Nonreciprocal behavior of the spin pumping in ultra-thin film of CoFeB

Since semiconductor based charge devices are approaching their fundamental limit,^1–3 there have been tremendous efforts on development of emerging technologies.^4,5 One promising candidate is spintronic devices that utilize both charge and spin of electrons for data storage and processing.^6–8 Spin pumping is a mechanism where nonequilibrium spin polarized electrons are injected from a magnetic layer into a nonmagnetic material in direct contact with the magnetic layer due to the dynamical magnetization state.^9–11 Spin pumping is free from the impedance mismatch of the magnetic and nonmagnetic layers and has been successfully demonstrated in nonmagnetic metallic layers,^11–14 semiconductors,^15,16 and recently in topological insulators.^17,18 Injected spin current is usually detected through the inverse spin Hall effect (ISHE) of the nonmagnetic layer that translates the spin current into a charge current. Recently, there has been a proposal of spin logic device based on the spin pumping.¹⁹ This proposal utilizes the spin torque oscillator (STO) for the local magnetizations excitation and spin injection. Nonreciprocal behavior of spin waves has been previously reported.^20–22 Since spin waves could potentially have a significant contribution to the spin pumping signal,²³ it is expected that spin pumping also demonstrates nonreciprocity effect for opposite magnetizations directions. Knowing that the spin pumping signal is already rectified by the ISHE, it is more appropriate for logic applications compared to the spin waves based logic devices.²⁰ 

In this letter, we have systematically investigated the spin pumping nonreciprocal behavior in Ta/Co₂₀Fe₆₀B₂₀ structure for different thicknesses of the CoFeB layer. Magnetization dynamics is excited in the CoFeB layer using an asymmetric coplanar waveguide. A microwave sinusoidal voltage is applied to the coplanar waveguide and the output dc-voltage is measured while the frequency/magnetic field has been swept. It is found that by reduction of the CoFeB thickness from 10 nm down to 1.6 nm, the nonreciprocity factor, which is the ratio of the spin pumping output signal at opposite magnetic field polarities, is doubled.

The optical micrograph of the fabricated device is given in Fig. 1. Initially, MgO (3 nm)/CoFeB (x nm)/Ta (3 nm) has sputtered deposited on a Si/SiO₂ (100 nm) substrate. The thickness of the CoFeB is varied from 10 nm down to 1 nm. An ultra-high vacuum (UHV) six-target Shamrock sputtering system with an in-situ ion-milling source has been used for the multilayer deposition. Photolithography with negative tone resist ma-N2403 has been utilized to pattern ferromagnetic regions followed by argon ion milling of the film. In order to isolate the film structure from the coplanar waveguide, 30 nm of SiO₂ has been deposited using an e-beam evaporator. After patterning the waveguides and contacts, Ta (3 nm)/Cu (100 nm)/Pd (5 nm) has been deposited, followed by lift-off of the resist. The samples have field-annealed in a vacuum system with a base pressure of less than 1 × 10⁻⁶Torr and a temperature of 300 °C. A magnetic field of 0.4 T is applied in x-direction during the annealing. Vibrating sample magnetometer characterization of unpatterned thin film sample shows that the CoFeB film becomes fully perpendicular for the CoFeB film less than 1.6 nm. Since ISHE signal will be lost for the perpendicular magnetic films, only the spin pumping results for the film down to 1.6 nm are presented.

The dimension of the CoFeB layer in Fig. 1 is 620 × 310 μm² and the asymmetric coplanar waveguide is of GS-form with a signal (S) line of 15 μm, a ground (G) line of 45 μm, and the spacing between the G and S is about 15 μm. A microwave signal generated by a 20 GHz Agilent microwave generator is injected into the waveguide and the output dc-voltage is measured using a Keithley 2182A Nanovoltmeter. During the measurement, a magnetic field is applied in y-direction and by sweeping the frequency of the microwave generator, the output voltage is tested at each frequency. A 3D schematic of the device structure is shown in the inset of Fig. 1.

The spin-orbit interaction is responsible for the ISHE—a process that converts a spin current into an electric voltage (charge current). Heavy metals like Pt and Ta have strong spin-orbit interaction and allow observation of ISHE at room temperature. The electric field induced by the ISHE can be written as^11,24 $EISHE∝Js×σ$ where J_s is the spin current injected from CoFeB into Ta and σ is the spin polarization vector of the spin current defined by the bias magnetic field. The spin current is generated due to the spin pumping at the ferromagnetic and nonmagnetic material interface.

