Dynamical behaviour of ultrathin [CoFeB (tCoFeB)/Pd] films with perpendicular magnetic anisotropy

CoFeB-based ultrathin films with perpendicular magnetic anisotropy are promising for different emerging technological applications such as nonvolatile memories with low power consumption and high-speed performance. In this work, the dynamical properties of [CoFeB (tCoFeB)/Pd (10 Å)]5 multilayered ultrathin films (1 Å ≤ tCoFeB ≤ 5 Å) are studied by using two complementary methods: time-resolved magneto-optical Kerr effect and broadband ferromagnetic resonance. The perpendicular magnetization is confirmed for multilayers with tCoFeB ≤ 4 Å. The effective perpendicular magnetic anisotropy reaches a clear maximum at tCoFeB = 3 Å. Further increase of CoFeB layer thickness reduces the perpendicular magnetic anisotropy and the magnetization became in-plane oriented for tCoFeB ≥ 5 Å. This behaviour is explained by considering competing contributions from surface and magnetoelastic anisotropies. It was also found that the effective damping parameter αeff decreases with CoFeB layer thickness and for tCoFeB = 4 Å reaches a value of ~ 0.019 that is suitable for microwave applications.

Among different materials, CoFeB-based thin films have received great attention since 2010, when Ikeda et al. 9 demonstrated that this alloy in contact with a MgO layer can show PMA. This behaviour can be achieved when the CoFeB layer is thin enough, and the CoFeB/MgO interfacial anisotropy contribution 9,16,17 overcomes the volumetric terms of the anisotropy energy 18 . Afterwards, several works have been focused on the optimization of the PMA in CoFeB thin films by using different materials for the capping and/or buffer layers 19 , including Ta 20,21 , Hf 22,23 , Mo 24,25 , Ru 26,27 , V 26 , Nb 27 , Pt 28,29 , Pd 30-32 and Au 33 .
Moreover, CoFeB alloys show higher spin polarization than Co, Fe and Ni (up to 65% vs. around 45%) 34 , and can be grown with a tuned damping parameter (α) 9,35 . Since damping determines the temporal performance of magnetic devices such as the timescale for magnetization reversal or spin-transfer-torque (STT) switching, α is a key parameter for the development of several technological applications. In particular, materials with low α have been suggested for high-speed spintronic devices, such as in STT-based systems with low switching and power consumption 8,36 , as well as in magnetic tunnel junctions (MTJs) with high signal-to-noise ratio 9 , and in magnonic devices 37 . On the other hand, systems with high α values have been suggested for spin pumping and inverse spin Hall effect applications [38][39][40] . Therefore, understanding the behaviour of the α parameter is of particular importance.
Although it was reported that the Gilbert damping (α Gilbert ) for Co 40 Fe 40 B 20 alloy can be as low as 0.004 41,42 , the estimated effective damping (α eff ) increases substantially at low thickness 9 which is detrimental to the development of STT-and MTJs-based devices. For example, it was reported that 1 or 1.3 nm thick CoFeB layers with Although CoFeB/Pd multilayers with strong PMA were first reported in 2010 30,31 , subsequent works have been mainly focused on understanding the contributions of the volumetric (K v ) and surface (K s ) anisotropy terms to the PMA as a function of the CoFeB layer thickness and the number of CoFeB/Pd bilayers 32,58,59 . In this paper, we have studied the dynamical behaviour of ultrathin [CoFeB (t CoFeB )/Pd (10 Å)] 5 films with CoFeB thicknesses ranging from 1 to 5 Å by using both vector network analyzer based ferromagnetic resonance (VNA-FMR) and time-resolved magneto-optical Kerr effect (TR-MOKE) measurements. We observed that PMA was achieved for t CoFeB ≤ 4 Å, and both K v and K s were estimated. In addition, we have performed a systematic study of previously unreported characteristic magnetic parameters such as the CoFeB saturation magnetization and the damping parameter in ultrathin CoFeB/Pd films. Moreover, the effective damping parameter and its related intrinsic and extrinsic contributions were analyzed as a function of t CoFeB . Figure 1a and b show the in-plane and out-of-plane hysteresis loops of the [CoFeB (t CoFeB )/Pd (10 Å)] 5 multilayer stacks, respectively. The loops indicated that our samples show PMA when the CoFeB thickness (t CoFeB ) ranged from 1 to 4 Å. However, the easy magnetization axis lays in-plane for the largest t CoFeB (5 Å).  