Low Gilbert Damping Constant in Perpendicularly Magnetized W/CoFeB/MgO Films with High Thermal Stability

Perpendicular magnetic materials with low damping constant and high thermal stability have great potential for realizing high-density, non-volatile, and low-power consumption spintronic devices, which can sustain operation reliability for high processing temperatures. In this work, we study the Gilbert damping constant (α) of perpendicularly magnetized W/CoFeB/MgO films with a high perpendicular magnetic anisotropy (PMA) and superb thermal stability. The α of these PMA films annealed at different temperatures (Tann) is determined via an all-optical Time-Resolved Magneto-Optical Kerr Effect method. We find that α of these W/CoFeB/MgO PMA films decreases with increasing Tann, reaches a minimum of α = 0.015 at Tann = 350 °C, and then increases to 0.020 after post-annealing at 400 °C. The minimum α observed at 350 °C is rationalized by two competing effects as Tann becomes higher: the enhanced crystallization of CoFeB and dead-layer growth occurring at the two interfaces of the CoFeB layer. We further demonstrate that α of the 400 °C-annealed W/CoFeB/MgO film is comparable to that of a reference Ta/CoFeB/MgO PMA film annealed at 300 °C, justifying the enhanced thermal stability of the W-seeded CoFeB films.


Methods
Sample preparation and magnetic characterization. In this work, we grow a series of W(7)/ Co 20 Fe 60 B 20 (1.2)/MgO(2)/Ta(3) thin films on Si/SiO 2 (300) substrates (thickness in nanometers) with a magnetron sputtering system (<5 × 10 −8 Torr). These films are post-annealed at varying temperatures (T ann = 250-350 °C for 1 hour, 400 °C for 30 minutes) within a high-vacuum furnace (<1 × 10 −6 Torr). After post-annealing, the magnetic properties and damping constants of these films are systematically investigated as a function of T ann . For comparison, a reference sample of Ta(7)/Co 20 Fe 60 B 20 (1.2)/MgO(2)/Ta (3) is also prepared to examine the effect of seeding layer to the damping constant of these PMA films. The effective saturation magnetization (M s ) and anisotropy of these films are measured with the Vibrating Sample Magnetometer (VSM) module of a Physical Property Measurement System (Quantum Design, DynaCool).

TR-MOKE measurements and data reduction.
The magnetization dynamics of these PMA thin films are determined using the all-optical Time-Resolved Magneto-Optical Kerr Effect (TR-MOKE) method [29][30][31][32][33][34] . This pump-probe method utilizes ultra-short laser pulses to thermally demagnetize the sample and probe the resulting Kerr rotation angle (θ K ). In the polar-MOKE configuration, θ K is proportional to the change of the out-of-plane component of magnetization 35 . Details of the TR-MOKE setup are provided in Section S2 of the SI.
The TR-MOKE signal is fitted to the equation where A, B, and C are the offset, amplitude, and exponential decaying constant of the thermal background, respectively. D denotes the amplitude of oscillations, f is the resonance frequency, ϕ is a phase shift (related to the demagnetization process), and τ is the relaxation time of magnetization precession. Directly from TR-MOKE measurements, an effective damping constant (α eff ) can be extracted based on the relationship α eff = 1/(2πfτ). However, α eff is not an intrinsic material property; rather, it depends on measurement conditions, such as the applied field direction (θ H ), the magnitude of the applied field (H ext ), and inhomogeneities of the sample (e.g. local variation in the magnetic properties of the sample) 36,37 .
To obtain the Gilbert damping constant, the inhomogeneous contribution needs to be removed from α eff , such that the remaining value of damping is an intrinsic material property and independent of the measurement conditions. To determine the inhomogeneous broadening in the sample, the effective anisotropy field ( = H K M 2 / k,eff eff s ) needs to be pre-determined from either (1) the magnetic hysteresis loops; or (2) the fitting results of f vs. H ext obtained from TR-MOKE. The resonance frequency, f, can be related to H ext through the Smit-Suhl approach by identifying the second derivatives of the total magnetic free energy, which combines a Zeeman energy, an anisotropy energy, and a demagnetization energy [38][39][40] . For a perpendicularly magnetized thin film, f is defined by Eqs 1-4 40 .
This set of equations permits calculation of f with the material gyromagnetic ratio (γ), H ext , θ H , H k,eff , and the angle between the equilibrium magnetization direction and the surface normal (θ, determined by Eq. 4). The measured values of f as a function of H ext can be fitted to Eq. 1 by treating γ and H k,eff as fitting parameters. To minimize the fitting errors resulting from the inhomogeneous broadening effect that is pronounced at the low fields, we use measured frequencies at high fields (H ext > 10 kOe) to determine H k,eff .
With a known value of H k,eff , the Gilbert damping constant of the sample can be determined through a fitting of the inverse relaxation time (1/τ) to Eq. 5. The two terms of Eq. 5 take into account, respectively, contributions from the intrinsic Gilbert damping of the materials (first term) and inhomogeneous broadening (second term) 36 : in the magnetic properties (ΔH k,eff ), analogous to the linewidth broadening effect in Ferromagnetic Resonance measurements 42 . The magnitude of dω/dH k,eff can be calculated once the relationship of ω vs. H ext is determined with a numerical method. Both α and ΔH k,eff (the inhomogeneous term related to the amount of spatial variation in H k,eff ) are determined via the fitting of the measured 1/τ based on Eq. 5. In this way, we can uniquely extract the field-independent α, as an intrinsic material property, from the effective damping (α eff ), which is directly obtained from TR-MOKE and dependent on H ext . It should be noted here that the inhomogeneous broadening of the magnetization precession is presumably due to the multi-domain structure of the materials, which becomes negligible in the high-field regime (H ext  H k,eff ) as the magnetization direction of multiple magnetic domains becomes uniform. This is also reflected by the fact that the derivative in the second term of Eq. 5 approaches zero for the high-field regime 43 . Figure 1 plots the magnetic hysteresis loops and associated magnetic properties extracted from VSM measurements. With the increase of T ann , M s for the W/CoFeB/MgO films decreases from ~780 to ~630 emu cm −3 (Fig. 1e). The PMA in the W/CoFeB/MgO films is dominated by the interface anisotropy (K i ), which increases from 1.4 to 2.8 erg cm −2 (excluding the dead-layer thickness effect) with T ann up to 400 °C (Fig. 1g). If the film thicknesses are corrected by subtracting the dead layer, K i will change from 1.3 to 1.6 erg cm −2 as T ann increases from 250 to 400 °C, which agrees better with literature values 44 . Details about the determination of K i including the dead-layer effect are provided in Section S1 of the Supplementary Information (SI).

