Magnetization Dynamics in a Current-Driven Magnetic Nano-Pillar with Dipole-Dipole Coupling between Magnetic Layers (PREPRINT)

摘要

The small-amplitude uniform magnetization excitations in a magnetic nano-pillar with two ferromagnetic layers coupled by the dipole-dipole interaction are considered. We showed that the dipole magnetic field in this system can be fully described by two diagonal tensors for every layer The spectrum of coupled oscillations is found. It consists of two modes, the lower mode is quasi-antisymmetric at small bias fields and excited by current, the upper mode is quasi-symmetric at small bias fields and excited by microwave magnetic field. It is demonstrated that this spectrum can be described by the traditional Kittel expressions with decreased saturated magnetization and renormalized external magnetic field. We also demonstrated that for realistic nano-pillar parameters this renormalization does not exceed 10% for the lower quasi-antisymmetric mode at small bias fields, and 50% for the upper quasi- symmetric mode at small bias fields.