Spin-torque ferromagnetic resonance measurements utilizing spin Hall magnetoresistance in W/Co₄₀Fe₄₀B₂₀/MgO structures

Spin-torque ferromagnetic resonance (ST-FMR) is emerging as an effective technique for studying the properties of magnetic materials since it was reported by Tulapurkar and Sankey et al.^1,2 In the first stage of this method, a radio frequency current (I_rf) is applied to exert an oscillating torque on the magnetic moment and to make it oscillate around the equilibrium state, often due to the spin-transfer torque.^1–3 This results in the resistance oscillation (R_rf) due to the magnetoresistance effects, such as tunnel magnetoresistance (TMR) and giant magnetoresistance (GMR).^1–3 Consequently, a rectified dc voltage is generated as a result of the mixing of the I_rf and the R_rf. Hence, the ST-FMR spectrum provides rich information about material properties, such as resonance frequency and field, magnetic anisotropy and Gilbert damping constant (⁠$α$⁠).^2–5 

Alternatively, spin-orbit torque (SOT)^6–8 has also been employed for exciting magnetization oscillations in the ST-FMR technique, where I_rf is applied in the film plane, and R_rf usually originates from the anisotropic magnetoresistance (AMR) effect.^7–13 In this scheme, unlike TMR or GMR cases,^1–3 a reference magnetic layer is not required, which simplifies the device structure. However, AMR usually decreases with a decrease in the thickness of film,¹⁴ which dramatically limits the studies of ultrathin ferromagnetic materials using ST-FMR.

More recently, spin Hall magnetoresistance (SMR) was observed in the heavy metal (HM)/ferromagnetic insulator (FI) or HM/ferromagnetic metal (FM) structures, which depends on the angle between the magnetization (M) and the direction of the spin-polarized electrons induced by the spin Hall effect.¹⁵ The ST-FMR utilizing SMR has been used to study magnetic properties in the HM/FI structure.^16–18 For HM/FM structure, compared with AMR, SMR is more dependent on the spin-dependent scattering at the HM/FM interface, which therefore makes it less dependent on the FM thickness. Experimentally, large SMR has been observed in the W/CoFeB/MgO structures with the CoFeB layer as thin as 0.8 nm.^19,20 The sizable SMR enables studying the magnetic properties of ultrathin CoFeB ferromagnetic layers, utilizing the ST-FMR technique.

In this work, we investigate the magnetic properties of both the as-grown and the annealed W/Co₄₀Fe₄₀B₂₀(CoFeB)/MgO multilayers with different CoFeB layer thicknesses using the ST-FMR technique. We obtain pronounced ST-FMR spectra due to the large SMR in the W/CoFeB bilayers in all the samples. By analyzing the ST-FMR spectra, we can study the influence of annealing and CoFeB layer thickness on the anisotropy and damping constants. This work demonstrates that the SMR-based ST-FMR is an effective method to probe the magnetic properties of ultrathin ferromagnetic films.

The film structures studied in this work consist of W(5)/CoFeB(t)/MgO(2)/Ta(2) (thicknesses in nm), which were deposited on thermally oxidized Si (001) substrates using a high-vacuum magnetron sputtering system at room temperature. The Ar sputtering pressure was 3 mTorr with a base pressure of less than 2 × 10⁻⁸ Torr. Subsequently, the multilayer films were patterned into standard Hall bars (length of 130 $μm$ and width of 20 $μm$⁠) and rectangular-shaped strips (length of 20 $μm$ and width of 20 $μm$⁠) using optical lithography and dry etching for SMR and ST-FMR measurements, respectively. Cr(10)/Au(100) metal stacks were deposited as contacts for electrical measurements.

The saturation magnetization (M_s) and the effective magnetic anisotropy energy (K_eff) of the as-grown samples were first characterized using vibrating sample magnetometer (VSM), as the reference for the ST-FMR measurement. All as-grown films exhibited in-plane magnetic anisotropy. Fig. 1(a) shows the nominal CoFeB thickness dependence of areal saturation. CoFeB saturation magnetization (⁠$Ms0$⁠) of about 1008 ± 50 emu/cm³ and the magnetic dead layer (t_dead) of about 0.32 ± 0.10 nm were determined by linearly fitting the data using the $MstCoFeB=Ms0(tCoFeB−tdead)$ equation. The value of $KefftCoFeB$ as a function of t_CoFeB is shown in Fig. 1(b). By fitting the data with the following equation:^21,22

the interfacial magnetic anisotropy K_i is determined to be about 0.70 ± 0.02 erg/cm². The negative values of $KefftCoFeB$ indicate the in-plane anisotropy nature of all of these as-grown films.

