Voltage controlled magnetic anisotropy (VCMA) is a novel method to switch magnetizations in low-power and ultra-fast applications based on magnetic tunnel junctions (MTJs). Here we explore the ferromagnetic resonance (FMR) technique to probe VCMA in situations where other methods cannot be applied. We quantify VCMA in CoFeB/MgO/CoFeB MTJ nanopillars with in-plane magnetizations where our FMR method is unique in providing direct information about VCMA. We observe a quadratic shift of the FMR resonance field when a voltage bias is applied across the MTJ. The VCMA energy corresponding to the quadratic shift varies with an energy factor of 8.2μJ/m2 for 1 V2/nm2. These results are important for understanding magnetodynamics in MTJ-based applications with in-plane magnetizations.

Control and manipulation of magnetic moments is the central theme of spintronics research. The goal is to use the moments in various practical devices, e.g. to retain data in magnetic memory applications, like in magnetic random access memory (MRAM) based on magnetic tunnel junctions (MTJs). Voltage controlled magnetic anisotropy (VCMA)1–7 currently attracts considerable attention as a novel method to switch magnetizations in MTJs because of its potential to increase speed and reduce power consumption in such MTJ-based applications.

In many systems, e.g. MTJs with out-of-plane magnetizations, VCMA can be probed experimentally using standard magnetoresistance measurements. By measuring the effective coercive field as a function of the applied voltage the VCMA field can be probed directly because it is parallel/antiparallel to the out-of-plane applied field and simply adds up to the MTJ’s intrinsic coercivity at zero voltage bias.7,8 This simple method, however, cannot be used in MTJs with in-plane magnetizations because the in-plane switching is not controlled by a perpendicular (VCMA) field.9 Instead, the perpendicular anisotropy energy should be deduced from the integral of magnetic hysteresis loop10,11 which quantifies the work done on the material by the applied field. In this work we show that the ferromagnetic resonance (FMR) technique can be used to provide direct information about VCMA in MTJs with in-plane magnetizations.

Our in-plane MTJs are made of CoFeB(2nm)/MgO(0.8nm)/CoFeB(2.4nm)/Ru(0.85nm)/CoFe(2.5nm)/PtMn(15nm) multilayers deposited onto oxidized Si substrates by rf/dc magnetron sputtering at the University of Minnesota,12 and then patterned (E-beam lithography) into pillars with elliptical cross-sections with sizes on the order of 100 nm and aspect ratios of about 2.5.13 The resistance-area products for the MTJs were 4Ωμm2. In total, we tested 25 MTJs. All samples demonstrate typical tunneling magnetoresistances (TMRs) of about 100% at room temperature.

In our experiments, we apply both rf and dc currents to MTJs using a bias tee. The dc bias results in a maximum electric field developing across the tunneling barrier of MTJs of 0.6V/nm. Amplitude modulated microwaves (20% modulation depth; frequency range from 3-14 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 small 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 Vdc produced by the dc bias and a small rectified Vω produced by the microwaves. The latter provides a means to probe bias-driven magnetodynamics3–5,14–17 as |Vω| peaks at resonance. We detect dc and rectified (resonance) voltage across MTJs using techniques already described.16,17 At room temperature we have measured the rectified voltage Vω as a function of an external magnetic field B applied in the plane of the in-plane MTJs. Such Vω(B) spectra were measured at different frequencies and power levels of the applied microwaves and different dc bias currents.

Figure 1a shows a representative Vω(B) spectrum measured at 10 GHz and small dc bias (10 mV) where VCMA is negligible. FMR (dip in Vω) of the free layer is clearly visible at ±100 mT. Other dips/peaks are associated with FMR of the reference MTJ layer and other resonance modes of the free layer as will be described later.

FIG. 1.

(a) Schematic of the experimental setup. (b) The relative orientation of the free-layer magnetization M, applied magnetic field B, and VCMA field. (c) FMR dynamics: the precessional M cone is shown relative to the film plane (xy-plane).

FIG. 1.

(a) Schematic of the experimental setup. (b) The relative orientation of the free-layer magnetization M, applied magnetic field B, and VCMA field. (c) FMR dynamics: the precessional M cone is shown relative to the film plane (xy-plane).