As the CoFeB thickness was varied, while both the Pd thickness (1 nm) and the number of CoFeB/Pd bilayers (5) were kept constant, the rise of M Sat with the CoFeB film thickness could be associated with the increase of the volume magnetic moment contribution while the surface/interface magnetization term should remain constant 32 . Therefore, the experimental magnetization data can be fitted by a linear dependence (the continuous line in Fig. 2a) and the surface/interfacial magnetization term can be estimated from the extrapolation of this linear dependence to zero thickness. Our analysis determined that the surface/interfacial magnetization of CoFeB/ Pd interfaces is (170 ± 60) emu/cm 3 , which agrees with the value of (180 ± 10) emu/cm 3 reported by Ngo et al. 32 .

Results and discussion
In addition, the magnetization per unit area (M Sat_sheet ) vs. the CoFeB film thickness (t CoFeB ) is shown in Fig. 2b. As described by Engel et al. 63 , M Sat_sheet in superlattices can be estimated from where I is the measured magnetic moment, N is the number of bilayers, A is the area of the films (determined from the software analysis of digital photographs of the samples), M eff_CoFeB is the effective CoFeB saturation magnetization, t CoFeB is the CoFeB layer thickness, M eff_Pd is the effective magnetization of the polarized Pd induced by the ferromagnetic proximity effect [63][64][65] , and t Pd is the Pd layer thickness (10 Å). A linear fit of (M Sat_sheet vs. t CoFeB ) is also plotted in Fig. 2b. Assuming that the magnetic moment is uniformly induced in the entire Pd layer, M eff_Pd = (120 ± 20) emu/cm 3 was estimated from the extrapolation of the linear fit to zero CoFeB layer thickness (t CoFeB = 0 Å). This saturation magnetization is in good agreement with previous studies on Co/Pd multilayers [64][65][66] . Additionally, an effective CoFeB saturation magnetization value of M eff_CoFeB = (1760 ± 80) emu/cm 3 was obtained from the linear fit slope.
This value seems to be too large in comparison with the values previously reported for Co 40 70 , or in CoFeB multilayers in which the boron atoms diffused out of the CoFeB alloy due to the application of an annealing process (1900 emu/cm 3 for Ta/Co 40 Fe 40 B 20 /MgO multilayers) 71 . However, in 2013, Sinha et al. 72 studied the perpendicular magnetic anisotropy in Ta/CoFeB (t nm)/MgO multilayers with CoFeB thickness ranging from 0.8 to 5 nm. In agreement with the literature, they reported that the linear fit slope of (M Sat_sheet vs. t) provides an effective CoFeB saturation magnetization of M eff_CoFeB = 1210 emu/cm 3 for thicker samples (t ≥ 2.2 nm). But large M eff_CoFeB values, such as 1790 emu/cm 3 , were determined for the thinnest CoFeB layers (t ≤ 2.2 nm). Therefore, it was suggested that the effective saturation magnetization increases from its bulk value below a certain magnetic layer thickness. This behaviour was confirmed in our work as well as in Ref. 32  Anisotropy energy terms. The origin of PMA in ultrathin multilayer stacks, such as (CoFeB/Noble metal) bilayers, is based on the competition between the volumetric (K v ) and surface (K s ) terms of the anisotropy energy 18 . To distinguish between both contributions, we performed ferromagnetic resonance measurements when the DC external field was applied perpendicular to the sample plane. In general, the FMR spectrum of a thin film depends significantly on the presence of different anisotropies, such as the magnetocrystalline, shape, magnetoelastic and surface contributions, and it can be described through the Kittel equation 20,73,74 : www.nature.com/scientificreports/ where (γ/2π) = (gµ 0 /h) is the gyromagnetic ratio; g is the g-factor; µ 0 is the Bohr magneton; h is Planck's constant; H is the external applied DC magnetic field; H eff is the effective anisotropy field, that is positive for the films with perpendicular magnetization in the absence of external magnetic field and negative for films with in-plane magnetization; θ H is the angle of the external applied magnetic field and θ 0 is the equilibrium angle of the sample magnetization. The equilibrium angle θ 0 can be derived from the equation: When thin films are saturated and θ H = θ 0 , Eq. (2) can be reduced to 74 : Figure 3a shows the perpendicular VNA-FMR spectrum of the [CoFeB (4 Å)/Pd (10 Å)] 5 multilayer thin film with PMA as well as a black line, which corresponds to the fits using the Kittel formula (Eq. 4).