Results and Discussion
We attribute the decrease of M s at high T ann to the growth of a dead layer at the CoFeB interfaces, which becomes prominent at higher T ann . To quantitatively determine the thickness of the dead layer as T ann increases, we prepare four sets of PMA stacks of W(7)/CoFeB(t)/MgO(2)/Ta(3). One set contains five stacks with varying thicknesses for the CoFeB layer (t = 1.2, 1.5, 1.8, 2.2, and 2.5 nm) and is post-annealed at a fixed T ann . Four T ann of 250, 300, 350, and 400 °C are used for four sets of the PMA stacks, respectively. The annealing conditions are the same as those for the W(7)/CoFeB(1.2)/MgO(2)/Ta(3) samples discussed previously. We measure the magnetic hysteresis loops of these samples using VSM and plot their saturation magnetization area product (M S × t) as a function of film thickness (t) in Fig. 2. Linear extrapolation of the M S × t data provides the dead-layer thickness, at which the magnetization reduces to zero as illustrated by the x-axis intercept in Fig. 2. The slope of the linear fit also provides intrinsic saturation magnetization (M s,0 ), which corresponds to the saturation magnetization after the removal of the dead-layer effect. The values of M s0 (Fig. 1f) show an increasing trend with T ann from ~1300 to ~1600 emu cm −3 , which agrees well with previous measurement results for W/CoFeB/MgO films 44 . By repeating this measurement at varying θ H , we can show that α is an intrinsic material property, independent of θ H . Figure 4a plots the resonance frequencies derived from TR-MOKE and model fittings for the 400 °C sample at two field directions (θ H = 76° and 89°). For the data acquired at θ H = 89°, a minimum f occurs at H ext ≈ H k,eff . This corresponds to the smallest amplitude of magnetization precession, when the equilibrium direction of the magnetization is aligned with the applied field direction at the magnitude of H k,eff 40 . The dip at this local minimum diminishes when θ H decreases, as reflected by the comparison between the red (θ H = 89°) and blue (θ H = 76°) lines in Fig. 4a. With the H k,eff extracted from the fitting of frequency data with θ H = 89°, we generate the plot of theoretically predicted f vs. H ext (θ H = 76° theory, blue line in Fig. 4a), which agrees well with experimental data (open squares in Fig. 4a).
The inverse relaxation time (1/τ) should also have a minimum value near H k,eff for θ H = 89° if the damping was purely from Gilbert damping (as shown by the solid lines in Fig. 4b,d); however, the measured data do not follow this trend. Adding the inhomogeneous term (dotted lines in Fig. 4b,d) more accurately describes the field dependence of the measured 1/τ (open symbols in Fig. 4b,d) It should be noted that the dip of the predicted 1/τ occurs when the frequency derivative term in Eq. 5 approaches zero; however, this is not captured by the measurement. Figure 4c,e depict the field-dependent effective damping (α eff ) calculated using the Gilbert damping (α) extracted from fitting the measured 1/τ.
With the knowledge that the value of α extracted with this method is the intrinsic material property, we repeat this data reduction technique for the annealed W/CoFeB/MgO samples discussed in Fig. 1. The symbols in Fig. 5 represent the resonance frequencies and damping constants (both effective damping and Gilbert damping) for all samples measured at θ H ≈ 90°. The fittings for the resonance frequency based on Eq. 1 (red lines) are also shown to demonstrate the good agreement between our TR-MOKE measurement and theoretical prediction. The uncertainties of f, τ, and H k,eff are calculated from the least-squares fitting uncertainty and the uncertainty of measuring H ext with the Hall sensor.
