The damping of precession is a critical issue in high frequency magnetism, which can be described by the damping constant α in various magnetic systems.^[1,2] The α determines the switching time of the magnetization for ultra-high frequency devices. For example, in high-frequency magnetic recording, the switching time strongly depends on α and the magnetization reversal is faster when the damping constant is appropriate.^[3] The Gilbert damping constant defined as is proportional to the critical current density J_c in spin-transfer-torque devices, where γ is the gyromagnetic ratio, and M_s is the saturation magnetization.^[4] Therefore, it is crucial to understand and control the damping constant for practical applications. Many theoretical studies have been carried out in an effort to understand the origin of the damping constant.^[5–7] It is well-known that α contains both intrinsic and extrinsic contributions. The intrinsic part largely depends on the fundamental properties such as M_s and spin–orbit coupling, while the extrinsic part is generally explained by the defect-induced two magnon mode and/or the local resonance mode, both of which are associated with magnetic inhomogeneities within the material.^[8] In particular, much attention has been focused on the control of α using various methods, such as doping with rare earth or other transition metal elements.^[9,10] For example, Rantschler et al. and Fassbender et al. reported the variation of α in 3d, 4d, and 5d transition metal doped FeNi films and the increase of the damping constant in permalloy films with the increase of Cr-doping, respectively.^[11,12] More recently, Guo et al. have reported that the rare-earth Gd doping reduces the magnetic damping constant of FeCo films as probed by ferromagnetic resonance (FMR).^[4]

In our previous work, the damping constant of CoIr films has been investigated thoroughly with thickness, substrate temperature, and Ir content.^[13] CoIr films with a certain Ir content exhibit strong negative magnetocrystalline anisotropy, which means that the c-plane of the hcp-CoIr crystal is the easy magnetization plane and the c-axis is the corresponding hard axis.^[14] The properties enhance the high frequency magnetic properties and the critical film thickness for the Néel type domain wall changing into Bloch type, and strictly restrict the magnetic moments in-plane of micrometer thick soft magnetic thin films (SMTFs).^[15,16] Recently, the reduction of magnetic damping constant in Rh-incorporated CoIr system has been reported.^[17] It is also reported that the doping elements B^[18] and SiO₂^[19] have an effect on soft magnetic properties of CoIr system. To understand the effects on the damping constant and gain control of the magnetic damping behavior, we prepared oriented hcp-CoIr thin films with different additives of B, Ni, and SiO₂. We have studied the effects of these additives on the damping constant by using ferromagnetic resonance.

The layer structure of the films prepared by direct current (DC) magnetron sputtering was substrate/Ti/Au/ (P=B, Ni, and SiO₂), as shown in Fig. 2(a). The Si wafer with surface oxidation was used as a substrate. The amorphous Ti layer of 3 nm provided an flat and clean surface that assists the oriented growth of the Au layer with (111) plane parallel to the thin film, and the oriented Au layer of 10 nm was used to induce the oriented growth of soft magnetic layer with its c-axis normal to the film surface. Both Ti layer and Au seed layer were made with pure Ar at a pressure of 0.25 Pa, then the magnetic layers were deposited on the seed layer with 0.3 Pa Ar gas. Both the Co target with five Ir chips and the corresponding P target were used. The substrate from the targets about 15 cm away was mounted on a turntable, which was rotated about its central axis. The in-plane uniaxial anisotropy can be induced by placing the substrates slightly off-centered on the turntable. The contents of P can be varied by changing the gun power while keeping the CoIr gun power at 60 W. In the following discussion, as shown in Table 1, the studied samples will be denoted as Px corresponding to the film with magnetic layer.

Fig. 1.

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	Fig. 1. The coordinate system used for measurements and data analysis of the FMR spectra.

Fig. 2.

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	Fig. 2. (a) The layer structure of the systems and (b) the XRD patterns for SiO8.7, Ni7.1, and B8.7 films. (c) The typical transmission electron microscopy (TEM) image showing the columnar type growth of magnetic layer. (d) and (f) The high resolution imaging of the magnetic layer revealing the degree of c-axis orientation.

Table 1.

Table 1.

Table 1. Naming method for films where P denotes B, Ni, or SiO2. . CoIr P/x Naming method Co79Ir21 B/x=0, 3, 6.5, 8.7, 10.8 Bx Co79Ir21 Ni/x=0, 3.4, 5.3, 7.1, 10.6 Nix Co79Ir21 SiO2/x=0, 3.5, 5.2, 7, 8.7 SiOx

Table 1. Naming method for films where P denotes B, Ni, or SiO2. .

