Saturation of VCMA in out-of-plane magnetized CoFeB/MgO/CoFeB magnetic tunnel junctions

Control and manipulation of magnetic moments is one of the central themes of research in spintronics which uses the moments in various practical devices, e.g. to retain data in magnetic memory applications. For instance, the spin-transfer torque (STT) phenomenon^1–3 offers unprecedented spatial and temporal control in random access memory (STT-RAM) devices based on magnetic tunnel junctions (MTJs). Today, voltage controlled magnetic anisotropy (VCMA)^4–9 attracts considerable attention as a novel method to control and manipulate magnetizations in low power and fast switching MTJs.

Ferromagnetic resonance (FMR) is a standard spectroscopic technique which is used to probe anisotropies in magnetic materials. Here we use FMR to probe magnetodynamics in CoFeB/MgO/CoFeB MTJ pillars which allows us to quantify the effect of magnetic anisotropies in the MTJs and, in particular, VCMA. Specifically, we evaluated MTJs with perpendicular magnetizations (pMTJs) and large (20 μm) diameters.

The pMTJs were grown at the University of Arizona¹⁰ with the following composition: Ta (6 nm)/Ru (10 nm)/Ta (6 nm)/CoFeB (0.7 nm)/MgO (1.9 n¹m)/CoFeB (1.6 nm)/Ta (10 nm)/Ru (20 nm) and were patterned using optical photolithography into pillars with 20 μm diameter. The MTJ pillars have resistance-area product of 3.8 MΩ·μm² and demonstrate tunneling magnetoresistance (TMR) ratios of about 100% at room temperature.

In our experiments, we apply a magnetic field (up to 270 mT) perpendicular to the MTJ layers and both rf and dc currents using a bias tee (see experimental schematic in Fig. 1a). The maximum dc bias of ±2.1 V (8 mA) results in an electric field developing across the tunneling barrier of ±1.1 V/nm. Amplitude modulated microwaves (20% modulation depth; frequency range from 9-14 GHz) are supplied to the sample from an rf generator. The actual amplitude of rf current across MTJs can be determined by comparing the increase in the MTJ’s resistance produced by Joule heating from the dc and microwave currents. We estimate the rf currents across our large samples to be about 0–4 mA when power output is set to -20–17 dBm at the generator.

When a combined rf and dc bias is applied to the device, the resulting dc voltage across the contact includes V_dc produced by the dc bias and a small rectified V_ω produced by the microwaves. The latter provides a means to probe bias-driven magnetodynamics^{7–9,14–17} as $Vω$ peaks at resonance. We detect dc and rectified (resonance) voltage across MTJs using techniques already described.^3,16,17 At room temperature we have measured the rectified voltage V_ω as a function of an external magnetic field B applied perpendicular to the film plane. Such V_ω(B) spectra were measured at different frequencies and power levels of the applied microwaves and different dc bias currents. The electrical bias is expected to produce an effective VCMA field which acts along the gradient of the potential, i.e. parallel or antiparallel to the applied B (see Fig. 1b). Both shape anisotropy and VCMA can be quantified by their influence on the resonance behavior of the precessing magnetization (see Fig. 1c).

Figure 2a shows a representative V_ω(B) FMR spectrum. FMR (peak in V_ω) of the free layer is clearly visible at ±90 mT. The large (off-scale) signal around 20 mT is due to the MTJ being in the antiparallel state. Note that the current density applied to the MTJ is too low to support the excitation of STT-FMR; we thus suggest VCMA as the dominant contributor to the FMR excitation^8,9 in our experiments.

The frequency-field relationship for FMR of the MTJ’s free layer can be modeled by Kittel’s equation. For a perpendicularly magnetized MTJ the equation takes the form:

where γ is the gyromagnetic ratio, B is the applied field, M is the saturation magnetization and K₁ denotes the VCMA energy density modeled as (first order) uniaxial anisotropy.