Figure 2(a) shows the variation of the longitudinal resistance (R_yy) as the magnetic field (with the magnitude of 2T) rotating in three planes (the xy-, xz-, and yz-planes). Since the magnetic field is larger than the saturation fields of all the samples, the magnetization aligns along the magnetic field direction. The R_yy varies while the magnetization rotates in the xy- and xz-planes, but remains nearly constant while the magnetization rotates in the yz-plane, which are the typical signatures of SMR.^19,20 When a current is applied along the y-direction, as marked in Fig. 2(b), it generates accumulated spin polarized electrons at the HM/FM interfaces due to the spin Hall effect.¹⁵ The direction of spin polarization is along the x-direction. The R_yy depends on the relative angle of M with respect to the x-direction. Fig. 2(c) shows the dependence of SMR on the CoFeB layer thickness. The SMR slightly increases and reaches the saturated value (about 0.5%) when the CoFeB layer thickness is greater than 1.0 nm. The SMR does not significantly rely on the CoFeB layer thickness, which is consistent with the previous work.²⁰ The saturated value of SMR in our device is comparable to that reported in Ref. 19, but slightly smaller than that reported in Ref. 20. The difference in SMR value may be due to the difference in the phase of the W layers. In this structure, the AMR is negligible since the resistance is almost invariable when the field rotates in the yz-plane.

The schematic diagram of the ST-FMR measurement setup is shown in Fig. 3(a). A microwave-frequency (GHz) charge current I_c,rf with a power of 4 dBm and modulated (f_mod ≅ 20 kHz) by the lock-in amplifier was applied to the device. The rectified voltage was detected by a lock-in amplifier. An in-plane magnetic field with a fixed angle θ_H of 45° was swept between −0.5 T and +0.5 T. Fig. 3(b) shows the ST-FMR spectra for the as-grown sample with a 1.1 nm thick CoFeB layer. The results can be well fitted to a Lorentzian function consisting of a symmetric and an antisymmetric Lorentzian component⁷ 

where Δ is the linewidth (full width at half maximum), H₀ is the resonant magnetic field, S is the symmetric Lorentzian coefficient that is proportional to the oscillating spin current I_s,rf, whereas A is the antisymmetric Lorentzian coefficient that is proportional to the Oersted field (H_rf) generated by I_c,rf. The inset shows the spectrum of 6 GHz for both positive and negative magnetic fields. Fig. 3(c) shows the resonance frequency f as a function of the resonant field H₀ for different CoFeB layer thicknesses. The results are fitted using the Kittel equation^7,9,11

where $γ$ is the gyromagnetic ratio. The extracted effective magnetization fields (4πM_eff) are shown in Fig. 3(d). 4πM_eff decreases dramatically from 1.282 ± 0.006 T to 0.010 ± 0.003 T as the thickness of CoFeB layer reduces from 3 nm to 0.8 nm. The decreasing 4πM_eff reflects the gradual increasing contribution of the interfacial anisotropy with decreasing thickness, as expected from²³ the equation $4πMeff=4πMs−2Ki/MstCoFeB$⁠. The effective magnetic anisotropy K_eff was calculated using $Keff=−12Ms4πMeff$⁠. K_efft_CoFeB as a function of the thickness of CoFeB layer was determined by the ST-FMR, as shown in Fig. 1(b), which is consistent with the results obtained using VSM.

We have also studied the magnetic damping based on the frequency dependence of resonance linewidth as shown in Fig. 4(a). The resonance linewidth, which usually includes intrinsic and extrinsic origins, is given by^9,11

$Δ0$ is the extrinsic contribution (e.g., inhomogeneous broadening) to the linewidth, which is usually independent of frequency. The second term is the intrinsic contribution, which is linearly proportional to the frequency. The values for studied samples were obtained by fitting the data, as shown in Fig. 4(b). The $α$ value increases from 0.0097 ± 0.0001 to 0.0400 ± 0.0005 when the CoFeB thickness decreases from 3.0 nm to 1.0 nm. Such a thickness dependence of $α$ is attributed to two-magnon scattering^24,25 and the spin pumping effect.^25–27 The α values in our structures are comparable to the results in the W/CoFeB bilayer structure reported by Pai et al.,⁹ but a little larger than that of Ta/CoFeB/MgO,²⁸ which is likely due to the different interfacial morphologies and spin mixing conductance in spin pumping.^25,27 The inset of Fig. 4(a) shows the results for the sample with the 0.8 nm CoFeB layer, which cannot be fitted linearly. This nonlinearity probably originates from the fact that the 0.8 nm thick CoFeB film becomes discontinuous, and the magnetization is not saturated in the film plane, i.e., there exists a distribution of magnetization angles in the film relative to the applied field direction.²⁹ 