The FMR measurements are performed in a Joel electron paramagnetic resonance spectrometer at 9 GHz in a scanning DC magnetic field (0–20 kOe). The magnetic field is applied by an electromagnet, and the sample is fixed onto a 0–360 rotatable quartz rod and a goniometer is used to control the rotation of the quartz rod. For magnetic thin films, FMR based on the approximation of spatially uniform precession of the magnetization over the whole film is analyzed in the following. Figure 1 shows the coordinate system used for the FMR measurements and data analysis. The film plane is in the x–y plane and the film normal direction is parallel to the z-axis. , , and are amplitude, polar, and azimuthal angles of the magnetization vector . The static field is applied in plane with an azimuthal angle and the small microwave magnetic field h is applied along the z-axis. Then, the total magnetic free energy per unit volume of the film is given by the following equation:^[20] 1 where is the angle between the easy axis of the film and the x-axis, K_u is the in-plane uniaxial anisotropy (IPUA), and K_grain is the negative magnetocrystalline anisotropy (NMA). The first, second, and third terms in Eq. (1) represent the Zeeman energy, demagnetization plus NMA energy, and the IPUA energy, respectively.

Solving the Landau–Lifshitz–Gilbert (LLG) equation with weak damping, the standard condition for resonance becomes 2 where ω is the angular frequency of ∼18π GHz and F is the free energy. The resonance field as a function of field orientation can be expressed by the following equation:^[16] 3 where H_r is the resonance field, ϕ₀ is the value of at the equilibrium position, is the in-plane uniaxial anisotropy field, and ( ) is the total out-of-plane anisotropy field. When the condition , H_r is fulfilled, and the resonance field can then be expressed as 4 Furthermore, the following equilibrium equation of the magnetization vector is required: 5 For the spectral linewidth, we have considered the following expression:^[21] 6 The first term represents the homogeneous broadening due to intrinsic contributions. The second term is the contribution from the angular dispersion of the easy axis originating from inhomogeneities due to defects and/or internal stress. is a frequency and angle independent term that is related to thermal history, as well as the preparation process of the material. Considering the conditions of and , the expression for linewidth can be obtained 7 We have performed numerical fitting to match the experimental data for each sample with Eqs. (4)–(7) by using MATLAB program to obtain the damping constant α as well as and .

In Fig. 2(b), we present the x-ray diffraction (XRD) patterns for SiO8.7, Ni7.1, and B8.7 films. Only two diffraction peaks can be observed for all the samples corresponding to the Au-seed layer (111)-plane and hcp- magnetic layer (002)-plane, respectively. As shown in Fig. 2(c), the total cross section of the layered structure and, most importantly, the columnar type growth of magnetic layer can be seen. It is shown in Figs. 2(d)–2(e) that the high magnification image of the magnetic layer reveals a high degree of crystallinity and orientation of the c-plane. And Figure 2(f) for B8.7 film reveals the mixing of crystal and amorphous regions. Moreover, these doped elements or oxides atoms may replace Co atoms in CoIr phase or reside at the interstitial site or fill at the interspace between individual grains, which usually leads to lattice distortion and refined crystallite grains.

Typical in-plane magnetic hysteresis loops for sample B8.7, Ni5.3, and SiO8.7 are shown in Figs. 3(a), 3(b), and 3(c), respectively. The difference between the hysteresis loops measured along the easy axis and along the hard axis is obvious, suggesting that the samples are provided with an in-plane uniaxial anisotropy. Induced by the oblique deposition technique, the uniaxial anisotropy can be explained with the framework of the so-called self-shadowing model.^[22] As shown in Fig. 3(d), the saturation magnetization increases gradually as the Ni contents increase, and decreases as the B and SiO₂ contents increase. The linear trend is similar to what was reported for FeGaB,^[23] indicating the successful addition of the P contents in our films.

Fig. 3.

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	Fig. 3. (a)–(c) In-plane hysteresis loops measured with the external magnetic field applied along the easy axis and hard axis for sample B8.7, Ni5.3, and SiO8.7. (d) The saturation magnetization determined for all the films as a function of doping level x.

To get H_u and K_grain, we measure the resonance frequency f_r by vector network analyzer (VNA) with applied field along the easy axis. As shown in Figs. 4(a)–4(c), the square of the obtained f_r has a linear relationship with H_app.^[24] A reasonable agreement between the experimental data and numerical fitting can be obtained. Consequently, H_u and can be estimated from intercept and slope of the fitting line. The extracted H_u, , and corresponding are shown in Figs. 4(d), 4(e), and 4(f), respectively. First, H_u changes slightly around 30 Oe except for the maximum B doped sample B10.8 which reaches about 165 Oe. The reason may come from the strong strain and misalignment of the c-axis of the hcp-type grains at higher B doping.^[23,25] Second, decreases with P-doping for all three systems increasing. Third, the calculated increases gradually with x increasing, which can be explained by the lattice distortion induced orbital selective behavior of the CoIrP grains and the appearance of amorphous regions.^[26,27] Fortunately, below about x = 8, our films still possess the required negative magnetocrystalline anisotropy.

Fig. 4.

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	Fig. 4. (a)–(c) Numerical fitting of the linear relation between the applied magnetic field Happ and the square of the resonance frequency fr. (d) The determined effective in-plane anisotropy field Hu, (e) the total effective out-of-plane anisotropy field , and (f) the magnetocrystalline anisotropy constant Kgrain as a function of x.

