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

Abstract

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 (t_CoFeB)/Pd (10 Å)]₅ multilayered ultrathin films (1 Å ≤ t_CoFeB ≤ 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 t_CoFeB ≤ 4 Å. The effective perpendicular magnetic anisotropy reaches a clear maximum at t_CoFeB = 3 Å. Further increase of CoFeB layer thickness reduces the perpendicular magnetic anisotropy and the magnetization became in-plane oriented for t_CoFeB ≥ 5 Å. This behaviour is explained by considering competing contributions from surface and magnetoelastic anisotropies. It was also found that the effective damping parameter α_eff decreases with CoFeB layer thickness and for t_CoFeB = 4 Å reaches a value of ~ 0.019 that is suitable for microwave applications.

Introduction

Since the mid 1970s ^1,2, materials with perpendicular magnetic anisotropy (PMA) have been studied for a large diversity of applications including, but not limited to, perpendicular recording media^1,2,3,4, patterned magnetic media^5,6, high-density spin-transfer torque magnetic random access memories (STT-MRAM)^7,8,9 and more recently in skyrmion-based devices^10,11,12 and synthetic antiferromagnets for biomedical applications^13,14,15.

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 energy¹⁸. 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 layers¹⁹, including Ta^20,21, Hf^22,23, Mo^24,25, Ru^26,27, V²⁶, Nb²⁷, Pt^28,29, Pd^30,31,32 and Au³³.

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 ratio⁹, and in magnonic devices³⁷. 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 Co₄₀Fe₄₀B₂₀ alloy can be as low as 0.004^41,42, the estimated effective damping (α_eff) increases substantially at low thickness⁹ 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 PMA show α_eff parameters of 0.012³⁵ and 0.027⁹, respectively. This rise has been associated with the fact that the α_eff parameter contains contributions from both intrinsic and extrinsic terms⁴³. The intrinsic term or α_Gilbert is constant with the resonance frequency but shows temperature dependence^43,44. Devolder et al.³⁵ studied the correlation between α_Gilbert and the g-factor (g) in CoFeB thin films as a function of the alloy composition and annealing conditions. As it was expected in transition metals, the dependence α_Gilbert ≈ (g − 2)² was reported⁴⁵.

On the other hand, it has been suggested that the extrinsic term can be due to different effects such as⁴⁶:

• 1. An inhomogeneity contribution based on the local variations of the magnetization and/or the magnetic anisotropy field due to structural defects and/or thickness variations⁴³. In particular, Devolder et al.³⁵ studied the damping parameter of Co_xFe_80−xB₂₀ ultrathin films and reported that the inhomogeneity term should be constant with the resonance frequency while it should depend on the sample composition, thickness, and materials used for the capping and/or buffer layers.

• 2. A two-magnon scattering (TMS) contribution^47,48. Regarding this term, Liu et al.⁴¹ performed out-of-plane angular dependence FMR measurements of CoFeB thin films, and they reported that the damping mechanism depends on the layer thickness. It was suggested that α_eff is mainly governed by the Gilbert damping in thicker (≥ 4 nm) CoFeB films, while inhomogeneous broadening and two-magnon scattering are the main factors for films thinner than 2 nm.

• 3. A contribution from the spin-pumping effect^49,50. Although this effect was first suggested by Berger⁵¹, it was experimentally confirmed by Mizukami et al.^52,53 that the damping of non-magnetic/magnetic/non-magnetic trilayers depends on the non-magnetic material. Large damping parameters were determined when non-magnetic materials with a strong spin–orbit coupling, such as Pt and Pd, were used. Iihama et al.²⁰ investigated the damping parameter of Ta/CoFeB/MgO and Ta/CoFeB/Ta thin films using an all-optical pump-probe method, and they claimed that the enhancement of α_eff is caused by the spin pumping effect at the Ta/CoFeB interfaces.

• 4. Any change in the magnetization of a ferromagnetic material placed on top of a coplanar waveguide (CPW) induces eddy currents. These eddy currents generate a magnetic field in the ferromagnet that opposes the original change and provides a damping mechanism (α_eddy)^54,55. Moreover, the generated eddy currents also affect the CPW, and an extra damping mechanism, known as radiative damping (α_rad), should be considered^56,57.

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.

Results and discussion

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).

Figure 1

In-plane (a) and out-of-plane (b) hysteresis loops of [CoFeB (t_CoFeB)/Pd (10 Å)]₅ multilayer thin films with t_CoFeB = 1 (Black filled square), 2 (red open square), 3 (green filled circle), 4 (dark blue open circle) and 5 Å (light blue filled triangle).

