Si/Ni/Dy/Al wedge sample

To further investigate the damping by spin currents, the normal metal is switched and dysprosium is used as the spin sink. The wedge sample

Si(100)/Ni/5nmDy/-∆Θ

τ

Figure 6.25: TR MOKE spectra for the Si(100)/5nmDy/xnmNi/2nmAl wedge sample at µ0H=−150mT,ϕ(H) = 30^◦out-of-plane andF^pump= 50mJ/cm².

2nmAl is made with a varied nickel layer thickness from 1nm to 60nm. The time resolved MOKE spectra are taken with extra precaution to make equivalent and systematic measurements on the entire wedge sample. The measurements are done in an external field of µ₀H=150mT, ϕ(H) = 30^◦ out-of-plane, under a pump fluence of Fpump=50mJ/cm². Fig. 6.25 shows the TR MOKE spectra on the wedge sample with nickel layer thicknesses less than 10nm, from which the incoherent magnon background is extracted. The dependence of the oscillation amplitudes on the nickel layer thickness as well as the reduced number of vis-ible oscillations for thinner films is observable. The precession frequency and damping parameter are extracted from the time resolved spectra and plotted versus the thickness of the nickel layer on the Si/Ni/Dy/Al wedge sample in Fig. 6.26 and Fig. 6.28.

The complicated frequency distribution can be classified into three regions of the nickel layer thickness: the saturation plateau at ≈8GHz for thicknesses around 10nm, the slow rise of 1GHz over 40nm thickness for thicker samples, and a sharp drop of 2GHz over 6nm thickness for thinner samples. The change in precession frequency for thicker layers results from the mode conversion between the main k = 0 mode and the standing spin-wave modes. The giant drop in frequency for thinner layers is caused by the change in the gyromagnetic ratio from spin current emission. Independently of the change of the precession

6.5 Non-local damping

frequency, only the main mode and the corresponding damping parameters are considered within this chapter.

Fig. 6.27 plots the exponential decay timeτ_α, extracted from fitting the time resolved spectra in Fig. 6.25, versus the nickel layer thickness. τα decreases non-uniformly by reducing the thickness of the nickel layer, taking values from τ_α = 440ps for a 13nm nickel layer down toτ_α = 136ps for a 2nm nickel layer.

For the approximately 3nm, nickel layer the damping time slightly increases by

≈10%, similar to the wedge sample with palladium.

Fig. 6.28 plots the damping parameter of the maink= 0 mode versus the nickel layer thickness on the Si/Ni/Dy/Al wedge sample. The damping parameter is almost constant at 0.033(2) for nickel layer thicknesses between 10nm and 20nm.

By reducing the thickness of the nickel layer to under 10nm a giant increase of the damping parameter is observed, up to α = 0.18 for 2nm. This additional damping for thin nickel films is from spin-current damping. There is a slight homogeneous increase of 20% of the damping parameter is observed for thicker nickel layers, with the maximum value at a thickness of 35nm.

To characterize the spin pumping strength, the damping parameter is fitted with Eq. 6.36 and the fit is also presented in Fig. 6.28. The proposed model from Tserkovnyak and Brataas agrees for thicknesses smaller than 20nm. The intrinsic damping of α₀ = 0.012(5) and a spin pumping coefficient a= 0.32(3) are determined from the fit. The corresponding real part of the mixing interface conductance isG^↑↓r = 4.5·10¹⁵Ω⁻¹m⁻², similar to the wedge sample with palla-dium. The Tserkovnyak and Brataas model describes the damping parameter enhancement due to the spin current emission, which is the dominating pro-cess for thin ferromagnetic layers but insufficient to completely describe the thickness dependence of the damping parameter. Therefore, Eq. 6.36 agrees well with the experimental results only for nickel layer thicknesses smaller than

ν

Figure 6.26: Precession frequency versus nickel layer thickness for the Si(100)/5nmDy/xnmNi/2nmAl wedge sample at µ0H = −150mT, ϕ(H) = 30^◦ out-of-plane andF^pump= 50mJ/cm². The line is a guide for the eyes.

τα

Figure 6.27: Exponential decay time τα versus nickel layer thickness for the Si(100)/5nmDy/xnmNi/2nmAl wedge sample atµ0H=-150mT,ϕ(H) = 30^◦out-of-plane and Fpump= 50mJ/cm². The line is a guide for the eyes.

20nm.

The additional increase of the damping parameter for thicknesses larger than 20nm has a different origin than the spin pumping. Both the Kittel k = 0 and standing spin-wave mode are present at these thicknesses. The increase in damping parameterαfor the Kittel mode indicates that there are the additional dissipation processes, in which the magnetic energy is transferred from the Kittel to the standing spin-wave mode. The effectivity of the mode conversion depends on the wavevector k=π/dof the standing spin wave, which explains the non-monotonic behavior of the damping parameter.

α

Figure 6.28: Damping parameter versus nickel layer thickness for the Si(100)/5nmDy/xnmNi/2nmAl wedge sample at µ0H = −150mT, ϕ(H) = 30^◦ out-of-plane andF^pump= 50mJ/cm². The line is a fit according to Eq. 6.36.

6.5 Non-local damping

νν

Figure 6.29: Normalized frequency change versus nickel layer thickness for the Si(100)/5nmDy/xnmNi/2nmAl wedge sample atµ0H =−150mT,ϕ(H) = 30^◦ out-of-plane andFpump= 50mJ/cm². The line is a fit according to Eq. 6.34.

The non-homogeneous decay in the frequency spectrum can also be explained by applying the theory of non-local damping by the spin current emission. The experimental values fit well with Eq. 6.34, as shown in Fig. 6.29, with the imaginary part of the conductance tensorG^↑↓_i = 1.7·10¹⁶Ω⁻¹m⁻². This value is slightly smaller than that for the Ni/Pd wedge sample.

A damping parameter enhancement from the spin current emission is observed for nickel/dysprosium layers with 5nm Dy and nickel layer thicknesses smaller than 10nm. When the thickness of the nickel layer approaches the λopt, the increase in damping parameter of the Kittelk= 0 mode is observed, resulting from the mode conversion to the standing spin wave. The reduction of the Kittel mode frequency from 9GHz to 6GHz is observed for thicknesses of less than 50nm.