Orbital moment probed spin orbit coupling effects on anisotropy and damping in CoFeB thin films

Abstract

A strong correlation between coercivity, in-plane uniaxial magnetic anisotropy (UMA) and Gilbert damping constant in technologically important CoFeB thin films is demonstrated on the basis of static and dynamic magnetization measurements through compositional and stress variations. A large UMA is induced in CoFeB films over a wide range of Fe/Co ratios as a consequence of oblique co-sputtering from Co₂₀Fe₆₀B₂₀ and Co targets. The UMA and damping variations are consistent with the calculated Landé g-factor, whose asymmetry gives rise to UMA and anisotropic damping via spin orbit coupling. The study highlights the fabrication of films having reasonable anisotropy with tailored damping properties.

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Introduction

Soft ferromagnetic thin films possessing uniaxial magnetic anisotropy (UMA) are used in many applications such as magnetic recording, information storage and microwave devices.¹ The physical origin of UMA stems from spin orbit coupling (SOC) which is fundamentally controlled by the orbital magnetism.^2,3 Another important phenomenon which has its origin in the SOC is the magnetic Gilbert damping which signifies the rate at which the magnetization precession in a material damps out when it is acted upon by an external field H.^4–6 This damping is quantified by the constant α i.e., Gilbert damping parameter. A low α value is required for several spintronic devices, most importantly in spin-transfer torque magnetic random-access memories (STT-MRAMs) and spin torque nano-oscillators (STNOs).⁷ Both UMA and α are critical parameters for high performance spintronic devices and since theoretically both have their origin in SOC, the two are expected to be correlated to each other. There exist significant controversy in magnetic multilayers exhibiting out-of-plane UMA i.e., perpendicular magnetic anisotropy (PMA) regarding correlation of PMA with the damping behavior as several reports suggested direct relation,^8,9 while others ruled out any correlation between them.^10,11 Such contradictory data exists as the PMA in multilayers is solely not varied by the SOC but the surface/interface effects also play an important role. However, thin films exhibiting in-plane UMA are likely to show the SOC based correlation between the anisotropy and damping in the absence of any geometric effects.

In this report, we intend to study the relationship between the in-plane UMA and damping in CoFeB thin films which has not been investigated so far. The CoFeB is widely preferred electrode in the magnetic tunnel junctions (MTJs).¹² Apart from that, it is important to understand and tune its magnetization dynamics for high frequency applications.^13,14 In our work, Co₂₀Fe₆₀B₂₀ and pure Co targets have been obliquely co-sputtered to induce changes in the film-composition as well as the film-stress which further lead to substantial changes in the UMA and magnetic damping. The angle and frequency dependent ferromagnetic resonance (FMR) measurements were performed to determine the Landé g-factor which will provide information on the orbital moment arising from SOC. The strong connection between the g-factor asymmetry and the UMA and their direct impact on the damping constant values elucidate the spin orbit effects based origin of both UMA and damping in CoFeB thin films.

Experimental details

Thin films of Ta (5 nm)/Co_xFe_yB_z (23 nm)/Ta (5 nm) were deposited on naturally oxidized Si substrate using pulsed DC magnetron sputtering with base pressure of 2 × 10⁻⁷ Torr. The schematic depicting the position of the substrate and targets within the deposition chamber is shown in Fig. 1(a). It is evident that Co₂₀Fe₆₀B₂₀ and Co target do not face the substrate normally but at an angle Φ and are located opposite to each other. The composition of the CoFeB films was systematically varied by changing the power applied to the Co-target (P_Co) from 0 to 70 W (films labelled as Co-00, 30, 40, 50, 60, and 70, respectively), while a constant power of 140 W was applied to Co₂₀Fe₆₀B₂₀ target. The X-ray reflectivity (XRR) measurements were performed to determine the deposition rates of Co₂₀Fe₆₀B₂₀ and Co target at different powers so to maintain a constant thickness (∼23 nm) in CoFeB thin films. The resulting ratio of Fe/Co in the films was determined from energy-dispersive X-ray spectroscopy (EDX) and was found to be consistent with the composition calculated on the basis of the deposition rates of the two targets (see Table 1). The crystallographic structure of the films was studied using PANanalytical X'pert PRO X-ray diffractometer which revealed the amorphous nature of the films for all the compositions (not shown). The static magnetic characterization was performed by employing the vibrating sample magnetometer (VSM) option of Physical Property Measurement System (PPMS) (Quantum Design make EverCool II model). The dynamic magnetic response of the films was recorded over the frequency f range of 5–13 GHz using the broadband lock-in amplifier ferromagnetic resonance (LIA-FMR) set-up with in-plane field configuration. In the stated set-up, a pair of Helmholtz coil provides a small modulation field of 1.3 Oe @ 211.5 Hz. The samples were placed with film side facing the coplanar waveguide (CPW). The field-swept FMR spectra were recorded at constant microwave frequencies and then fitted with the derivative of the Lorentzian function to obtain the resonance field H_r and field linewidth ΔH (FWHM).