However, we should note that we were not able to achieve a good signal-to-noise ratio from samples with the thinnest CoFeB thicknesses (t CoFeB = 1-3 Å). For these samples, our analyses were complemented by performing TR-MOKE measurements. All-optical pump-probe technique has been successfully used for understanding the dinamical response of the ultrafast magnetization, the magnetization precession and the effective damping, in materials with perpendicular anisotropy such as [Co/Pt] n 75,76 and [Co/Pd] 8 62 multilayers, L1 0 -FePt alloy epitaxial thin films 73 or Ta/CoFeB/MgO(Ta) thin films 20 . As an example, Fig. 3b shows the TR-MOKE signals for [CoFeB (2 Å)/Pd (10 Å)] 5 and as a function of the external applied magnetic field. An ultrafast demagnetization process on the subpicosecond timescale is observed after the application of the pump pulse, followed by a quick remagnetization stage that shows a precessional response in the last section. Both the ferromagnetic resonance frequency (f FMR ) and the damping parameter (α) characterize the oscillatory response of the magnetization and it can be fitted by 73,77 : where θ 0 and A are the background magnitudes, and t 0 is the background recovery time. The final term represents the precessional motion where B, f FMR , φ and τ are the amplitude, frequency, phase, and relaxation time, respectively. A good agreement between the model and the experimental data is shown in Fig. 3 (b) and the fits of the f FMR field-dependence were performed through the set of Eqs. (2) and (3) 20,73 .
The main results of our VNA-FMR and TR-MOKE fits are summarized in Table 1. The gyromagnetic ratio and g-factor did not show any significant dependence with the CoFeB thickness, and we obtained average values of (2.99 ± 0.03) GHz/kOe and (2.14 ± 0.03), respectively, in agreement with the literature 23,35,68,78 .
On the other hand, and as observed in the hysteresis loops, the fitted data of H eff shows a transition from positive values for t CoFeB ≤ 4 Å, meaning that the multilayer films show perpendicular magnetization in the absence of external magnetic field, to negative ones (with in-plane magnetization) for t CoFeB = 5 Å (See Fig. 4a). The sample with perpendicular magnetization and the larger positive H eff values corresponds to the multilayer thin film with t CoFeB = 3 Å. Also, we should note that the H eff value for t CoFeB = 1 Å is larger than for t CoFeB ≥ 2 Å. This behavior, in combination with the fact that Co 20 Fe 60 B 20 , with a body-centered-cubic (bcc) crystalline structure, has a lattice H + H eff for perpendicular geometry  Moreover, K eff can be phenomenologically separated into a volume contribution K v (erg/cm 3 ) and a contribution from the interfaces K s (erg/cm 2 ), and it can be approximately described by the Néel model 80 :   www.nature.com/scientificreports/ where the origin of the factor of 2 in the last term is due to the presence of two identical interfaces per magnetic layer, and t is the magnetic layer thickness. Therefore, both K v and K s can be obtained by plotting (t × K eff ) versus t. According to the Néel model 80 , (t × K eff ) should show a linear dependence on t, where K v is the linear dependence slope, and 2K s corresponds to the intercept with the vertical axis. However, our data shows a deviation from the linear behavior at small CoFeB thicknesses (see Fig. 4b) as already observed in different systems like in Co/Au 81 and Ni/Cu 82-84 multilayer thin films. This deviation was explained using a phenomenological model that includes the shape anisotropy term, the bulk magnetocrystalline and magnetoelastic anisotropy energies, the surface magnetocrystalline and surface magnetoelastic anisotropy terms 83 or the second-order of the magnetoelastic contribution 84 .
