Influence of MgO barrier quality on spin-transfer torque in magnetic tunnel junctions

Magnetic tunnel junction (MTJ) based spin torque nano-oscillators (STNOs) can generate^1–3 and detect⁴ radio-frequency (RF) signals for wireless communication using the concept of spin transfer torque (STT).^5,6 The RF signal from the STNO is generated by the precession of the free layer magnetization, which is caused by the transfer of angular momentum by the spin-polarized current from the fixed ferromagnetic layer.⁷ The spin transfer torque has an in-plane (IP) component (⁠$τ∥$⁠) predicted by Slonczewski⁵ and Berger⁶ and a perpendicular or out-of-plane (OOP) torque (⁠$τ⊥$⁠), generally referred as the field-like torque (FLT), as predicted later by Zhang et al.⁸ The magnitude of the FLT is challenging to measure due to several experimental artifacts that may affect the measurements.^1,9–13 It is also equally difficult to calculate the bias dependence of FLT, and reported theoretical works predict both quadratic^14,15 and linear dependences¹⁶ of the FLT on the bias voltage.

The experimentally measured magnitude of FLT was found to be small in metallic systems such as spin valves^17–19 but much larger (∼40% to ∼50%) of the in-plane STT in MTJs,^20,21 where it significantly affects the magnetization dynamics. FLT also affects the synchronization and modulation phenomena in STNOs.^22–24 Despite significant experimental progress, there exists a controversy about the bias dependence of FLT in MTJ-STNOs, with results so far disagreeing both qualitatively and quantitatively.^1,9–13,25

Possible reasons for this controversy could be the different barrier quality of the MTJ used by various groups. In general, the thin insulating barriers of the MTJ are susceptible to degradation and breakdown with the presence of pinholes which might result in a decrease in the tunneling magnetoresistance (MR) ratio. Especially, it is known that there can be reduction in the MR ratio due to the presence of pinholes,^26,27 which are the source of higher resonance non-uniform modes and can change the dynamics in MTJ based devices.²⁸ Pinholes might short the interface between two CoFeB/MgO interfaces. The diffusion of boron into the MgO barrier also influences the pinhole creation.²⁹ Skowroński et al.³⁰ discussed the influence of the MgO tunnel barrier thickness on the spin torque ferromagnetic resonance (STFMR) signals and torques in MTJ-STNO devices. They found that the in-plane and perpendicular spin torques do not depend on the MgO barrier thickness, in agreement with the free electron model for in-plane torque.³¹ However, the bias dependence of torques in MTJs with the same barrier thickness but a different MR ratio is not yet explored.

In this work, we present a study of the bias voltage dependence of spin torkance (the derivative of spin torque with respect to bias voltage) as a function of the MR ratio. We use the field-modulated spin torque ferromagnetic resonance (FM-STFMR) technique^32,33 to estimate and compare the spin torque for three different devices. The FM-STFMR curve shows a better signal-to-noise ratio (SNR) and the presence of some low power modes, which were not even detected in the commonly employed radio-frequency modulated (RFM)-STFMR method.^10,11 We show that the out-of-plane (OOP) torkance in our devices is an order of magnitude smaller than the in-plane (IP) torkance. The OOP torkance decreases slightly with the MR ratio, while the IP torkance shows a strong dependence on the MR ratio and hence the barrier quality.

