Metallic ferromagnetic films with magnetic damping under 1.4 × 10−3

Low-damping magnetic materials have been widely used in microwave and spintronic applications because of their low energy loss and high sensitivity. While the Gilbert damping constant can reach 10−4 to 10−5 in some insulating ferromagnets, metallic ferromagnets generally have larger damping due to magnon scattering by conduction electrons. Meanwhile, low-damping metallic ferromagnets are desired for charge-based spintronic devices. Here, we report the growth of Co25Fe75 epitaxial films with excellent crystalline quality evident by the clear Laue oscillations and exceptionally narrow rocking curve in the X-ray diffraction scans as well as from scanning transmission electron microscopy. Remarkably, the Co25Fe75 epitaxial films exhibit a damping constant <1.4 × 10−3, which is comparable to the values for some high-quality Y3Fe5O12 films. This record low damping for metallic ferromagnets offers new opportunities for charge-based applications such as spin-transfer-torque-induced switching and magnetic oscillations.

These results from polycrystalline films motivated the studies reported here that were guided by the expectation that the lower defect density in high-quality epitaxial films of Co 25 Fe 75 will lead to reduced damping 22 as compared to their polycrystalline counterparts. In this study we grow Co 25 Fe 75 epitaxial films using off-axis sputtering on two kinds of substrates with the goal of further reducing the magnetic damping of this promising metallic FM towards an unprecedented level. X-ray diffraction (XRD) and scanning transmission electron microscopy (STEM) verify that these films are single crystal with high crystalline quality. Variable frequency FM resonance (FMR) measurements confirm that these films exhibit significantly reduced Gilbert damping-<1.4 × 10 −3 -in contrast to polycrystalline films.

Results
Epitaxial growth of Co 25 Fe 75 . The growths were done using ultrahigh vacuum, off-axis sputtering with a base pressure lower than 2 × 10 −10 Torr, which has previously been used to grow high-quality epitaxial films of various metals and oxides [27][28][29][30][31][32] . A Co 25 Fe 75 sputter target 5 cm in diameter was prepared by annealing a pressed target of a stoichiometric Co and Fe powder mixture at 600°C under H 2 gas flow. The Co 25 Fe 75 target was mounted on a horizontal sputtering source. The substrate was positioned at a horizontal distance of 5.4 cm from the target and 7.5 cm below the central axis of the target with the sample surface perpendicular to the target surface, which results in an average deposition angle of 54°relative to the target normal. We first grew 10 nm polycrystalline Co 25 Fe 75 films on Si at room temperature with a 3 nm Cu seed layer and 5 nm Cr cap, which exhibited a low damping constant similar to that previously reported 23 . The Cr, Cu, and Co 25 Fe 75 films were grown at Ar pressures of 10, 5, and 10 mTorr using DC sputtering with growth rates of 1.7, 3.6, and 2.4 nm/min, respectively. Co 25 Fe 75 epitaxial films of 6.8 and 34 nm thicknesses were deposited at a substrate temperature of 300°C directly on (001)-oriented MgO and MgAl 2 O 4 (MAO) substrates (purchased from MTI), followed by a Cr capping layer grown at room temperature. MgO is a commonly used substrate with a lattice constant of a = 4.212 Å, which has a 3.9% lattice mismatch with Co 25 Fe 75 when considering the 45°rotation between the body-centered-cubic (BCC) lattice of Co 25 Fe 75 and the face-centered-cubic (FCC) lattice of MgO. MgAl 2 O 4 (a = 8.083 Å) was used because it has a much better lattice match (within 0.4%) with Co 25 Fe 75 .