Fig. 1 (a) Schematic of the co-sputtering setup showing the oblique deposition. Also shown are resulting EA and HA in the deposited film. (b) M–H loops for Co-00 film measured along the EA and HA. (c) Variation of H_c and H_k-static as a function of P_Co.

Table 1 The composition and magnetic properties (extracted from the M–H and FMR measurements) of the various films

Sample name	Composition	Fe/Co ratio	Hc (Oe)	Hk-static (Oe)	Hk-dynamic (Oe)	α∥
Co-00	Co20Fe60B20	2.9	32	148	144.8	0.0106
Co-30	Co24Fe57B19	2.4	23	80	77.3	0.0094
Co-40	Co29Fe53B18	1.8	17	62	66.2	0.0069
Co-50	Co34Fe50B16	1.5	11	56	54.4	0.0057
Co-60	Co39Fe46B15	1.2	13	74	75.0	0.0060
Co-70	Co43Fe43B14	1.0	19	92	92.9	0.0068

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Results and discussion

The static magnetization M–H measurements revealed a very well defined UMA for all the samples. In Fig. 1(b), we present the M–H loops of the Co-00 sample recorded along the easy and hard axes (EA and HA) (loops for other samples not shown for brevity). Such high UMA results from the oblique deposition geometry which is likely to generate anisotropic stress in the films.¹⁵ Since CoFeB is known to be highly stress sensitive owing to the large positive saturation magnetostriction coefficient (λ_s),¹⁶ the resulting stress causes the breakdown of the azimuthal symmetry in the deposited films, and thereby inducing the UMA in the incident direction (in-plane projection of the Φ angle).^17–19 This conjecture is supported by the fact that the films deposited while rotating the substrate holder (i.e., under isotropic stress conditions) understandably exhibited negligible amount of anisotropy.

Fig. 1(c) present the changes in the coercivity H_c and magnetic anisotropy field H_k-static of the films as P_Co is varied. Here, the H_k-static values were calculated by the difference in the saturation field H_s along the EA and HA. The first notable feature from the H_c and H_k-static behaviour is that both followed the same trend with P_Co. This direct relationship is inevitable, since increase in anisotropy also brings the enhancement of the wall coercivity as suggested by Hoffmann.²⁰ For Co-00 (Co₂₀Fe₆₀B₂₀) films, we simultaneously obtained highest values of H_k-static (148 Oe) and H_c (32 Oe). Upon co-sputtering with the Co target from the opposite side, there occurs steep fall in the values of H_k-static and H_c for Co-30 films. Such large change cannot be accounted on the basis of compositional variation only, and can be due to the change in the deposition kinetics on co-sputtering which might have possibly reduced the anisotropic stress. The same trend continues with gradual decrease in values till the minimum values of H_k-static (56 Oe) and H_c (11 Oe) were reached corresponding to the Co-50 film. However, on further increasing the P_Co, both H_k-static and H_c exhibited a gradual rise. The probable cause behind the latter increase in H_k-static and H_c could be the substantial compositional variation in terms of lower boron (B) content in Co-60 and Co-70 compared to the Co-00 films. A similar enhancement in the anisotropy values were reported in Co₆₈Fe₂₂B₁₀ compared to (CoFe)₈₀B₂₀ films, and also in Co_67.2Fe_28.8B₄ alloy films owing to the structure more closely related to that of a distorted bcc lattice at lower boron concentration.^21,22

Based on the compositional dependence of H_k-static, we tried to distinguish between the Néel–Taniguchi (N–T) directional ordering model and bond-orientational anisotropy (BOA) as the possible mechanism for the microstructural origin of anisotropy in our films. In N–T model, UMA is induced by the preferential orientation of individual atomic pairs and the anisotropy is supposed to show strong composition dependence in terms of changing Fe/Co ratio. The highest anisotropy is expected corresponding to Fe/Co ratio of unity which is certainly not observed in our case.²³ On the other hand, the BOA refers to the orientational anisotropy in the distribution of atomic bonds between the nearest neighboring atoms.^24,25 It should be noted that in BOA, the change in anisotropy is mainly contributed by the stress variations with negligible influence from the changes in the Fe/Co ratio. Also, within this model a relatively strong anisotropy is anticipated in Co-60 and Co-70 owing to lower boron content that results in higher λ_s compared to Co-00 films.¹⁶ Therefore, BOA seems to be the responsible mechanism for the observed UMA in the films deposited at oblique incidence.