To understand and control the damping constant for practical applications, we measure the typical FMR absorption derivative profiles as shown in Figs. 5(a), 5(b), and 5(c) for samples B8.7, Ni5.3, and SiO8.7, respectively. The resonance profiles are reasonably sharp and symmetric and the Gaussian and Lorentzian profiles are used to fit the experimental data. Clearly, for all three systems, Lorentzian fits give better results and values are easily determined. This means that the intrinsic relaxation process, which can be described by the LLG equation, is the main contribution to the FMR linewidth.^[28,29] It is known that the local FMR absorption profiles will spread out in the applied FMR field due to inhomogeneities. If the spreading follows Gaussian distribution, then the superposition of all local absorption profiles will show Gaussian shape to the lowest order and this will broaden the observed FMR spectrum. Therefore, the measured absorption profiles should be a superposition of Gaussian profile associated with inhomogeneities and Lorentzian profile associated with the relaxation process.^[30,31] In Eq. (5), the intrinsic contribution and contribution to the FMR linewidth will be considered. In addition, plays a minor role in determining the spectral linewidth and can be ignored to some extent. For example, the reported value is about 0.1 mT in polycrystalline FeTiN films and less than 0.3 mT in yttrium iron garnet nanometer films.^[28,29]

Fig. 5.

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	Fig. 5. (a)–(c) Typical FMR spectra for films B8.7, Ni5.3, and SiO8.7, respectively. The green dotted line and red dashed curve are Gaussian and Lorentzian fits to the data, respectively.

According to this discussion, the damping constants affected by the doping are thoroughly investigated. The linewidths deduced for Bx as a function of the field orientation are displayed in Figs. 6(a)–6(e). The black solid lines are numerical fits to the experimental data with Eq. (7). Obviously, this model can only partly match with the experimental data. Other factors such as mosaicity as well as two-magnon scattering process^[32,33] should be considered in the future to get better matching between theory and experiments. However, the average in-plane linewidth shown in Fig. 6(f) as open black squares has the same trend with the fitted value which is mainly ascribed to the intrinsic Gilbert damping when the external magnetic field is applied either along the easy or along the hard axis.^[33] A similar tendency suggests that the change in is mainly caused by the variation of the intrinsic Gilbert damping. The extracted α plotted as a function of x in Fig. 6(g) has the decreasing tendency as the B content increases. The shown in Fig. 6(h) does not change much with x. The only small reduction of might be associated with misfit and/or dislocations resulting from defects and/or internal stress.^[34]

Fig. 6.

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	Fig. 6. (a)–(e) The angle dependence of the linewidth for the oriented hcp- Bx films, (f) the and average in-plane linewidth , and (g) the damping constant α. (h) The angular spreading of the uniaxial field as a function of x.

For Nix films, Figure 7(a)–7(e) show the linewidth as a function of the field orientation. The fitted results are plotted in Figs. 7(f)–7(h) as a function of x. As x increases, both and show approximately the same value and an oscillating behavior. The same trend suggests again that the change in is mainly caused by the variation of the intrinsic Gilbert damping. The same behavior is also observed for α as shown in Fig. 7(g). The shows a decrease with increasing x, similar to the Bx system.

Fig. 7.

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	Fig. 7. (a)–(e) The angle dependence of the linewidth for the oriented hcp- Nix films. (f) The and average in-plane linewidth , (g) the damping constant α, and (h) the angular spreading of the uniaxial field as a function of x.

The same analysis procedures have been done for the SiOx samples, as shown in Figs. 88(a)–88(e). As seen from Figs. 8(f)–8(h), the values of and first show a slow decrease and then faster increase with x, which suggests an intrinsic Gilbert damping. The change of α with x is also similar to the change of , and shows a small decrease with increasing x.

Fig. 8.

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	Fig. 8. (a)–(e) The angle dependence of the linewidth for the films with SiO2 addition. (f) The and average in-plane linewidth , (g) the damping constant α, and (h) The angular spreading of the uniaxial field as a function of x.

For better comparison, we summarize our results of the damping constant in Fig. 9. Although the intrinsic part largely depends on spin–orbit coupling effect, the magnetic damping mechanism in ferromagnetic materials has not been clarified so far.^[35] However, in practical application, the damping constant can be controlled by using the method of doping the third content into the material. For clarity, the data are normalized to the initial value with zero doping. Obviously, SiO₂-doping is more effective in tuning the damping constant for the CoIr film.

Fig. 9.

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	Fig. 9. The normalized damping constant α for all samples as a function of x.

In summary, soft magnetic thin films of (P = B, Ni, and SiO₂) have been fabricated by DC magnetron sputtering. As x increases, the saturation magnetization decreases gradually for B and SiO₂ doping, while it increases with x for Ni doping. The measured absorption profiles consist of mainly the Lorentzian profile associated with the intrinsic relaxation process. The experimental angular dependence of is numerically analyzed based on the LLG equation. The change of is mainly caused by the variation of the intrinsic Gilbert damping, while the part originating from inhomogeneities only plays a minor role. The extracted α and are thoroughly investigated as a function of x and our results show that the damping constant can be controlled by doping the third content into the materials of interest.