Magnetic moment

Moreover, the hysteresis loops were used to obtain the values of the saturation magnetization (M_Sat), which are shown in Fig. 2a. We observed that M_Sat increases with the CoFeB film thickness from (280 ± 50) to (700 ± 50) emu/cm³ for t_CoFeB = 1 and 5 Å, respectively. This behavior was already observed in ultrathin films, such as for example in Pt/Co/Pt⁶⁰, Ta/CoFeB (t nm)/SiO₂ (t = 1, 2, 3, 4, 6, 10 13 nm)⁶¹, [Co (t nm)/Pd]₈⁶² and [CoFeB (t nm)/Pd (1.0 nm)]₁₀ (t = 0.4, 0.6, 0.8, 1.0 and 1.2 nm) multilayer films³² with perpendicular anisotropy.

Figure 2

(a) Saturation magnetization, M_Sat as a function of the CoFeB layer thickness (t_CoFeB). (b) M_{Sat_sheet} as a function of the CoFeB layer thickness (t_CoFeB). The continuous red lines are linear fits.

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 constant³². 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/cm³, which agrees with the value of (180 ± 10) emu/cm³ reported by Ngo et al.³².

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

$$M_{Sat\_sheet} = I/\left( {N \times A} \right) = M_{eff\_CoFeB}\times t_{CoFeB} + M_{eff\_Pd}\times t_{Pd}$$

(1)

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/cm³ 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/cm³ was obtained from the linear fit slope.

This value seems to be too large in comparison with the values previously reported for Co₄₀Fe₄₀B₂₀ thin films and estimated from the hysteresis loops (1000³⁰ or 1034 emu/cm^331,67), ferromagnetic resonance measurements (1019 emu/cm³⁶⁸) or the linear fit of the magnetization per unit area (M_{Sat_sheet}) vs the CoFeB film thickness (1120⁶⁹, 1150²⁵ or 1200 emu/cm³²⁶). Usually, such large M_sat values have been reported for CoFeB alloys fabricated with lower B concentration, such as ≈ 1670 and 1830 emu/cm³ for (Co₃₅Fe₆₅)₉₀B₁₀ and (Co₃₅Fe₆₅)_87.5B_2.5 respectively⁷⁰, 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/cm³ for Ta/Co₄₀Fe₄₀B₂₀/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/cm³ for thicker samples (t ≥ 2.2 nm). But large M_{eff_CoFeB} values, such as 1790 emu/cm³, 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, where Ngo et al. reported M_{eff_CoFeB} = 1550 emu/cm³ in CoFeB (t nm)/Pd multilayered thin films.

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 energy¹⁸. 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:

$$f_{FMR} = \frac{\gamma }{2\pi }\sqrt {\left( {H\cos \left( {\theta_{0} - \theta_{H} } \right) + H_{eff} \cos^{2} \left( {\theta_{0} } \right)} \right) \times \left( {H\cos \left( {\theta_{0} - \theta_{H} } \right) + H_{eff} \cos \left( {2\theta_{0} } \right)} \right)}$$

(2)

where (γ/2π) = (gµ₀/h) is the gyromagnetic ratio; g is the g-factor; µ₀ 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 θ₀ is the equilibrium angle of the sample magnetization. The equilibrium angle θ₀ can be derived from the equation:

$$H\sin \left( {\theta_{H} - \theta_{0} } \right) = \frac{1}{2}H_{eff} \sin \left( {2\theta_{0} } \right)$$

(3)

When thin films are saturated and θ_H = θ₀, Eq. (2) can be reduced to⁷⁴:

$$f_{FMR} = \frac{\gamma }{2\pi }\left( {H + H_{eff} } \right)\quad {\text{for perpendicular geometry}}$$

(4)

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).

Figure 3

(a) VNA-FMR spectra of the [CoFeB (4 Å)/Pd (10 Å)]₅ multilayer thin film with the external magnetic field applied perpendicularly to the sample plane. The black line corresponds to the fits using the Kittel formula (Eq. 4). (b) Time-resolved magneto-optical Kerr effect (TR-MOKE) signals of a [CoFeB (2 Å)/Pd (10 Å)]₅ multilayer thin film under different external applied fields (H = 5650, 5060, 4695, 4310 Oe and 3900 Oe) and when H was applied at θ_H = 78°. Theoretical curves (solid curves) are fits to the experimental data (open symbols) using Eq. (5). Data was moved along the vertical axis for clarity.