More recently, this non-linearity was also reported for NM/CoFeB/MgO thin films (where NM was Ta 69 or Hf 23 ) and it was fitted using the equation proposed by Gowtham et al. 69 : where K eff v is the effective volumetric contribution that should include the shape anisotropy term and both the bulk magnetocrystalline and bulk magnetoelastic anisotropy energy contributions; K eff s is the effective surface term that includes the surface magnetocrystalline and magnetoelastic anisotropy terms as well as the secondorder term of the bulk magnetoelastic contribution; and coefficient K 3 is related to the second-order term of the surface magnetoelastic contribution.
In agreement with Engel et al. 63 , we have estimated that (t CoFeB x K eff_CoFeB ) = (t CoFeB+Pd x K eff ) where t CoFeB+Pd (t CoFeB ) is the thickness of the CoFeB/Pd bilayer (CoFeB layer), K eff is the measured effective anisotropy energy of the [CoFeB/Pd] 5 system and K eff_CoFeB is the effective anisotropy energy of a CoFeB thin film. Therefore, both K v_CoFeB and K s_CoFeB can be obtained by plotting (t CoFeB x K eff_CoFeB ) versus t CoFeB (shown in Fig. 4b).
As thin films are generally in a state of biaxial stress (σ x = σ y = σ in_plane and σ z = σ out_of_plane = 0), the magnetoelastic anisotropy term can be defined by 18,85 : where λ s and σ in_plane are the saturation magnetostriction coefficient and the in-plane applied stresses, respectively. Moreover, σ in_plane is related to the in-plane strain ε in_plane , via the Young's modulus (E) and the Poisson ratio (ν) 86 : As the magnetoelastic anisotropy term favors that the magnetization lies perpendicular to the sample plane and the saturation magnetostriction coefficient of amorphous Fe 40 Co 40 B 20 is positive λ s = 20 × 10 -687 , the magnetic layer should be under tensile stress with σ in_plane ≈ (11 ± 3) × 10 10 dyne/cm 2 (≈ (11 ± 3) GPa). Using the Young's modulus E = 160 × 10 10 dyne/cm 2 (= 160 GPa) for CoFeB and the Poisson ratio ν = 1/3 88 , the analysis indicates a tensile in-plane strain of ε in_plane ≈ (0.05 ± 0.01). This value is of the same order of magnitude than the strains reported by Gowtham et al. 69 for Hf/Co 20 Fe 60 B 20 /MgO heterostructures with thicker CoFeB layers. The in-plane tensile strain in our ultrathin films should be related to the large lattice mismatch (≈36%) 18 between Pd (3.88 Å) 89 and CoFeB (2.86 Å for bcc) 79

lattice parameters.
