Variation of effective damping with temperature in permalloy/Gd heterostructures

In this study, we systematically investigate the temperature dependence of effective damping in FeNi (permalloy or Py)/Gd bilayer based on broadband ferromagnetic resonance. Despite a significant increase in the effective damping of the Py/Gd bilayer with decreasing temperature, we show that the spin pumping is not responsible for the result. By combining our findings with systematic measurement data of Py/Cu/Gd contrast samples, we conclude that an effective damping enhancement from a decrease in temperature is due to the temperature-dependent magnetic moment of Gd and antiferromagnetic coupling between Py and Gd. Further, we perform a semiquantitative analysis of the experimental data using the Landau-Lifshitz-Gilbert equations that consider the antiferromagnetic coupling between Py and Gd, and estimated the damping parameters in the range of 0.3–0.4 for Gd films with thicknesses of 5 and 8 nm. Our results suggest that to analyze the spin transport in heterostructure with several magnetic layers, it is necessary to commence from the fundamentals of magnetization dynamics considering interlayer coupling and avoid the overuse of spin pumping.

Figure 1

Hysteresis loops of (a) Py, (b) Py/Gd(8), and (c) Py/Cu(3)/Gd(8) at 300 and 60 K. Temperature dependence of the reduced magnetization $M/M_{\mathrm{S}}^{@300\mathrm{K}}$ at 10 kOe for (d) Py/Gd(5) and (e) Py/Gd(8) bilayers. (f) The dashed curve represents the relationship between the theoretical critical temperature and Gd thickness, and the symbols represent the experimental data.

Figure 2

(a) Raw FMR spectra of Py/Gd(5) sample. Inset: FMR spectra at 15 GHz at two representative temperatures. (b) Frequency as a function of resonance field for Py/Gd(5) bilayer at 100 K; solid lines represent fits to Eq. (3). (c) FMR linewidths as a function of frequency for Py/Gd(5) at different temperatures.

Figure 3

(a) Effective gyromagnetic ratio and (b)–(g) effective damping of Py/Gd and Py/Cu/Gd series samples as a function of temperature. The arrows in (b)–(f) indicate the critical temperatures at different thicknesses of Gd.

Figure 4

Measured effective damping as a function of Gd layer thickness at different temperatures. The solid lines represent fitted curves according to Eq. (5). Inset shows the change in spin-diffusion length with temperature.

Figure 5

Effective damping as a function of normalized temperature. The symbols are the same as those used in Fig. 3. The diamond symbols indicate the effective damping for Py/Gd(3) from Khodadadi et al. [18].

Figure 6

Temperature-dependent effective damping of Py/Gd(5) and Py/Gd(8), symbols are experimental data, dashed lines are theoretical curve calculated using Eq. (7).