We next show the results for the samples annealed at 250 °C for 0.5 h in a vacuum environment. After annealing, the samples with t_CoFeB $≥$ 1.2 nm show an in-plane magnetic anisotropy, and the samples with t_CoFeB = 1.0 and 1.1 nm show a perpendicular magnetic anisotropy, determined by the anomalous Hall measurement (not shown here). For the samples with in-plane magnetic anisotropy, the ST-FMR spectra are similar to those of the as-grown samples. However, the spectra of the perpendicularly magnetized samples are significantly different from those of the in-plane samples. In the spectra of the perpendicularly magnetized samples, additional peaks are observed as shown in Fig. 5(a). Therefore, the resonance frequency dependence on the resonant field exhibits an additional low field branch, which cannot be simply fitted by the Kittel equation. The emergence of this additional branch in the perpendicularly magnetized samples is because the magnetization is not aligned with the external magnetic field as the magnitudes of the fields are below the alignment field (⁠$HaFMR$⁠).²⁹ We analyze the experimental results using the previously derived FMR condition^29,30

where W_x and W_y are the stiffness fields for the system with the first and second orders of PMA, respectively, that are defined as^29–31 

where H, H₁, and H₂ are the external magnetic field, the first order and second order anisotropy fields, respectively, θ is the polar angles of the magnetization M with respect to the z-axis. The magnetic free energy density for the system can be described as^29–32 

The first term is the Zeeman energy, and the last two terms are the first and second order PMA terms. The equilibrium value of θ could be calculated by minimizing the free energy. By using Equations (5)–(7) to fit the frequency dependencies of the resonant fields for the samples with 1.1 nm and 1.0 nm CoFeB layer, as displayed in Fig. 5(b), $μ0$H₁ values are determined to be −199.80 ± 0.07 mT and −166.88 ± 0.02 mT, and $μ0$H₂ values are found to be 0.98 ± 0.01 mT, and 1.26 ± 0.01 mT. The effective magnetization fields can be further calculated to be $4πMeff=μ0H1+12μ0H2$⁠, as shown in Fig. 5(c). Here, the alignment field, $HaFMR$⁠, is approximately equal to the absolute value of H₁. For H > $HaFMR$⁠, M is tilted to in-plane by the external field, and the ST-FMR signal, in this case, is similar to that of the sample with in-plane anisotropy. The 4πM_eff for both as-grown and annealed samples is shown in Fig. 5(c). For samples with t_CoFeB ≥ 1.2 nm, the values of 4πM_eff for annealed samples are smaller than those without annealing, revealing enhanced interfacial PMA after annealing. For very thin CoFeB layers, the signs of 4πM_eff change from positive to negative, indicating that the anisotropy field of the system changes from in-plane to out-of-plane.

Fig. 6(a) shows the frequency dependence of the ST-FMR linewidths for the annealed samples. For t_CoFeB ≥ 1.2 nm, the Δ-f curve still meets a linear relationship. For thinner CoFeB layers (t_CoFeB = 1.0 and 1.1 nm), the ST-FMR linewidths of the resonance peaks at H > $HaFMR$ exhibit large inhomogeneous broadening, which may be associated with spatial variations in the magnetic anisotropy and interfacial pinning of magnetic moments.^29,33 The α for both of the as-grown and the annealed samples with thicker CoFeB layers are plotted as a function of CoFeB thickness in Fig. 6(b). The similar feature demonstrates that the Gilbert damping is almost independent of the annealing effects in thick CoFeB layers.

In conclusion, we investigated the magnetic properties of W/CoFeB/MgO structures by using the ST-FMR technique based on a large SMR effect. The measurements were carried out on both the as-grown and the annealed samples with the different CoFeB layer thicknesses. We extracted the thickness-dependent effective anisotropy fields and damping constants by analyzing the ST-FMR spectra. A non-aligned resonance mode emerges for the annealed samples with thinner CoFeB layers, which have a perpendicular magnetic anisotropy. The observed low-frequency FMR mode has been rarely reported in the previous work, which hints that the ST-FMR technique utilizing SMR may have advantages. For the ST-FMR technique, the resonance signal is measured electrically through detecting the rectified magnetoresistance voltage due to the mixing of the I_rf and the R_rf. Therefore, the ST-FMR method is scalable to investigate the small size samples. Furthermore, SMR is more dependent on the spin-dependent scattering at the interface, which makes it less dependent on the film thickness. As a result, the ST-FMR measurement utilizing the SMR effect may have advantages for studying the magnetic properties of ultrathin ferromagnetic films or surface ferromagnetism.

This work was supported in part by C-SPIN and FAME, two of the six centers of STARnet, a Semiconductor Research Corporation program, sponsored by MARCO and DARPA. This work was also supported by the National Science Foundation (ECCS 1611570) and Nanosystems Engineering Research Center for Translational Applications of Nanoscale Multiferroic Systems (TANMS) Cooperative Agreement Award No. EEC-1160504. We would like to acknowledge the collaboration of this research with the King Abdul-Aziz City for Science and Technology (KACST) via The Center of Excellence for Green Nanotechnologies (CEGN). This work acknowledges the support by the Spins and Heat in Nanoscale Electronic Systems (SHINES), an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award No. SC0012670.