The layer structure of MTJ devices is the same as in our previous works,^34–38 and it consists of IrMn (5)/CoFe (2.1)/Ru (0.81)/CoFe (1)/CoFeB (1.5)/MgO (1)/CoFeB (3.5) (thicknesses in nm), where the composite CoFe/CoFeB represents the reference layer (RL), and the top CoFeB layer is the free layer (FL). The MTJs were prepared on AlTiC substrates using an Anelva C7100 magnetron sputtering system. The samples were annealed in the presence of a high field at $250 °C$⁠. The samples were then patterned using deep ultraviolet photolithography and ion milling into circular nanpillars.² We use the convention that a positive current corresponds to electrons flowing from the reference layer (RL) to the free layer (FL). The devices have a circular cross-section with an approximate diameter of 180 nm and a resistance-area product of 1.5 Ω (μm)². The direction of equilibrium magnetization of the reference layer is taken along the positive x-axis with $θ=0°$⁠, where θ is the in-plane field angle. The magnetization of FL is antiparallel to the RL magnetization at zero field. The FL magnetization can be coherently rotated with the external applied field for $θ=140°–220°$ so that the field angle is equal to the angle between the FL and RL.³⁵ All measurements were performed at room temperature. We apply a direct current (I) and a microwave current (I_rf) with frequency f_rf = 2–10 GHz, simultaneously through a bias-tee to the MTJ device. The injected RF power was fixed at −10 dBm. We discuss the results from three devices with MR ratios of 60%, 67%, and 73%, presumably due to different barrier qualities and pinholes present in the MgO-CoFeB interfaces. These devices were prepared under the same conditions. Figure 1(a) shows the magnetoresistance (MR) plots of the MTJ resistance versus in-plane magnetic field applied (H_app) along $θ=180°$ measured at room temperature. Apart from differences in the MR value, the coercivity and the interlayer exchange coupling fields are also different for the three devices. The differences in coercivity indicate different domain structures of the FL. Figure 1(b) shows the variation of resistance drop $[ΔRdc=R(I=0 mA)−R(I≠0 mA)]$ vs. dc bias voltage. Previous studies suggest various mechanisms behind this resistance drop with bias current or voltage, e.g., spin excitations localized at the interfaces,³⁹ the energy dependence in the electronic band structure of the magnetic electrodes,^40,41 and the presence of defect states within the tunnel barrier.^42,43 The difference in ΔR_dc for the three devices is likely due to different possible mechanisms.

In STFMR measurements, a dc voltage is produced as a result of mixing of the microwave current with the resistance oscillations (R_ac) generated by the dynamical response of the STNO. A common way of improving the signal-to-noise ratio (SNR) in STFMR^10,11 experiments is to use a lock-in technique, in which the injected RF signal is amplitude modulated and dc mixing voltage is measured across a lock-in amplifier. We will refer to this method as RF-modulated STFMR (RFM-STFMR). However, we found that the RFM-STFMR method is not very sensitive and leads to a frequency-dependent non-magnetic background in the STFMR spectra, which require significant post-processing of data. To overcome this problem, we have used the field modulated spin torque ferromagnetic resonance method (FM-STFMR) method.^32,33 We modulated the static magnetic field by a small ac field of ∼5 Oe which is produced by a pair of Helmholtz coils. The reference frequency (98 Hz) is supplied to the coils from a lock-in amplifier, where the spin-torque diode voltage (V_mix) is also measured. The RF current I_rf and the direct current I excite the free layer magnetization and cause resistance oscillations. A dc voltage is detected across the lock-in amplifier as a result of mixing between microwave current and resistance oscillations.

Figure 2 shows the FM-STFMR spectra for three different devices with varying dc bias voltages measured with a magnetic field of 300 Oe applied along $θ=185°$⁠. The full FM-STFMR spectra were obtained by sweeping the frequency. The FM-STFMR measures the derivative signal. Hence, the antisymmetric shape of FM-STFMR curves as seen from Fig. 2 implies a symmetric line-shape in the commonly used RFM-STFMR method. The FM-STFMR method eliminates frequency-dependent background signals of the non-magnetic origin and shows the presence of several low-power modes, which were not even detected in the RFM-STFMR method. The frequency of eigenmodes at the same H_app = 300 Oe is different due to different inter-layer exchange coupling, resulted from the varying barrier heights and barrier qualities. The device with higher MR, i.e., 73%, shows a strong single resonance mode. However, higher-order magnetic resonances are excited at higher currents for the 67% and 60% MR devices. Because these higher-order resonances have more nodal lines than the fundamental FMR, it would be difficult to excite them with just a uniform current, and non-uniform (arising, e.g., from pinholes) currents may be better at exciting these modes.

