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

Abstract

Spin-transfer is a typical spintronics effect that allows a ferromagnetic layer to be switched by spin-injection. Most of the experimental results about 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 damping factors are added, and can be positive or negative. The origin of the damping 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 Néel-Brown activation law is observed which leads to the introduction of a current-dependent effective temperature. In order to justify the introduction of these counterintuitive parameters (effective temperature and negative damping), a detailed thermokinetic analysis of the different sub-systems involved is performed. We propose a thermokinetic description of the different forms of energy exchanged between the electric and the ferromagnetic sub-systems at a Normal/Ferromagnetic junction.The derivation of the Fokker-Planck equation in the framework of the thermokinetic theory allows the damping 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 spin accumulation configuration. The effective temperature is deduced in the activation (stationary) regime, providing that the relaxation time that couples the magnetization to the spin-polarized current is shorter than the relaxation to the lattice.

Magnetization reversal driven by spin injection: A diffusive spin-transfer effect

“…Note that the GMR parameter ∆R is a function of β: expressed in terms of the spin diffusion length l sf it writes [14] ∆R/R =…”

“…First, in single domain ferromagnets, the reversible part of the hysteresis loop is not significantly modified under current injection, while the irreversible jump is drastically modified [14]. Second, the amplitude of spin-transfer is proportional to the giant magnetoresistance and to the amplitude of the current [15,16,17].…”

“…give L θϕ = −L ϕθ , and the symmetry imposes that L θθ = L ϕϕ [14]. Furthermore, the two transport coefficients left are not independent since they are both related to the Gilbert damping coefficient η and the gyromagnetic factor Γ .…”

“…The effect of the diffusion terms cannot be taken into account in the quasi-static hysteresis loop (i.e. for vanishing temperature or infinite measurement times) as a deterministic effective field (this point is discussed in the references [14,18]). A deterministic correction to the reversible part of the hysteresis (the quasi-static states) is hence not expected here.…”

Spin Hall effect and irreversible thermodynamics: Center-to-edge transverse current-induced voltage

“…In the present case of the spin Hall effect, there has been a time-interval of over forty years between the initial, seminal, work 3,4 and the present application of irreversible thermodynamics to test its consistency. (A number of recent works 16,22,23 have applied irreversible thermodynamics to magnetic systems, but they have not considered the spin Hall effect). The method, briefly, is as follows:…”