Effective damping. We then studied the behaviour of the damping parameter (α) as a function of the CoFeB thin film thickness and it was extracted from the frequency linewidths (Δf FMR ) in the VNA-FMR spectra. It was experimentally observed that the measured frequency linewidths (Δf FMR ) are broadened by extrinsic contributions, which affect the calculations of the damping parameter 90 . Therefore, we used Δf FMR to determine the apparent damping by 90 : Although α app and the intrinsic damping may differ, we should note that α app should give an upper limit for the intrinsic or Gilbert damping (α Gilbert ). Open symbols in Fig. 5a and b show the typical curves of the apparent damping versus the external applied magnetic field for the multilayers with t CoFeB = 4 and 3 Å, respectively. Although we cannot distinguish between the different extrinsic contributions to the linewidth, it is observed www.nature.com/scientificreports/ that α app approaches a constant value for large applied fields. We have defined this value as the effective damping α eff (see red lines in Figs. 5a and b). Again, we should note that the signal-to-noise ratio is significantly low for those samples with the thinnest CoFeB thicknesses (t CoFeB ≤ 3 Å), so optical studies were required to complete our analysis. From the pump-probe measurements, α app can be determined using 73,91 : where f FMR is the resonance frequency and τ is the relaxation time. Both values were fitting parameters in Eq. (5) and they were used to analyze the precessional dynamics (as it was shown in Fig. 3b). Figure 5a and b show the apparent damping versus the external applied magnetic field for multilayers with t CoFeB = 4 and 3 Å, respectively. Again α app approaches a constant value for large applied fields and we assumed that this value is α eff (see blue lines in Fig. 5a and b).
The evolution of the effective damping (α eff ) vs. the CoFeB film thicknesses (t CoFeB ) obtained by combining both types of measurements is summarized in Table 1 and shown in Fig. 6. It is important to note that both VNA-FMR and pump-probe have provided similar values. As one can see, samples may be separated into two groups: t CoFeB ≤ 3 Å and t CoFeB ≥ 4 Å. For the first group, the value of α eff is large and decreases quickly with thickness increase. It reaches some kind of saturation at t CoFeB = 4 Å and decreases only slightly (by 10%) for t CoFeB = 5 Å. As Azzawi et al. 92 reported in 2016, the non-continuity of thin films leads to the increase of the extrinsic contribution to the damping by adding an extra two-magnon scattering term. Therefore, we have suggested that the increase of α eff for the thinnest CoFeB layers (t CoFeB ≤ 3 Å) could be related to the abrupt rise of the two-magnon scattering contribution due to the non-continuity of the ultrathin layers. www.nature.com/scientificreports/ To better understand the effective damping of the samples with nearly continuous CoFeB layers (t CoFeB = 4 and 5 Å), we have tried to distinguish different contributions to the damping parameter that were briefly described in the introduction section. Remembering that eddy currents become important when the magnetic film thickness is comparable to or greater than the skin depth 90 , and the radiative damping is proportional to the magnetic layer thickness 57 , neither α eddy nor α rad should have significant contributions in our ultrathin films and they could be ignored. On the other hand, the literature suggests that the two-magnon scattering contribution (α TMS ) is minimized in the perpendicular geometry, such as the one mainly used in this work 93 . In particular, Liu et al. 41 studied the angular dependence of the two-magnon scattering contribution in a CoFeB thin film and confirmed that this effect is suppressed in the perpendicular configuration. They determined that the two-magnon contribution is significant when the sample magnetization angle, relative to the perpendicular direction or 0°, is pointed to an angle larger than 45°. Even α TMS can achieve a value as large as the intrinsic damping in the in-plane configuration. Therefore, the α TMS contribution could also be disregarded and the total measured damping should be mainly composed of the intrinsic term and the spin-pumping contribution: The spin-pumping contribution α s-p can be defined using the formula 94-96 : where g is the g-factor; µ 0 = (9.27400915 × 10 -21 ) erg/Oe is the Bohr magneton; M eff_CoFeB = (1760 ± 80) emu/cm 3 and t CoFeB are the effective saturation magnetization moment and the thickness of the CoFeB layer, respectively; g ↑↓ is the CoFeB/Pd interface spin mixing conductance; t Pd = 0.5 nm is half the Pd layer thickness and λ Pd = 9 nm 95 is the spin diffusion length for Pd layer. The factor of 2 is related to the fact that the CoFeB layer is sandwiched by two Pd layers.