By modeling the dependence of this voltage on the applied microwave frequency, one can extract information about the resonance frequency, linewidth, and magnitude of the spin torques. In the case of RFM-STFMR, the detected voltage V_mix(f) is given as¹⁰ 

where $C=14∂2V∂I2Irf2$ is the non-resonant background, (I_rf) is the RF current, $S(f)=11+(f−fr)2/σr2$ is the symmetric Lorentzian, $A(f)=(f−fr)σr1+(f−fr)2/σr2$ is the anti-symmetric Lorentzian, f_r is the resonance frequency, and σ_r is the spectral linewidth. The amplitudes of Lorentzian V_s and V_a are functions of spin-torque vectors

and

where $ℏ=h2π$ is the reduced Planck's constant, e is the electronic charge, $V=πr2t$ is the volume of the free layer, where r and t are the radius and thickness of the free layer, respectively, and $Ω⊥=γ(4πMeff+Happ)2πfr$⁠. $dVdI$ is the differential resistance, θ is the in-plane field angle, and $4πMeff$ is an effective magnetic anisotropy.

In FM-STFMR, the measured voltage signal is equivalent to the first derivative of the rectified root mean square (RMS) voltage signal, V_mix(f), i.e., $BmdVmix(f)dB$⁠,³² where B_m is the RMS amplitude of the modulated field. Hence, the measured experimental FM-STFMR spectra are fitted with the derivative of Eq. (1) [see Eq. (1) of Ref. 32] using B_m = 5 Oe. The fitted FM-STFMR spectra are shown in Figs. 2(a)–2(c), where fittings are shown by red solid lines. For the multi-modes shown in Figs. 2(b) and 2(c), Eq. (1) is modified by adding additional symmetric and antisymmetric functions for each mode. From the fitting of symmetric V_s and anti-symmetric V_a coefficients, resonance frequency (f_r) and the linewidth (σ_r) are extracted. For multi-modes, we have used the coefficient of symmetric and antisymmetric functions of the main mode only, i.e., the mode having maximum peak-to-peak voltage. The IP and OOP torkance were calculated from V_s and V_a using the following parameters: $ℏ=1.054×10−34 J s$⁠, e = 1.6 × 10⁻¹⁹C, M_s = 1000 emu/cc, r = 90 × 10⁻⁹m, t = 3.5 × 10⁻⁹m, and 4 π M_eff = 11 kOe.

The bias dependences of IP and OOP torkances are shown in Figs. 3(a) and 3(b), respectively. Figure 3(a) shows that IP torkance depends strongly on the bias voltage. The magnitude of STT is higher for higher MR devices. However, the OOP torkance is almost constant for all the devices, which implies a linear dependence of OOP torque on the bias voltage, which is consistent with our previous works.^13,34 In our previous work, we qualitatively predict the linear OOP torque from the frequency versus bias current. Furthermore, the linear dependence of OOP torque on bias voltage is consistent with other works^9,44 but inconsistent with other works.^10,11 Also, the magnitude of OOP torkance is two orders of magnitude below the magnitude of IP torkance, in contrast to previous works.^20,21 The OOP torkance also shows a change in its sign at higher bias. We also observe this behavior in other low MR devices (<65%), and it is because of the sign change in the antisymmetric amplitude (V_a) at higher bias. We believe that the origin of this is related to the second-order term in the field-like torque which appears as a linear term in torkance.

We further analyzed the OOP torkance by fitting the effective OOP-STT field b_J. Using the simple model as in Ref. 34, the lowest FMR resonance frequency can be expressed as

