Gilbert damping in NiFeGd compounds: Ferromagnetic resonance versus time-resolved spectroscopy

Engineering the magnetic properties (Gilbert damping, saturation magnetization, exchange stiffness, and magnetic anisotropy) of multicomponent magnetic compounds plays a key role in fundamental magnetism and its applications. Here, we perform a systematic study of ${\left({\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}\right)}_{100-x}{\mathrm{Gd}}_x$ films with $x=0\%$, 5%, 9%, and $13\%$ using ferromagnetic resonance (FMR), element-specific time-resolved x-ray magnetic resonance, and femtosecond time-resolved magneto-optical pump-probe techniques. The comparative analysis of field and time domain FMR methods, with complimentary information extracted from the dynamics of high-frequency exchange magnons in ferromagnetic thin films, is used to investigate the dependence of Gilbert damping on the Gd concentration.

Figure 1

XRD scans for ${\mathrm{Al}}_2{\mathrm{O}}_3\left(\text{substrate}\right)/\text{Ta}/\text{Cu}/{\mathrm{Py}}_{100-x}{\mathrm{Gd}}_x/\mathrm{Ta}$ samples with $x=0\%$, 5%, 9%, and 13% (from top to bottom). Scans are shifted vertically for better visibility.

Figure 2

Frequency dependence of the FMR (a) resonance field and (b) peak-to-peak linewidth at the magnetic field applied parallel to the ${\mathrm{Py}}_{100-x}{\mathrm{Gd}}_x$ film plane for different concentrations of Gd. Solid lines represent the fit.

Figure 3

(a) Precessional angle $\varphi \left(t\right)$ of Fe magnetic moments as a function of the delay time after the step-pulse field excitation in ${\mathrm{Py}}_{100-x}{\mathrm{Gd}}_x$ thin films with $x=5$%, 9%, and 13% (from top to bottom). (b) Free precession of Fe (blue solid circles) and Gd (red open circles) atoms in the ${\mathrm{Py}}_{91}{\mathrm{Gd}}_9$ film. The value of the applied bias field for all scans is ${\mu }_0{H}_B=0.8$ mT. The solid lines represent the fit. All measurements are taken at room temperature.

Figure 4

Variations of the MOKE rotation signal ${\psi }_K^{\prime }\left(t\right)$ measured on the Py sample for ${40}^{\circ }$ between the normal to the film surface and the external magnetic field. The fit was performed using Eq. (9) as a fit function. (b) Two-dimensional image of the variations of the MOKE rotation signal ${\psi }_K^{\prime }\left(t\right)$ measured on the same sample as in (a) for different pump-probe delays and angles $\theta$ between the external magnetic field and the normal to the film surface.

Figure 5

Fourier spectra of the MOKE rotation measured on Py for different angles $\theta$ between the surface normal and the external magnetic field. Solid lines depict the magnon frequencies obtained in the fitting procedure of the measured MOKE signals with the sum of the decaying cosine functions [see Fig 4].

Figure 6

Dots represent the magnon frequencies and the damping rates obtained for ${\mathrm{Al}}_2{\mathrm{O}}_3\left(\text{substrate}\right)/\text{Ta}/\text{Cu}/{\mathrm{Py}}_{100-x}{\mathrm{Gd}}_x/\mathrm{Ta}$ structures with different Gd dopings of (a) 0%, (b) 5%, (c) 9%, and (d) 13% in the fitting procedure of the measured MOKE signals with the sum of the decaying cosine functions. Different colors and dot types correspond to different magnon modes: n = 0, blue circles; 1, green triangles; 2, red squares. Black solid lines are the results of the modeling using the LLG equation with an adjustable dimensionless damping parameter $\alpha$. Solid red and black dashed lines demonstrate dependencies of the damping rate on the magnon frequency, calculated using depicted values of $M_{\mathrm{eff}}$ and ${\alpha }_{\mathrm{eff}}$, in the 2D and 3D cases, respectively.