The summary of the anisotropy and damping measured via TR-MOKE is shown in Fig. 6. Figure 6a plots H k,eff obtained from VSM (black open circles) and TR-MOKE (blue open squares), both of which exhibit a monotonic increasing trend as T ann becomes higher. Discrepancies in H k,eff from these two methods can be attributed to the difference in the size of the probing region, which is highly localized in TR-MOKE but sample-averaged in VSM. Since H k,eff determined from TR-MOKE is obtained from fitting the measured frequency for a localized region, we expect these values more consistently describe the magnetization precession than those obtained from VSM. The increase in H k,eff with T ann has previously be partially attributed to the crystallization of the CoFeB layer 37 . For temperatures higher than 350 °C, this increasing trend of H k,eff begins to lessen, presumably due to the diffusion of W atoms into the CoFeB layer, which is more pronounced at higher T ann . The W diffusion process is also responsible for the decrease in M s of the CoFeB layer as T ann increases (Fig. 1e). Subsequently, the decrease in M s leads to a further-reduced demagnetizing energy and thus a larger H k,eff .
Similar observation of M s has been reported in literature for Ta/CoFeB/MgO PMA structures and attributed to the growth of a dead layer at the heavy metal/CoFeB interface 1 . Figure 6b summarizes t dead as a function of T ann with t dead increasing from 0.17 to 0.53 nm as T ann changes from 250 to 400 ο C, as discussed in Section II. Figure 6c depicts the dependence of α on T ann , which first decreases with T ann , reaches a minimum of 0.015 at 350 °C, and then increases as T ann rises to 400 °C. Similar trends have been observed for Ta/CoFeB/MgO previously (minimum α at T ann = 300 °C) 37 . We speculate that this dependence of damping on T ann is due to two competing effects: (1) the increase in crystallization in the CoFeB layer with T ann which reduces the damping, and (2) the growth of a dead layer, which results from the diffusion of W and B atoms and is prominent at higher T ann .
As the amorphous as-deposited CoFeB film begins to form ordered phases at elevated temperatures, the number of scattering sites in the film tend to decrease 45,46 . The increase in crystallinity of the W/CoFeB/MgO film with T ann is demonstrated by the XRD analysis detailed in Section S5 of the SI. At T ann = 400 °C, the dead-layer formation leads to a larger damping presumably due to an increase in scattering sites (diffused W atoms) that contribute to spin-flip events, as described by the Elliot-Yafet relaxation mechanisms 18 . Additionally, W atoms can increase the spin-orbit coupling and thus the damping as the inter-diffusion increases with T ann 47 . The observation that   our W-seeded samples still sustain excellent PMA properties at T ann = 400 °C confirms their enhanced thermal stability, compared with Ta/CoFeB/MgO stacks which fail at T ann = 350 °C or higher. While the damping constants are comparable for the W/CoFeB/MgO and Ta/CoFeB/MgO films annealed at 300 °C, our work focuses on the enhanced thermal stability of W-seeded CoFeB PMA films that can maintain a relatively low damping constant (0.020 at 400 °C). Such an advantage enables W-seeded CoFeB layers to be viable and promising alternatives to Ta/CoFeB/MgO, which is currently widely used in spintronic devices.

Conclusion
In summary, we deposit a series of W-seeded CoFeB PMA films with varying annealing temperatures up to 400 °C and conduct ultrafast all-optical TR-MOKE measurements to study their magnetization precession dynamics. The Gilbert damping, as an intrinsic material property, is proven to be independent of measurement conditions, such as the amplitudes and directions of the applied field. The damping constant varies with T ann , first decreasing and then increasing, leading to a minimum of α = 0.015 for the sample annealed at 350 °C. Due to the dead-layer growth, the damping constant slightly increases to α = 0.020 at T ann = 400 °C, which demonstrates the improved enhanced thermal stability of W/CoFeB/MgO over the Ta/CoFeB/MgO structures. This strongly suggests the great potential of W/CoFeB/MgO PMA systems for future spintronic device integration that requires materials to sustain a processing temperature as high as 400 °C.