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]₈⁶² multilayers, L1₀-FePt alloy epitaxial thin films⁷³ or Ta/CoFeB/MgO(Ta) thin films²⁰. 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:

$$\theta = \theta_{0} + A \times e^{{ - t/t_{0} }} + B \times \sin \left( {2\pi f_{FMR} t + \varphi } \right) \times e^{ - t/\tau }$$

(5)

where θ₀ and A are the background magnitudes, and t₀ 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 Co₂₀Fe₆₀B₂₀, with a body-centered-cubic (bcc) crystalline structure, has a lattice parameter of 2.86 Å⁷⁹, leads us to believe that both the 1 and 2 Å thick CoFeB layers are discontinuous thin films. Even, the continuity of the 3 Å thick CoFeB layers could be in question, which will be suggested below during the discussion related to the damping parameter. So for now, both thinner samples (t_CoFeB = 1 and 2 Å) were excluded in the subsequent analysis.

Table 1 Summary of the results for [CoFeB/Pd]_N multilayer systems (N = 5 bilayers) as a function of the CoFeB thickness (t_CoFeB): the saturation magnetization (M_sat) extracted from VSM; the gyromagnetic ratio (γ/2π) and g-factor (g) determined from VNA-FMR fits using Eq. (4); Effective anisotropy field (H_eff) determined from VNA-FMR (Eq. 4) and TR-MOKE (Eqs. 2, 3 and 5); Effective anisotropy energy (K_eff) determined from Eq. (6); The effective damping (α_eff) determined from VNA-FMR and TR-MOKE. Data extracted from the VNA-FMR measurements is shown in black. Data extracted from the TR-MOKE measurements is given in italics and red.

Figure 4

(a) H_eff and (b) (t_CoFeB+Pd × K_{eff_CoFeB}) as a function of the CoFeB layer thickness (t_CoFeB = 1 – 5 Å) for [CoFeB (t_CoFeB)/Pd (10 Å)]₅ multilayer thin films. While black open circle are the experimental data determined from the VNA-FMR measurements, black open triangle were determined from the TR-MOKE studies. The red solid line in (b) is the fitting to the model described by Eq. (8).

From the fitted data, the effective anisotropy energy (K_eff) can be estimated according to (summarized in Table 1):

$$K_{eff} = \frac{1}{2}\left( {H_{eff} \times M_{sat} } \right)$$

(6)

Moreover, K_eff can be phenomenologically separated into a volume contribution K_v (erg/cm³) and a contribution from the interfaces K_s (erg/cm²), and it can be approximately described by the Néel model⁸⁰:

$$K_{eff} = K_{v} + \left( {2K_{s} /t} \right)$$

(7)

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 model⁸⁰, (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/Au⁸¹ and Ni/Cu^82,83,84 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 terms⁸³ or the second-order of the magnetoelastic contribution⁸⁴.

More recently, this non-linearity was also reported for NM/CoFeB/MgO thin films (where NM was Ta⁶⁹ or Hf²³) and it was fitted using the equation proposed by Gowtham et al.⁶⁹:

$$K_{eff} \times t = K_{v}^{eff} \times t + 2 \times K_{s}^{eff} + \left( {K_{3} /t} \right)$$

(8)

where $K_{v}^{eff}$ is the effective volumetric contribution that should include the shape anisotropy term and both the bulk magnetocrystalline and bulk magnetoelastic anisotropy energy contributions; $K_{s}^{eff}$ is the effective surface term that includes the surface magnetocrystalline and magnetoelastic anisotropy terms as well as the second-order 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). Using Eq. (8) to fit the experimental data, we have estimated that $K_{v\_CoFeB} = \left( { - 16.2 \pm 0.3} \right) \times 10^{6} \;{\text{erg/cm}}^{3}$, $K_{s\_CoFeB} = \left( {0.53 \pm 0.01} \right) \;{\text{erg/cm}}^{2}$ and $K_{3} = \left( { - 1.48 \pm 0.05} \right) \times 10^{ - 8} \;{\text{erg/cm}}$. Our values are close to the data previously reported in the literature for Hf/CoFeB/MgO²³ and Ta/CoFeB/MgO thin films⁶⁹.

Assuming that the CoFeB layer is amorphous, its bulk magnetocrystalline anisotropy energy contribution should be null. Therefore, we suggest that the volumetric term could be formed by:

$$K_{v\_CoFeB} = K_{sh\_CoFeB} + K_{me\_CoFeB} = \left( { - 16.2 \pm 0.3} \right) \times 10^{6} erg/cm^{3}$$

(9)

where $K_{sh\_CoFeB} = - 2\pi M_{{eff_{CoFeB} }}^{2} = \left( { - 19 \pm 2} \right) \times 10^{6} \;{\text{erg/cm}}^{3}$ is the shape anisotropy term and $K_{me\_CoFeB} = \left( {3 \pm 1} \right) \times 10^{6} \;{\text{erg/cm}}^{3} \left( { = \left( {3 \pm 1} \right) \times 10^{5} \;{\text{J/m}}^{3} } \right)$ is the magnetoelastic anisotropy contribution.