Here, N_x (N_y) is an effective demagnetizing factor along the x (y) direction parallel to the direction of the applied field, H_IEC is an effective field on the FL arising from the interlayer coupling between the FL and RL, and H_d is an effective out-of-plane demagnetizing field. We estimate H_IEC from the loop-shifts in Fig. 1(a) to be 130, 135, and 108 Oe for the 73%, 67%, and 60% MTJs, respectively. Fitting the FMR frequency at zero bias gives $(Ny−Nx)Ms$ equal to 10, 10, and 30 Oe for the three MTJs, and (assuming that the magnetic properties of the FL in the three MTJs are the same) H_d − N_xM_s = 9350 Oe for the three junctions, in reasonable agreement with $4πMeff=11$ kOe from the OOP torkance. The FMR frequencies as a function of bias current can then be fitted as shown in Fig. 4, assuming a linear dependence of b_J for the 73% and 67% MR MTJs (b_J ≈ aI, with a = 0.83 and 1.57 Oe/mA, respectively) but a quadratic behavior for the 60% MTJ: b_J ≈ aI + bI² with a = 0.3 Oe/mA and b = 0.3 Oe/(mA)². The FMR frequencies depend sensitively on H_IEC. Therefore, under the assumption that the FL is very similar in the three devices, the FMR frequency for the MR = 60% devices is the largest as this device has the smallest loop shift and H_IEC. The OOP torkance is proportional to $dbJ/dV=d/(dV)(aI+bI2)$⁠, where b is non-zero only for the MR = 60% MTJ. Inserting $R=R(V)=R0(1−ΔrV)$ [Fig. 1(b)], we get to first order in V that $dbJ/dV≈a/R0+(2aΔr/R0+2b/R02)V$⁠. The constant term a is related to spin mixing arising in the dynamics of the spin diffusion,¹⁶ while $Δr$ accounts for the voltage-dependent decrease in the MTJ resistance.^39–43 The almost constant OOP torkance for the 73% and 67% MR devices is related to the smallness of $ΔrV<0.2$⁠, while for the 60% MR device, the term $b/R0$ dominates over the term $aΔr$⁠.

Using the free electron model for elastic tunneling in symmetric MTJs, the IP torkance is predicted as^10,31

where $(dIdV)∥$ is the differential conductance in the parallel state and P is the spin polarization of the tunneling current in the junction. According to Julliere's model, the spin polarization is related to the MR as⁴⁵ $MR=2P1P21−P1P2$⁠. Here, $P1=P2=P$ as our MTJs have symmetric junctions. Using this expression, we calculate P ≈ 0.52 for the device with MR = 73%. Using the parallel conductance for our device as $133 Ω$⁠, we calculated $dτ∥/dV sin θ$ to be equal to $0.0124 ℏ2eΩ−1$⁠. From Fig. 3(a), we found the absolute value of $dτ∥/dV sin θ$ to be $0.011ℏ2eΩ−1$ at zero bias, which is in good agreement with the above calculated value. However, for other two devices, the measured torkance at zero bias shows a much lower value than the expected torkance from Eq. (5). This disagreement might be related to inelastic tunneling due to pinholes, which tend to decrease the torkance due to elastic tunneling and results in lower in-plane spin torkance. However, FLT is not significantly affected by the barrier quality.

In conclusion, we report the results from three devices with MRs of 60%, 67%, and 73% due to different barrier qualities. We find that the bias dependence of torques depends on the MR ratio, and this could be the reason for reported different behaviors of torques as functions of bias voltage, especially the field-like torque. FM-STFMR shows a much better sensitivity than the conventional RFM-STFMR used by other groups. We observed that with decreasing MR, multiple resonant modes are seen, which can be ascribed to asymmetric modes originating from inhomogeneous magnetization precession in the FL due to non-uniform currents (arising, e.g., from pinholes). We found that the quality of the barrier certainly has an effect on the in-plane torkance, and larger MR means larger efficiency in spin-symmetric injection, which should lead to larger in-plane spin transfer torque. Our results show the presence of a much smaller OOP than IP torkance, with field-like spin torque almost linear in bias voltage.

The partial support by the Department of Science and Technology, India, under Fast-Track Scheme, and Indo-French Centre for the Promotion of Advanced Research, India, under Project No. 5604-3, is gratefully acknowledged. The support from the Swedish Foundation for Strategic Research (SSF) and the Swedish Research Council (VR) is gratefully acknowledged. D.T. acknowledges support from University Grant Commission, India. R.S. acknowledges support from the Ministry of Human Resource Development (MHRD), India, and the work by O.G.H. was funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences Division of Materials Sciences and Engineering.