Spin transfer in an open ferromagnetic layer: from negative damping to effective temperature

Spin transfer is a typical spintronics effect that allows a ferromagnetic layer to be switched by spin injection. All experimental results concerning spin transfer ( quasi-static hysteresis loops or AC resonance measurements) are described on the basis of the Landau-Lifshitz-Gilbert equation of the magnetization, in which additional current dependent terms are added, like current dependent effective fields and current dependent damping factors, that can be positive or negative. The origin of these terms can be investigated further by performing stochastic experiments, like one-shot relaxation experiments under spin injection in the activation regime of the magnetization. In this regime, the Neel-Brown activation law is observed which leads to the introduction of a current dependent effective temperature. In order to define these counterintuitive parameters ( effective temperature and negative damping), a detailed thermokinetic analysis of the different sub-systems involved is performed. This report presents a thermokinetic description of the different forms of energy exchanged between the electric and the ferromagnetic subsystems at a normal/ferromagnetic junction. The derivation of the Fokker-Planck equation in the framework of the thermokinetic theory allows the transport parameters to be defined from the entropy variation and refined with the Onsager reciprocity relations and symmetry properties of the magnetic system. The contribution of the spin polarized current is introduced as an external source term in the conservation laws of the ferromagnetic layer. Due to the relaxation time separation, this contribution can be reduced to an effective damping. The flux of energy transferred between the ferromagnet and the spin polarized current can be positive or negative, depending on the spin accumulation configuration. The effective temperature is deduced in the activation ( stationary) regime, provided that the relaxation time that couples the magnetization to the spin polarized current is shorter than the relaxation to the lattice.