Theoretical Study of Damping In Perpendicular Anisotropy Materials along Multiple Crystal Orientations

The damping constant α represents the elimination of the magnetic energy and affects the time scale of devices: therefore it is one of the most fundamental features of magnetism. However, there is no integrated model to describe the multiple damping mechanisms, including spin-orbit exchange relaxation, interfacial effects and magnon scattering. Here, we apply Kambersky’s torque correlation technique, within the tight-binding method, to multiple materials with high perpendicular magnetic anisotropy in superlattice and MgO based thin film structures. These materials play a key role in spintronic devices owing to their stability even for nanometer dimensions. The total damping shows a size effect that it is linearly dependent on the magnetic material, and decreases for thicker magnetic layers. This behavior is consistent with experimental data. The interfacial damping is also dependent on the nonmagnetic material and interfacial orientation, for crystals growing along (001), (111), and (011) orientations. We find that the origin of the interfacial damping includes both the distorted electronic states at the interface and the spin-orbit interaction in polarizable materials such as Pt or Pd. Integration of three magnon scattering within this picture will also be discussed.