Close modal

The frequency-field relationship for FMR of the MTJ’s free layer can modeled by Kittel’s equation.

f=γ2πBB+M2μ0K1M
(1)

where M is the saturation magnetization and K1 denotes the VCMA energy density modeled as (first order) uniaxial anisotropy.

The grey density plot in Fig. 2b shows the frequency dependence of the spectrum from Fig. 2a (brighter color indicates larger Vω). Using Eq. 1 we were able to successfully fit the first uniform free layer mode (see blue curve in Fig. 2b). The free layer resonance modes (dark features) are concentrated at low fields (±150 mT) while the pinned layer resonances (light features) occur at higher fields (>100 mT). As discussed in the work by Helmer et al.,18 the lowest frequency free layer resonance most likely indicates excitations localized near the edge of the MTJ. The higher free layer resonances represent the first and second uniform free layer resonance, respectively. We can see that at low magnetic fields (<20 mT), where intralayer dipole interactions become more significant the first uniform free layer mode and edge mode merge.

FIG. 2.

(a) FMR Vω(B) spectrum recorded at 10 mV dc bias and 10 GHz rf current (14 dBm). (b) The grey density plot shows FMR spectra at different frequencies (brighter color indicates larger Vω). Solid blue curve is the Kittel’s fit (Eq. 1).

FIG. 2.

(a) FMR Vω(B) spectrum recorded at 10 mV dc bias and 10 GHz rf current (14 dBm). (b) The grey density plot shows FMR spectra at different frequencies (brighter color indicates larger Vω). Solid blue curve is the Kittel’s fit (Eq. 1).

Close modal

We observe a shift of the resonance field as a function of the dc bias applied to the MTJ. Figure 3 shows (a) Vω(B) spectrum measured at constant (10 mV) bias and (b) the bias dependence of this Vω(B) spectrum as a grey density plot (brighter color indicates larger Vω). The shift of the free layer FMR (at around ±100 mT) and of other resonances is obvious. The shift is quadratic with respect to the bias and can be associated with the out-of-plane VCMA induced by the dc bias.19,20

FIG. 3.

(a) Vω(B) spectrum measured at constant (10 mV) bias and (b) the bias dependence of this Vω(B) spectrum as a grey density plot (brighter color indicates larger Vω). The frequency of applied microwaves is 10 GHz (14 dBm).

FIG. 3.

(a) Vω(B) spectrum measured at constant (10 mV) bias and (b) the bias dependence of this Vω(B) spectrum as a grey density plot (brighter color indicates larger Vω). The frequency of applied microwaves is 10 GHz (14 dBm).

Close modal

Figure 4 shows the dc bias dependence of the resonance field and VCMA energy density per unit area extracted from the bias dependent Vω(H) spectra of Fig.3. The observed shift is quadratic with a maximum magnitude of approximately 4μJ/m2 at 0.5 V. The quadratic fit is K1tE=8.2V2+0.9V.

FIG. 4.

Shift of the resonance/coercive field (black/grey symbols; left scale) and the VCMA energy density per unit area (right scale) plotted as a function of applied bias. Solid curve is the quadratic fit.

FIG. 4.

Shift of the resonance/coercive field (black/grey symbols; left scale) and the VCMA energy density per unit area (right scale) plotted as a function of applied bias. Solid curve is the quadratic fit.

Close modal

We note that the FMR shift observed in our experiments with MTJ nanopillars can also be caused by a field-like torque due to the spin-transfer torque (STT) effect. There were previous reports of a quadratic dependence of the field-like torque on bias voltage,21,22 however we observe a shift in the resonance field that is larger by a factor of 5-10. Nevertheless, due to the high current density in our MTJ nanopillars STT and VCMA are likely to be combined.

In summary, we investigated voltage controlled magnetic anisotropy (VCMA) in CoFeB/MgO/CoFeB magnetic tunnel junctions (MTJs) with in-plane magnetizations using ferromagnetic resonance (FMR) technique. We observed a quadratic shift in the resonance field as a function of the bias voltage applied to MTJ. These measurements demonstrate the power of FMR to probe VCMA directly in situations where other methods cannot be used. These results are important for understanding magnetodynamics in MTJs with in-plane magnetizations in the presence of VCMA.

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.

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