

Abstract

Since the discovery of antiferromagnetic coupling of ferromagnetic layers across a nonmagnetic metallic spacer layer, the magnetic superlattices (SL) have become an object of intense interest of both theoretical as well as experimental studies. The problem of RKKY-reminiscent spin polarization oscillations, with a long period and giant interface magnetoresistance attracted the most attention. The recently discovered, π/2 coupling between magnetizations of the neighbouring magnetic layers [1] added new interest to the problem. This type of ordering suggests that along with the bilinear coupling of the type J 1 m1 • m2 between magnetizations of adjacent layers there is an additional multipolar interaction. There were many attempts describing the mechanisms that give rise to biquadratic exchange, being a speciflc form of coupling between magnetic quadupole moments of the ions (for details see Refs. [2, 3] and references therein). The aim of the paper is to study a new intrinsic mechanism that originates in multipolar exchange coupling. In the following we will show that the quadrupole-quadupole coupling can arise in a quite natural way from direct scattering of conduction electrons on magnetic multipole moments in the manner similar to bilinear RKKY interaction. The starting point for any description of metallic magnetic systems is the case of dilute alloys, when a few TM or RE ions are immersed in the sea of conduction electrons. The coupling of the ionic spin Sn with the itinerant electron spin σ is usually taken as the contact interaction [4]: Hex = -2JSn σδ(r). In the case of non-s magnetic ion state along with the scattering due to dipolar contact interaction there appears also scattering of conduction electrons on quadupolar moments. Kondo [5] has proved that the interaction Vqc (k) between conducting electrons and the quadrupoles is given by