Characterization of crystalline quality. The crystalline quality of the epitaxial Co 25 Fe 75 films was quantified by several methods. Figure 1a shows 2θ−ω scans obtained using triple-axis X-ray diffractometry of Cr(2.8 nm)/Co 25   Characterization of in-plane magnetization. Magnetic hysteresis loops of Cr(2.8 nm)/Co 25 Fe 75 (6.8 nm) on MgO and MAO were measured at room temperature using a vibrating sample magnetometer at various in-plane orientations defined by ϕ H , the angle between the applied magnetic field (H) and the Co 25 Fe 75 [100] axis (see Fig. 3a). Figure 3b shows two hysteresis loops for Cr(2.8 nm)/Co 25 Fe 75 (6.8 nm)/MgO measured at ϕ H = 0°and 45°where the small diamagnetic background from MgO has been subtracted. The ϕ H = 0°loop has a sharp magnetic reversal with a coercive field (H c ) of 20 Oe while the ϕ H = 45°loop has a higher saturation field and H c = 23 Oe. By comparing the two hysteresis loops, we conclude that Co 25 Fe 75 [100] (ϕ H = 0°) is the easy axis and Co 25 Fe 75 [110] (ϕ H = 45°) is the in-plane hard axis within the framework of in-plane cubic anisotropy. The saturation magnetization, 4πM s = 2.46 ± 0.02 T, of the film on MgO is extracted from the hysteresis loop, which has been confirmed by a measurement using a SQUID magnetometer.
The inset to Fig. 3b shows a closer view of the hard-axis loop (ϕ H = 45°), which allows us to obtain the in-plane magnetocrystalline anisotropy. By applying separate linear fits to the saturated high field regime and the region between 200 and 0 Oe, we extract the in-plane magnetocrystalline anisotropy of 260 ± 10 Oe between the [100] and [110] axes 33 . This is in agreement with the in-plane cubic anisotropy H 4|| obtained from FMR measurements described below. Figure 3c shows the in-plane hysteresis loops for Cr(2.8 nm)/Co 25 Fe 75 (6.8 nm)/MAO, from which we obtain 4πM s = 2.34 ± 0.02 T and an in-plane magnetocrystalline anisotropy of 295 ± 10 Oe.
To probe the dynamic magnetic properties of the Co 25 Fe 75 epitaxial films, we performed angular-dependent FMR measurements on our films. Figure 4a shows the derivative spectra of FMR absorption for the Cr(2.8 nm)/Co 25 where θ is the out-of-plane angle and ϕ the in-plane angle for the orientation of the equilibrium magnetization (M) with respect to the easy axis, 4πM eff = 4πM s −H 2⊥ is the effective saturation magnetization, and H 2⊥ is the out-of-plane uniaxial anisotropy. H 4⊥ , H 4∥ , and H 2∥ are the out-of-plane cubic, in-plane cubic, and in-plane uniaxial anisotropy, respectively. By substituting Eq. (1) into the FMR resonance condition 15,34 , we can calculate H res for a given ϕ H , where γ is the gyromagnetic ratio and ω is the resonance angular frequency. For in-plane angular FMR, θ = 90°and the H 4⊥ term drops out; the in-plane equilibrium angle ϕ is determined by numerically minimizing the free energy density. Figure 4b shows the in-plane angular dependence of H res for Cr(2.8 nm)/Co 25 Fe 75 (6.8 nm)/MgO and the fit using Eq. (2) and γ/2π = 29.5 ± 1.0 GHz T −135 , which agrees well with the experimental data and gives H 2∥ = 0 ± 5 Oe, H 4∥ = 275 ± 5 Oe, and 4πM eff = 2.25 ± 0.02 T. The obtained H 4|| agrees with the value (260 Oe) determined from the magnetometry measurements in Fig 3b. Figure 4c shows the in-plane angular dependence of H res for Cr(2.8 nm)/Co 25 Fe 75 (6.8 nm)/MAO. From the fitting to the data, we obtain H 2∥ = −5 ± 5 Oe, H 4∥ = 325 ± 5 Oe, and 4πM eff = 1.96 ± 0.02 T, where the value of H 4|| is close to the anisotropy (295 Oe) obtained in Fig. 3c. Measurement of Gilbert damping. Frequency-dependent FMR absorption was measured between 3 and 18 GHz using a microwave stripline by sweeping the magnetic