Interface Enhancement of Gilbert Damping from First Principles

Abstract

The enhancement of Gilbert damping observed for Ni80Fe20 (Py) films in contact with the nonmagnetic metals Cu, Pd, Ta and Pt, is quantitatively reproduced using first-principles scattering calculations. The "spin-pumping" theory that qualitatively explains its dependence on the Py thickness is generalized to include a number of extra factors known to be important for spin transport through interfaces. Determining the parameters in this theory from first-principles shows that interface spin-flipping makes an essential contribution to the damping enhancement. Without it, a much shorter spin-flip diffusion length for Pt would be needed than the value we calculate independently.PACS numbers: 72.25.Mk, 76.50.+g, 75.70.Tj Introduction.-Magnetization dissipation, expressed in terms of the Gilbert damping parameter α, is a key factor determining the performance of magnetic materials in a host of applications. Of particular interest for magnetic memory devices based upon ultrathin magnetic layers [1][2][3] is the enhancement of the damping of ferromagnetic (FM) materials in contact with non-magnetic (NM) metals [4] that can pave the way to tailoring α for particular materials and applications. A "spin pumping" theory has been developed that describes this interface enhancement in terms of a transverse spin current generated by the magnetization dynamics that is pumped into and absorbed by the adjacent NM metal [5,6]. Spin pumping subsequently evolved into a technique to generate pure spin currents that is extensively applied in spintronics experiments [7][8][9].A fundamental limitation of the spin-pumping theory is that it assumes spin conservation at interfaces. This limitation does not apply to a scattering theoretical formulation of the Gilbert damping that is based upon energy conservation, equating the energy lost by the spin system through damping to that parametrically pumped out of the scattering region by the precessing spins [10]. In this Letter, we apply a fully relativistic density functional theory implementation [11][12][13] of this scattering formalism to the Gilbert damping enhancement in those NM|Py|NM structures studied experimentally in Ref. 4. Our calculated values of α as a function of the Py thickness d are compared to the experimental results in Fig. 1. Without introducing any adjustable parameters, we quantitatively reproduce the characteristic 1/d dependence as well as the dependence of the damping on the NM metal.

Spin Torque Study of the Spin Hall Conductivity and Spin Diffusion Length in Platinum Thin Films with Varying Resistivity

“…Fast saturation of the damping at very thin Pt thicknesses has also been observed previously [22,37,38]. However, Liu et al [47] have recently pointed out that this very rapid attenuation is likely due to strong SML at the FM/Pt interface, and used a first principles calculation and data [61] from this measurement method to obtain 5.5 nm has been determined from a low temperature, 3-10 K, study of spin pumping in lateral spin valves [39,41] This work seems to resolve the controversy regarding the differences in the value of s λ for Pt as obtained from various spin Hall and other experiments, and demonstrates that the spin…”

Interfacial Structure Dependent Spin Mixing Conductance in Cobalt Thin Films

“…The effective specific interface resistance between NM L;R 1 and NM L;R 2 (Ta) should be high [2,14], so it is expected that J L;R s2 ∼ 0, and the spin backflow J L;R s1 ≈ J L;R s pump ; thus, the damping enhancement should be negligible. However, for Ir=Ta overlayers, when NM R 1 (Ir) is thicker than the spin diffusion length, J R s pump may fully relax within NM R 1 ; now J R s1 ≈ 0, again J R s2 ∼ 0, and the damping should be enhanced.…”

“…However, a recent theoretical study by Liu et al developed a more complex picture of spin pumping [2], which explains the experimentally observed damping enhancements for various material combinations [14]. In this model the "effective" mixing conductance g eff ↑↓ contains terms that quantify not only relaxation of the spin current within the NM layer g ↑↓ , but also the ability of the spin current to cross the FM-NM interface, characterized by an effective specific interface spin resistance R Ã and relaxation associated with crossing the interface, termed spin memory loss δ. Chen and Zhang very recently proposed an alternate model, based on spin memory loss due to interfacial (Rashba, in their calculations) SOI [1].…”

“…A quantitative physical analysis of spin currents crossing interfaces [1][2][3] in ferromagnetic (FM) thin-film multilayers will provide a deeper fundamental understanding required for applications of such nanoscale magnetic systems in magnonics [4], spin caloritronics [5,6], and spintronics [7][8][9]. Precessional magnetization dynamics have been used extensively to access interfacial spin transport where spin current flows from magnetization precession in a FM thin film into an adjacent nonmagnetic (NM) layer.…”

Spin Orbit Coupling Controlled Spin Pumping and Spin Hall Magnetoresistance Effects

“…The effective spin mixing conductance (ESMC) across the NM/FM interface has elicited a great deal of attention because it governs the spin pumping efficiency [23][24][25][26][27] , i.e., the density of the dc spin current  s as follows 7,26 ,  s = ω 4π G ef f mix sin 2 θ, where G ef f mix is the real part of the complex ESMC, the cone angle θ of the FM magnetization procession is determined by the ferromagnetic resonance (FMR) power absorption, ω = 2πf with the radio frequency f . It is appealing to reveal the physical mechanism of the ESMC because it is intimately related to the electronic band structure of the NM layer and chemical states on the surface of the FM layer 23,24 .…”