The output spin pumping signal spectra characterized by the nanovoltmeter for the bias fields of ±400 Oe and CoFeB thickness of 1.6 nm are presented in Fig. 2(a). The spin pumping signal is expected to have a form of the symmetric Lorentzian function. Usually, there are contributions from the anisotropic magnetoresistance (AMR) and/or the anomalous Hall effect (AHE) of the magnetic layer (CoFeB) in the output voltage. Both AMR and AHE have the form of asymmetric Lorentzian functions and can be isolated from the output signal.^11,17,25 By fitting the experimental spectra to the form $V=VSPΔf2Δf2+(f−fr)2+VAsymΔf(f−fr)Δf2+(f−fr)2$⁠, the symmetric and asymmetric components are extracted where f_r is the resonant field and Δf is the linewidth of the spin pumping signal. By changing the polarity of the magnetic field, the polarity of the output dc-voltage altered which is in line with the inverse spin Hall characteristics.^26,27 However, in contrast to the previous reports of the spin pumping, the spin pumping at positive fields has more than two times larger amplitude than the negative field. The frequency spectra of the output dc-voltage at magnetic fields of ±200, ±400, and ±600 are shown in Fig. 2(b). As can be seen, by increasing the bias magnetic field, the frequency of the peak position of the ISHE induced voltage is shifted toward the higher frequency which is consistent with the frequency response of a ferromagnetic resonance (FMR)¹¹ and the output voltage polarity is opposite for ±magnetic fields.

We have also studied the effect of the microwave excitation power on the output dc-voltage. As seen in Fig. 2(c), by increasing the excitation signal amplitude from 1 V to 3 V at a constant bias field of 200 Oe, the output voltage amplitude increases from 1.6 μV to 18 μV while the peak position remains constant. In Fig. 2(d), the output voltage amplitude of the spin pumping signal (symmetric component) is plotted as a function of the excitation power. As seen, by increasing the excitation power, the output signal increases linearly, which is consistent with the previous reports.^11,12

We also have studied the effect of the CoFeB thickness on the spin pumping signal. The frequency spectra of the output dc-voltage for 1.6, 1.8, 2.0, 3.0, and 10 nm thicknesses of the CoFeB films at a bias field of 130 Oe are given in Fig. 3(a). By shrinking the thickness of the CoFeB from 10 nm down to 1.6 nm, the spin pumping peak frequency red shifted from 6 GHz to 0.6 GHz. For the devices with thickness of CoFeB less than 1.6 nm, we could not observe any ISHE induced dc-voltage at the output. It is well known that ultrathin film of CoFeB can obtain a perpendicular magnetic configuration in MgO/CoFeB/Ta sandwich due to the strong interfacial anisotropy.²⁸ Hence, the red shift in the frequency of the spin pumping peak position is due to the strong perpendicular anisotropy of the CoFeB that reduces the effective demagnetization field. We further performed the measurement at different magnetic fields for various thicknesses of the CoFeB in MgO/CoFeB/Ta sandwich. The spin pumping frequency as a function of the magnetic field is shown in Fig. 3(b). It is clear that by reducing the thickness of the CoFeB from 10 nm down to 1.6 nm, the spin pumping frequency shows a red-shift behavior. Furthermore, the dependence of the frequency over the magnetic field changes from a quadratic to a linear behavior. In order to understand the field dependence of the spin pumping frequency, one can utilize the modified Kittel formula

where γ is the gyromagnetic ratio, H_k is the anisotropy field, and M_eff is the effective saturation magnetization. Effective saturation magnetization can be written as $4πMeff=4πMs−Hik$ where H_ik is the interfacial perpendicular anisotropy field.

Furthermore, the ferromagnetic line-width can be written as¹¹ 

in which α is the Gilbert damping constant of the ferromagnetic material. Since the interfacial anisotropy is inversely proportional to the thickness of the film,²⁹ H_ik is small for a thick film of CoFeB; therefore, in a small magnetic field where H ≪ 4πM_s, we have $f∝(H+Hk)(4πMs)$ and the frequency has a quadratic behavior relative to the magnetic field. For ultrathin film of the CoFeB, the interfacial anisotropy is significant and comparable to the demagnetization field (⁠$4πMs≃Hik$⁠); therefore, Eq. (1) can be simplified to $f∝(H+Hk)$ where the spin pumping frequency has a linear dependence with respect to the magnetic field.