field at various fixed frequencies. A small modulation of the magnetic field was applied to enable the measurement of differential absorbed power with a Schottky diode detector and a lock-in amplifier. Figure 5a, Fig. 5c, d using the same procedure for Fig. 4. The extracted values for in-plane anisotropies and effective saturation magnetization are: H 4∥ = 260 ± 5 Oe, H 2∥ = 0 ± 5 Oe, and 4πM eff = 2.19 ± 0.02 T for the film on MgO; H 4∥ = 315 ± 10 Oe, H 2∥ = −5 ± 5 Oe, and 4πM eff = 1.91 ± 0.02 T for the film on MAO, which agree with the results in Fig. 4. Figure 5e shows the corresponding frequency dependencies of ΔH for the two samples. Below~8 (7) GHz for the film on MgO (MAO), the data deviate from the linear dependence found above it. When comparing the hard-axis saturation fields of~600 Oe to the H res of 581 Oe (592 Oe) at 8 (7) GHz for the film on MgO (MAO), we can understand these two regimes as follows. The films exhibit linear frequency dependence of ΔH above a threshold field where the magnetization is fully aligned. Below the threshold, the magnetization is not fully aligned, leading to non-uniform magnetization which inhomogeneously broadens the linewidth 16 . We first apply a linear fit in Fig. 5e in the frequency regime above 8 (7) GHz for the film on MgO (MAO), from which the damping constant can be determined using ΔH = ΔH inh + 4παf ffiffi 3 p γ , where ΔH inh is the inhomogeneous broadening 36 . For Co 25 Fe 75 (6.8 nm)/MgO, α = (7.1 ± 0.6) × 10 −4 and ΔH inh = 9.2 ± 0.3 Oe; for Co 25 Fe 75 (6.8 nm)/MAO, α = (1.16 ± 0.02) × 10 −3 and ΔH inh = 1.8 ± 0.1 Oe. If we choose a higher threshold field corresponding to 10 (9) GHz for the film on MgO (MAO), we obtain α = (8.5 ± 0.6) × 10 −4 and ΔH inh = 8.4 ± 0.3 Oe for the film on MgO, and α = (1.21 ± 0.02) × 10 −3 and ΔH inh = 1.5 ± 0.1 Oe for the film on MAO. The small ΔH inh in the Co 25 Fe 75 film on MAO can be attributed to the high crystalline quality of the film. The damping constant in the film on MAO is slightly larger than that on MgO, for which the reason is unknown at this point. We note that FMR measurements at higher frequencies, e.g., 40 or 70 GHz, would further improve the accuracy for the extracted values of intrinsic damping in our films; however, we do not have this capability and will pursue such measurements through collaboration in the future. Based on our measurements, we are confident that the intrinsic damping constant in our epitaxial Co 25 Fe 75 films is below 1.4 × 10 −3 , which is obtained when we assume ΔH inh = 0 for Co 25 Fe 75 /MAO.

Discussion
The measured Gilbert damping constant-<1 × 10 −3 -is extremely low for metallic FMs and, remarkably, is comparable to those reported for YIG films 7 . The lowest α (7.1 × 10 −4 ) for our epitaxial Co 25 Fe 75 films is considerably lower than the values reported for polycrystalline Co 25 Fe 75 films 23 (2.1 × 10 −3 ) and epitaxial Fe films (1.9 × 10 −3 ) 22 . Considering our measured damping constant also includes contributions from spin pumping into the Cr capping layer 37 and radiative loss into the environment and stripline 23 , the intrinsic damping of our Co 25 Fe 75 films should approach the calculated intrinsic value in the mid-low 10 −4 regime [23][24][25][26] .
In summary, we observe extremely low magnetic damping in Co 25 Fe 75 epitaxial thin films with excellent crystalline quality. This is the first direct measurement of a Gilbert damping constant in the 10 −4 regime for metallic FM films, making it an ideal material for exploration of spintronic applications requiring metallic FMs.
Data availability. Data that support the findings of this report are available from the corresponding author upon request.