Next, the angle dependent field-swept FMR measurement of the sample series was performed at 9 GHz, where we measured the corresponding resonance field H_r at different angles θ (defined as an angle between EA and H). The angular plots shown in Fig. 2(a) revealed the existence of two-fold symmetry which is a clear indicator of the UMA. The data was fitted with the following equation and the individual contributions of uniaxial and cubic anisotropy were separated.²⁶

Fig. 2 (a) The θ-dependence of H_r for sample series. Open symbols represent the experimental data and the solid lines are the fits to eqn (1). (b) Dependence of H_k-dynamic and H_cubic on P_Co.

Here, h is Planck's constant, g is Landé g-factor, 4πM_S is saturation magnetization, H_k-dynamic and H_cubic are the uniaxial and cubic anisotropy fields, respectively and θ_k-dynamic and θ_cubic are the angles that the respective easy axes of the uniaxial and cubic anisotropy make with the observed EA. From the fitting, the values of H_k-dynamic, H_cubic, θ_k-dynamic, θ_cubic and g²4πM_s were obtained as fitting parameters. It can be seen from Fig. 2(b) that for all the compositions, the uniaxial anisotropy is far more dominant than the cubic anisotropy. Also, the H_k-dynamic followed H_k-static excellently well (see Table 1).

Subsequently, the field-swept FMR spectra of the entire sample series were recorded over the f range of 5–13 GHz along EA and the spectra obtained for Co-00 are shown in Fig. 3(a). The so obtained f vs. H_r values plots (Fig. 3(b)) were fitted using the Kittel equation for EA configuration:²⁷

Fig. 3 (a) Frequency dependent field-swept FMR spectra for Co-00 along EA (numbers represent frequency in GHz). Solid symbols represent the experimental data and the solid lines are the fits to Lorentzian function. (b) Variation of f vs. H_r along EA for sample series. Open symbols representing the experimental data while the solid lines are the fits to eqn (2). (c) Dependence of g_∥ and g_⊥ on P_Co (inset showing Δμ_L/μ_B a function of P_Co). (d) Variation of 4πM_eff (along EA) and 4πM_s with P_Co.

Here, g_∥ is Landé g-factor along EA, H_k is the anisotropy field and 4πM_eff is the effective magnetization. For the precise determination of the g_∥ value with minimum error it is necessary to reduce the number of coupled fitting parameters. Therefore, we used the previously determined values of H_k-dynamic (shown in Table 1) in place of H_k in eqn (2) and then obtained the g_∥ and 4πM_eff as the fitting parameters.^28,29 The g-factor is related to the orbital angular momentum μ_L and spin angular momentum μ_S by the following relation: μ_L/μ_S = (g/2) − 1.³⁰ It can be seen from Fig. 3(c) that the resulting g_∥ values in the films are significantly higher than their bulk counterparts (∼2.09).³¹ In the literature, the g-factor values of up to 2.14 are reported for CoFeB films having small anisotropy fields (18–28 Oe).²⁹ Besides that, CoFeB films with PMA exhibited the g-factor values in the range 2.16–2.19.³² So, the obtained larger g_∥ values in the present study are the consequence of larger orbital contributions due to the high anisotropy field present in our films.^33,34 Based on the SOC, Bruno proposed in his model that the anisotropy of μ_L (w.r.t. EA and HA) i.e., μ_∥ − μ_⊥ (or Δμ_L) induces the UMA in a film.² Since the asymmetry of the g-factor w.r.t. EA and HA i.e., g_∥ − g_⊥ will yield Δμ_L,¹⁰ we next performed the similar FMR measurements along the HA. The obtained f vs. H_r values were fitted with the Kittel equation (still valid since H is sufficiently large to turn M parallel to HA), which takes up the following form for HA configuration, and thus obtained the g_⊥ values:³⁵

Fig. 3(c) shows that the g_∥ is larger than g_⊥ for all samples and emphasizes on fact that EA lies along the highest μ_L direction via SOC effects.^36,37 The g-factor asymmetry further indicates preferred directional bonding along the EA and thus hinting at the structural anisotropy originating from the BOA mechanism. As shown in the inset of Fig. 3(c), the variation of with P_Co is similar to that of H_k-dynamic (see Fig. 2(b)), which is consistent with the theory. Fig. 3(d) shows a general increasing trend of 4πM_eff (along EA) and 4πM_s (from VSM measurements) with P_Co and is due to compositional variations. The 4πM_eff essentially mimics the behavior of 4πM_s since 4πM_eff = 4πM_s − (2K_s/M_s)t_FM⁻¹, where t_FM is the thickness of the ferromagnetic layer and K_s is the surface anisotropy constant whose contribution is almost negligible in the thickness region of our interest.¹¹