Finally, we estimated the two-magnon term (α TMS ) for the sample with the most perfectly continuous CoFeB layers, namely the one with t CoFeB = 5 Å. As it was mentioned above, α TMS is negligible in the perpendicular geometry but can have an important contribution in the in-plane configuration. Therefore, for this sample we have compared the damping parameter, determined from in-plane VNA-FMR measurement (shown in Fig. 6) with the perpendicular one. While α eff OP = (0.018 ± 0.001), the in-plane value is α eff IP = (0.037 ± 0.008). Assuming that the difference between both values is due to the two-magnon contribution, we estimated that α TMS = (0.019 ± 0.005), confirming the importance of α TMS in the in-plane configuration and in agreement with literature 41 .
Summarizing, we have studied the magnetic behaviour of [CoFeB/Pd] 5 multilayered thin films using two complementary techniques. The thicknesses of the CoFeB films reported in the literature have usually ranged between 0.5 nm to a few tens of nm. Here, we focused our attention in multilayers where t CoFeB was varied between 1 and 5 Å. Our analysis determined an increase of the effective saturation magnetization from its bulk value to M eff_CoFeB = (1760 ± 80) emu/cm 3 . PMA was observed in the as-cast samples for CoFeB layer thickness ≤ 4 Å. This behaviour was modeled by considering volumetric and surface anisotropy contributions. Then, we confirmed the presence of a strong surface anisotropy contribution as well as a magnetoelastic anisotropy term. This last term suggests that our ultrathin CoFeB films are under in-plane tensile strain. Finally, an effective damping parameter as low as α eff ≈ (0.019 ± 0.001) was observed for the multilayer with 4 Å CoFeB thickness. We suggested that for t CoFeB ≥ 4 Å the layer is continuous and the main contribution to effective damping is coming from spin-pumping when for lower thicknesses α eff is dominated by two-magnon scattering.

Methods
[CoFeB (t CoFeB )/Pd (10 Å)] 5 multilayer thin films were sandwiched between a Ta(20 Å)/Pd(20 Å) seed bilayer and a 50 Å Pd capping layer. Samples were deposited at room temperature on Si(100) substrates using confocal dc magnetron sputtering with a base pressure below 2 × 10 −10 Torr and an Ar working gas pressure of 5 mTorr (more details are given in Ref. 58 ). The CoFeB layer thickness (t CoFeB ) was varied between 1 and 5 Å and this alloy was sputtered from a Co 40 Fe 40 B 20 target.
While room temperature magnetic hysteresis loops were measured in a vibrating sample magnetometer (VSM), the dynamical behaviour was studied by comparing TR-MOKE and VNA-FMR measurements. FMR measurements were carried out at room temperature using a coplanar waveguide (CPW) connected to a vector network analyzer. The samples were placed film down on the CPW, and the complex S 21 parameter was measured as a function of the external magnetic field over a frequency range up to 20 GHz 99 . The external DC magnetic field (H) was applied along (θ H = 90°) or perpendicular (θ H = 0°) to the sample plane for in-plane and perpendicular measurements, respectively, and was always perpendicular to the ac field generated by the CPW. On the other hand, the dynamical response of the magneto-optical signals was obtained by an ultrafast pump-probe system based on a commercial Titanium:sapphire laser amplifier (Femtolasers Compact Pro CE-phase) delivering sub-30-fs laser pulses (approximately 40 nm bandwidth centered at 800 nm) with ~ 1 mJ of energy at a repetition rate of 1 kHz and with carrier-envelope phase (CEP) stabilization capability, seeded by a CEP-stabilised ultrafast laser oscillator (Femtolasers Rainbow). Time-resolved measurements were performed in polar MOKE configuration using 0.7% and 99.3% of the pulse energy for the probe and pump pulses, respectively. The spot size ratio between (14) α eff = α Gilbert + α s−p (15)