Figure 2b shows an example of the frequency-field relationship observed in our pMTJ. The grey density plot shows the frequency dependence of the spectrum from Fig. 2a (brighter color indicates larger V_ω). Using Eq. 1 we were able to successfully fit the observed frequency-field relationship (see blue curve in Fig. 2b). When a dc bias is applied, we observe a shift of the resonance field as a function of the voltage. For relatively small voltages (up to 1 V) the shift is linear with respect to the applied bias and can be attributed to the out-of-plane VCMA induced by the dc bias.^{7–9,11–13} By measuring FMR spectra at different dc biases (not shown) we were able to quantify VCMA as we show next.

Figure 3 shows the dependence of the resonance field and VCMA energy density per unit area on the applied voltage bias. Open circles show the experimental values extracted from the bias dependent V_ω(B) spectra (not shown) as in Fig. 2. The increase in data scatter around zero bias is due to a small resonance signal at low biases; the rectified V_ω is proportional to the bias.^8,9,14–17 The linear fit to the data in Fig. 3 gives a slope of 28.5 mT/V for the resonance field which agrees very well with the negative bias region in the work by Miura et al.⁹ and corresponds to a slope of 7.8 μJ/m² for the magnetic anisotropy energy. The observed linear shift is consistent with the VCMA picture based on the bias-induced electron migration across the MgO/CoFeB interface.^11–13 However, other compelling mechanisms have been proposed.^18–22 

It is interesting to compare the above FMR-VCMA results with measurements of bias-dependent coercive field, which are sometimes used to quantify VCMA. Figure 3 shows the coercive field of the free layer (grey symbols; left scale) measured as a function of the applied bias voltage in the same MTJ. These data were extracted from magnetoresistance traces recorded at different applied biases (not shown). The linear fit to the coercive-field data (grey line in Fig. 3) gives a slope of 1.6 mT/V which is about 18 times smaller than the FMR result. We tentatively attribute this difference to the difference between the precession of a saturated magnetic moment and the switching process in a macroscopic (20 μm) multidomain film. The switching process in such a large pillar is likely dominated by the nucleation of magnetic domains which in aggregate seem to be less influenced by the VCMA effective field.

Finally, we have investigated VCMA at extremely high biases (above ±1 V). Figure 4 shows the resonance field and VCMA energy density per unit area (like Fig. 3) for voltages up to 2.1 V. These measurements were performed on a different MTJ (to show reproducibility of our data for different devices). At low biases (below ±1 V) we observed a linear dependence on the applied bias voltage with a slope of 27.1 mT/V for the resonance field and corresponding 7.4 μJ/m² slope for the magnetic anisotropy energy. These numbers are very similar to those in Fig. 3 that corroborates the FMR-VCMA results for different MTJs.

At biases beyond ±1 V we observe deviations from the linear behavior for both positive and negative bias polarities (see Fig. 4). At the highest biases the resonance field seems to saturate. The latter may indicate a saturation of the VCMA effect which could be associated with a saturation of the electron migration^11–13 across the MgO/CoFeB interface at high biases. Some theoretical insight into this process can be found in the work by Zhang et al.²³ who predicted a reduced VCMA at higher electrical biases. Further theoretical work is needed to provide a more quantitative picture of the saturation process in our FMR experiments.

In summary, we investigated voltage controlled magnetic anisotropy (VCMA) in perpendicularly magnetized CoFeB/MgO/CoFeB magnetic tunnel junctions (MTJs) using ferromagnetic resonance (FMR) technique. We observed a shift in the resonance field as a function of the bias voltage applied to MTJ which is linear for low biases (below ∼1V). At higher biases we observed a deviation from the linear behavior which indicates a saturation of the VCMA effect. These results are important for the design of MTJ-based spintronic applications.

This work was supported in part by C-SPIN, one of six centers of STARnet, a Semiconductor Research Corporation program, sponsored by MARCO and DARPA.