Damping by Slow Relaxing Rare Earth Impurities in ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$

Doping ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$ by heavy rare earth atoms alters the magnetic relaxation properties of this material drastically. We show that this effect can be well explained by the slow relaxing impurity mechanism. This process is a consequence of the anisotropy of the on site exchange interaction between the $4f$ magnetic moments and the conduction band. As expected from this model the magnitude of the damping effect scales with the anisotropy of the exchange interaction and increases by an order of magnitude at low temperatures. In addition, our measurements allow us to determine the relaxation time of the $4f$ electrons as a function of temperature.

Figure 1

FMR spectra for four different Ho doping concentrations measured at room temperature (RT) in the in-plane configuration using a frequency of 22 GHz. The red lines show the expected FMR lines given by the saturation magnetization, the $g$ factor, and the damping constant. In the calculation the upshift of the resonance field with increasing doping is caused by the decreasing magnetization. The $g$ factor was determined by out-of-plane FMR measurements and remains nearly unchanged up to a doping level of 6%. Note that for the 6% sample the discrepancy between the expected and the measured line position is about 300 Oe.

Figure 2

Frequency dependence of $\Delta H$ for (a) ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$ and Gd doped ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$, (b) Tb doped ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$, (c) Dy doped ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$, and (d) Ho doped ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$ films. All measurements are carried out in the parallel configuration at RT.

Figure 3

Damping parameter $\alpha$ determined from the slope of $\Delta H(f)$ shown in Fig. 2 as a function of the RE concentration.

Figure 4

Comparison of the contributed damping $\Delta {\alpha }_{\mathrm{RE}}$ (red bullets) to the anisotropy contribution arising from the anisotropic exchange interaction between the $4f$ moments and the conduction electrons $K^{\mathrm{ex}}$ (black line) as a function of orbital moment $L$ [16]. In addition, values of RE-induced damping in ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$ are plotted from Refs. 2 (gray squares), 1, 19 (gray star), and 20 (gray diamond). In Ref. 2 the damping is given as relaxation rates $\lambda$. These numbers were converted into Gilbert damping using $\alpha =\lambda /(\gamma 4\pi M)$.

Figure 5

Temperature dependence of the FMR linewidth ($\Delta H$) and the FMR field shift $S$ for a dopant concentration of 2.0% for Tb and Ho, 2.5% for Dy, and 5% for Gd. The measurements where carried out at 10 GHz in the parallel configuration. The field shift $S$ corresponds to the difference between the resonance fields of the doped and undoped samples. Note that the data for 2.5% Dy were multiplied by $4/5$ in order to be able to compare them to the Tb and Ho 2.0% data. The solid lines represent the expected behavior and were calculated from Eq. (1) by using three $4f$ transition energies. For the temperature dependence ${\tau }_{\mathrm{RE}}$ we used Eq. (13) of 17. The inset shows the temperature dependence of ${\tau }_{\mathrm{RE}}$ as determined from the present FMR measurements. The red bullets represents earlier measurement of ${\tau }_{\mathrm{RE}}$ for Nd doped YIG [17].