By curve fitting of Eq. (1) over the experimental results, γ, H_k, and H_ik for different thicknesses of the CoFeB film can be estimated. The anisotropy field H_k is found to be about 33 Oe for CoFeB (10 nm) and it drops to 12.5 Oe in CoFeB (1.6 nm) sample. The resultant curve fitting data are presented in Fig. 3(b) and a good match between the experimental and curve fitting data is observed. The damping constant of the CoFeB thin film is found to be about 0.015, 0.025, 0.035, 0.078, and 0.14 for the thicknesses of 10, 3, 2, 1.8, and 1.6 nm, respectively. As can be seen, at the transition from inplane to the perpendicular thickness, the CoFeB obtains its maximum damping constant which is consistent with previous FMR characterization.³⁰ The asymmetric component of Lorentzian output signal increases at very low thickness of CoFeB. Knowing that the asymmetric component of Lorentzian output signal is correlated to AMR/AHE signal, it seems that the AMR/PHE signal of CoFeB changes for ultra-thin film of CoFeB. This is expected due to the decrease of effective saturation magnetization and increase of effective spin orbit coupling of the magnetic layer. This is evident from the increase of the damping constant of CoFeB upon reduction of the CoFeB thickness. Detailed study of how the film thickness modifies the asymmetric Lorentzian component of the spin pumping signal is out of the scope of this study.

As mentioned above, in our experiment the spin pumping shows nonreciprocal behavior for ±magnetic field where the spin pumping at positive field has much larger amplitude compared to the spin pumping at the negative bias magnetic field with the same amplitude. The spin pumping nonreciprocity, A, is defined as the ratio of the peak amplitude of the spin pumping at positive field, V_P+(H), to the negative field, V_P+(H), such that $A=VP+(H)VP−(H)$⁠. It should be mentioned that only the symmetric component of the output signal is considered in the calculation of the spin pumping nonreciprocity factor. As seen in Fig. 4(a), the nonreciprocity of the spin pumping is almost independent of the bias magnetic field amplitude but is very different for different thicknesses of the CoFeB film. The spin pumping nonreciprocity factor is calculated from the experimental results for different thicknesses of the CoFeB films as demonstrated in Fig. 4(b). Interestingly, by shrinking the thickness of the CoFeB film from 10 nm down to 1.6 nm, the nonreciprocity of the spin pumping increases by more than 100%. As seen in Fig. 4(b), upon reduction of the magnetic layer thickness, the nonreciprocal behavior of the spin pumping single increases. From Fig. 3(b), it is concluded that upon reduction of the magnetic layer thickness, interfacial perpendicular magnetic anisotropy partially compensates the demagnetization field. Since the geometry of the waveguide and device are the same for all the samples, we believe the reduction of the effective demagnetization field is responsible for the nonreciprocal behavior of the spin waves.

The nonreciprocal behavior of the spin pumping signal might be understood in the context of spin waves contribution to the spin pumping. In our recent work, we reported on the relative contribution of spin waves and FMR to the spin pumping signal.²³ It is found that upon changing the magnetic field from almost zero up to 600 Oe, the ratio of the spin waves to FMR contribution changes from about 0.8 up to 1 indicating that this ratio almost field independent. Since the nonreciprocity factor presented in Fig. 4(a) also shows very weak field dependence, it is consistent with the assumption that spin waves are responsible for the nonreciprocity of the spin pumping signal. Considering the nonreciprocal behavior of the surface spin waves,²⁰ the nonreciprocal behavior of the spin pumping could be attributed to the nonreciprocal behavior of its spin waves contribution.