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:

$$K_{me\_CoFeB} = \frac{3}{2}\lambda_{s} \sigma_{in\_plane}$$

(10)

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:

$$\sigma_{in\_plane} = \frac{{E\varepsilon_{in\_plane} }}{{\left( {1 - \nu } \right)}}$$

(11)

As the magnetoelastic anisotropy term favors that the magnetization lies perpendicular to the sample plane and the saturation magnetostriction coefficient of amorphous Fe₄₀Co₄₀B₂₀ is positive λ_s = 20 × 10^–687, the magnetic layer should be under tensile stress with σ_{in_plane} ≈ (11 ± 3) × 10¹⁰ dyne/cm² (≈ (11 ± 3) GPa). Using the Young's modulus E = 160 × 10¹⁰ dyne/cm² (= 160 GPa) for CoFeB and the Poisson ratio ν = 1/3⁸⁸, 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/Co₂₀Fe₆₀B₂₀/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 parameter⁹⁰. Therefore, we used Δf_FMR to determine the apparent damping by⁹⁰:

$$\alpha_{app} = \frac{{\Delta f_{FMR} }}{{\left( {\frac{\gamma }{2\pi }} \right)\left( {2H + H_{eff} } \right)}}$$

(12)

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 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).

Figure 5

Apparent damping α_app as a function of the external applied magnetic field for CoFeB layer thickness of t_CoFeB = 4 (a) and 3 Å (b), extracted from VNA-FMR spectra (blavk open circle) and pump-probe measurements (black filled circle). The red (blue) solid lines are the average of α_app determined from the VNA-FMR spectra (pump-probe measurements) for large applied fields and correspond to the α_eff.

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:

$$\alpha_{app} = \frac{1}{{2\pi \times f_{FMR} \times \tau }} = \frac{1}{{\gamma \times \left( {H + H_{eff} } \right) \times \tau }}$$

(13)

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.

Figure 6

Evolution of the effective damping (α_eff) versus t_CoFeB and determined from the TR-MOKE measurements (black open triangle), the perpendicular VNA-FMR (black filled circle) and the in-plane VNA-FMR (red open circle) measurements.

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 depth⁹⁰, and the radiative damping is proportional to the magnetic layer thickness⁵⁷, 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 work⁹³. 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:

$$\alpha_{eff} = \alpha_{Gilbert} + \alpha_{s - p}$$

(14)

The spin-pumping contribution α_s-p can be defined using the formula^94,95,96:

$$\alpha_{s - p} = 2g\mu_{B} \frac{{g^{ \uparrow \downarrow } }}{{4\pi M_{eff\_CoFeB} }}\frac{1}{{t_{CoFeB} }}\left( {1 - e^{{ - 2t_{Pd} /\lambda_{Pd} }} } \right)$$

(15)

where g is the g-factor; µ₀ = (9.27400915 × 10^–21) erg/Oe is the Bohr magneton; M_{eff_CoFeB} = (1760 ± 80) emu/cm³ 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 nm⁹⁵ 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.

Considering the damping value for t_CoFeB = 4 Å (α_eff = (0.019 ± 0.001)) and assuming that α_Gilbert = 0.004^41,42,97, we have estimated that α_s-p ≈ (0.015 ± 0.001). From Eq. (15), the CoFeB/Pd interface spin mixing conductance value should be g^↑↓ ≈ (3 × 10⁺¹⁵) cm⁻². Although this is a rough estimation, g^↑↓ is of the same order of magnitude than the values already reported in the literature, particularly 2.21 × 10⁺¹⁵ cm⁻² for a CoFeB/Pd interface⁹⁸ or 0.722 × 10⁺¹⁵ cm⁻² for a β-Ta/CoFeB interface⁶¹.

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 literature⁴¹.

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/cm³. 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 Co₄₀Fe₄₀B₂₀ 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 S₂₁ parameter was measured as a function of the external magnetic field over a frequency range up to 20 GHz⁹⁹. 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 the pump and probe beams was adjusted to be 4:1 to assure that the probe spot hits a homogeneous pump illuminated area of the sample, and the pump fluence was fixed to 2 mJ/cm². In order to increase the signal-to-noise ratio of the TR-MOKE signal, the external DC magnetic field was applied at an angle of θ_H = 78°¹⁰⁰. All-optical measurements were performed under ambient conditions.