Size dependence of the relaxation rate for non-equilibrium redistributions of the magnetization in Ni–Fe heterestuctures: Exchange vs. relativistic damping scenarios

• The relaxation of non-equilibrium spin states in a Ni–Fe heterostructure is analyzed.
• Both the exchange (nonlocal) and relativistic (local) relaxations are accounted.
• The nonlocal relaxation is concurrent with the creation of a spin current.
• The role of the spin current increases for thinner metallic layers.
• For nanometer-size systems the relaxation is primarily driven by the spin current.

The relaxation of non-equilibrium redistributions of the magnetization in a model Ni–Fe heterostructure is analyzed on the basis of the Landau–Lifshitz equation with the relaxation terms proposed by Bar'yakhtar. Bar'yakhtar‘s terms account for both the relativistic (local) and exchange (nonlocal) relaxations. It is demonstrated that the role of the nonlocal relaxation term (a spin current flowing between layers) increases for smaller systems. For nanometer-size systems the nonlocal relaxation term significantly enhances the relaxation of the Ni layer magnetization back to equilibrium. The reason of this size dependence is a competition of fast magnetization dynamics, induced by the nonlocal relaxation term near an interface between metals and slow, relativistic dynamics, which occurs at each point of the Ni–Fe heterostructure. This study provides insight in how to achieve an exceptionally fast remagnetization in magnetic heterostructures after laser excitation.