In order to have a deeper insight into the mechanisms of fast precession magnetic damping, the plots of ΔH vs. f (Fig. 4(a)) along the EA were analyzed. The linear response in ΔH(f) observed for all the samples highlights the predominance of the intrinsic origin of magnetic damping which is believed to be based on the SOC mediated magnon-electron scattering.⁶ The ΔH vs. f plots were fitted with the equation:^38,39

Fig. 4 (a) Variation of ΔH vs. f along EA for sample series with open symbols representing the experimental data while the solid lines are the fits to eqn (4). (b) Dependence of α_∥ and α_⊥ on P_Co (inset showing Δα as function of P_Co). (c) Variation of α_∥ as a function of (g_∥ − 2)² for the sample series. (d) Dependence of ΔH₀ on P_Co along EA.

Here, ΔH₀ (zero frequency intercept) is the inhomogeneous linewidth broadening and is mainly contributed by the spatial dispersion in the direction and magnitude of both magnetic anisotropy and magnetization. It is remarkable to note that we have this interesting situation wherein the resulting α designated as α_∥ (Fig. 4(b)) follows exactly the same trend with P_Co as that of H_k-dynamic, g_∥, and Δμ_L/μ_B with minimum value of 0.00578 ± 0.00006 in Co-50 film compared to the highest value of 0.0106 ± 0.0002 in Co-00 (Co₂₀Fe₆₀B₂₀) films. Recently, such proportionality between damping and anisotropy was experimentally shown and justified by their similar dependence on the spin orbit coupling parameter ξ.⁴⁰ In the present work, based on the compositional variations only, we cannot account for the observed large changes in α, since the ξ is reported to remain nearly constant for the range of compositions studied.³¹ However, the SOC based damping variations are understood in terms of UMA driven changes in the orbital moment (which is also proportional to ξ in 3d magnetic alloys),⁴¹ and its anisotropy. This can also justify the observed strong connection between the damping and anisotropy. To substantiate this further, we carried out the measurement of damping along the HA (designated as α_⊥) and results (see Fig. 4(b)) clearly indicate that damping too exhibits anisotropy, with higher values along the EA.⁴² This damping anisotropy Δα (inset of Fig. 4(b)) stems from Δμ_L as the electron spin is coupled to orbital moment via SOC.⁴³ It is well known that if precession damping is attributed to SOC, then α and g-factor should be related as follows α ∝ (g − 2)², which signifies that the deviation of the g-factor value from that of free electron (g =∼ 2) measures the relative μ_L contribution to the SOC.⁴⁴ So we plot, in Fig. 4(c), α_∥ as a function of (g_∥ − 2)² for all the samples. The very presence of linear dependence confirms the SOC based origin of magnetic damping in these films. Thus, the variations of FMR probed g-factor asymmetry are consistent with the changes in anisotropy and damping and gives insight into the SOC based proportionality between anisotropy and damping in CoFeB thin films.

The stress variation in the films can be qualitatively understood from the variation of ΔH₀ (along EA) with P_Co as shown in Fig. 4(d). The higher ΔH₀ for Co-00 and Co-30 films was thought to be due to the relatively large amount of stress and defects present in them. Since greater inhomogeneity in anisotropy is generally expected either from the presence of grain boundaries in polycrystalline films or due to magnetostrictive stress effects.⁴⁵ Since our films are amorphous, the stress induced effects can be a dominant mechanism. Also, higher ΔH₀ could lead to higher observed values of H_c and α.⁴⁶ The homogeneity in the films was further greatly improved (inferred from reduction in ΔH₀) from co-sputtering at higher P_Co, thus indicating a low stress condition.

Conclusions

In summary, we reported the static and dynamic magnetic characterization of Co₂₀Fe₆₀B₂₀ thin films on excess Co incorporation. The strong connection between anisotropy and damping is explained through orbital magnetism contributions arising from the SOC effects. The origin of UMA is attributed to anisotropy in orbital moment which thereby causes anisotropy in damping. The SOC based origin was further ascertained by linear dependence of damping constant α_∥ on (g_∥ − 2)². A reasonably low α-value of 0.0057 was obtained for Co-50 films (Fe/Co ∼ 1.5) with anisotropy field of ∼54 Oe. Therefore, controlling Co concentration and stress by simple fabrication process can be an effective method to tune the coercivity, uniaxial magnetic anisotropy and damping in Co₂₀Fe₆₀B₂₀ system.

Acknowledgements

One of the authors (D. J.) acknowledges the financial support of MHRD, Government of India.

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