Spin wave excitations of a magnetic pillar with dipolar coupling between thelayers

Abstract

It is demonstrated analytically that the spectrum of small-amplitude spatially uniformmagnetization excitations in an in-plane magnetized magnetic pillar with two ferromagneticlayers coupled by dipole–dipole interaction can be approximately described by thetraditional Kittel formula with reduced saturation magnetization and effective anisotropyfield. The spectrum consists of a quasi-symmetric and a quasi-antisymmetric mode, and theapparent reduction of saturation magnetization for the quasi-symmetric mode (≤50%) is much larger than that for the quasi-antisymmetric mode (≤10%). The effect of dynamic dipolar coupling between the nano-pillar layers could be partlyresponsible for the apparent reduction of static magnetization seen in many spin-torqueexperiments performed on magnetic nano-pillars.