It is well known that surface spin waves demonstrate nonreciprocal behavior for opposite magnetic field polarities.^31,32 In a thick magnetic layer like most of the experiments on yttrium iron garnet (YIG),^33,34 the surface spin waves propagating on the top and bottom surfaces are decoupled from each due to the evanescent decay of the spin waves inside the thin film. Since the top and bottom surface usually are different due to the adjacent layer or the film quality, the spin waves propagating on the top and bottom surfaces have different amplitude. Moreover, due to the nature of surface spin wave, spin waves propagating on the top and bottom surfaces have opposite wavevectors. On the other hand, in a thin metallic layer line NiFe or CoFeB, magnetizations at each cross section of the thin film precess coherently. In thin metallic film, the origin of the surface spin wave nonreciprocal behavior is asymmetric excitation of the spin waves.^20–22 

The magnetic field due to the current passing through the waveguide has H_x and H_z components as presented in Fig. 5. The Karlqvist equation describes the magnetic field as²⁰ 

in which W is the width of coplanar waveguide, and H₀ = I/(2 W) where I is the current passing through the waveguide. As seen, the x-component of the excitation field is unipolar and is concentrated underneath of the waveguide, while the z-component changes its sign near the edges of the coplanar waveguide.

The spin waves excited by the z-component of the Oersted field are out of phase in left and right sides of the waveguide. The z-component of Oersted field is responsible for the nonreciprocal behavior of the surface spin waves.^20,22 By reduction of the magnetic layer thickness, the demagnetization field reduces due to the enhancement of the interfacial perpendicular anisotropy; thus, the spin waves launched by the z-component of the rf-field are improved. This is because the z-component of the rf-field generated by the coplanar waveguide now could modulate the z-component of the magnetization at a larger extent and the precession cone angle of the spin waves increases. This could explain the reason that the maximum nonreciprocity factor is obtained for the thin CoFeB film.

Based on the above discussion, only the nonreciprocal behavior of the surface spin waves could explain the nonreciprocal behavior of the spin pumping signal. However, according to Fig. 1, the device geometry is symmetric with respect to the waveguide. Since the spin waves propagation length is quite short in the Ta/CoFeB (<10 μm),¹¹ the spin waves nonreciprocal contribution to the output signal should be negligible. Dzyaloshinskii-Moriya interaction (DMI) at the Ta/CoFeB interface is the key mechanism that holds the nonreciprocity of the spin pumping signal and even amplifies the spin waves nonreciprocal behavior. DMI effect at the Ta/CoFeB interface generates an asymmetric behavior for the spin waves that is only a function of the spin wave wavevector direction.^35–37 This asymmetric behavior operates on both the frequency and amplitude of the spin waves. Due to the DMI effect, spin waves propagating toward ±x-directions in Fig. 5 have different attenuation length which is not a function of the in-plane component of the magnetization. This nonreciprocal behavior of the spin waves does not average out and creates a difference between the amplitude of the injected spin current for opposite magnetic field polarities, thus results to a difference in the amplitude of the spin pumping signal. However, separation of the intrinsic spin waves nonreciprocity from the extrinsic effect generated by DMI requires further investigation and is out of scope of this study. It should be pointed out that the geometry of the waveguide (GS form) is not responsible for the nonreciprocal behavior of the spin pumping signal. In our previous report for Ta/CoFeB (10 nm),¹¹ a similar waveguide in the GS form was utilized and no nonreciprocal behavior was observed. Moreover, the waveguide geometries are the same in all the samples; thus, any possible contribution from the waveguide shape is the same in all the samples.

In summary, we have carried out spin pumping experiments in Ta/CoFeB/MgO tri-layers structures for different thicknesses of CoFeB. It is found that the injected spin current shows nonreciprocal behavior for opposite magnetic field polarities. The nonreciprocity can be enhanced upon reduction of the magnetic film thickness. Considering that spin pumping can be performed on a magnetic film of about 1 nm and is free from the impedance mismatch, our experimental results suggest that spin pumping is an excellent candidate for efficient spin injection into different nonmagnetic materials at ultra-low energy. Moreover, there is a potential for the utilization of the spin pumping nonreciprocal behavior in spin based logic devices.

Authors would like to thank Dr. K. J. Lee for fruitful discussion on the experimental results.

This work was partially supported by the National Science Foundation Nanoelectronics Beyond 2020 (Grant No. NSF NEB 1124831), NSF MRSEC Program at University of Minnesota (Grant No. DMR-0819885), and by the C-SPIN center, one of six STARnet program research centers. A portion of this work was carried out in the Minnesota Nano Center.