Magnetic vortex dynamics can be generated in spin-valve (SV) multilayers when a spin-polarized current flows through a nanocontact (NC) 1–6. A highly non-uniform magnetic state, as the one of a vortex, can be formed in the SV free magnetic layer (FL) due to the current-induced, circular Oersted field (HOe) at the NC vicinity and can be driven into a dynamic, sub-GHz, gyroscopic precession under the spin-torque-transfer (STT) influence 1. This phenomenon can be applied to create tuneable, high frequency (HF) nano-devices.
In this Letter we investigate the influence of the FL and of the NC diameter on the magnetization dynamics in SV elements employing an unpinned artificial antiferromagnet (AAF) as polarizing (fixed) layer. The in- vestigated NCs have a rather large diameter and the measurements are conducted at zero or very weak in-plane applied magnetic fields. Under these conditions it is expected that strongly inhomogeneous, vortex-related, magnetization excitations can occur. The experimental results are discussed in the context of the available theoretical models.
The NCs were fabricated on top of SV mesas, 100 × 100 µm2 in size, of the multilayer sequence: MgO(5)/Ru(30)/Co70Fe30(3)/Ru(0.8)/Co70Fe30(2.2)/Cu(5)/ FL/Ta(2)/Ru(2.5). The subscripts stand for compositions in atomic percent and the layer thickness denoted in parentheses, in nm. The fabrication and measurement setup details are presented elsewhere 6. As FL we employ either an amorphous Co40Fe40B20(2.5) or a Co70Fe30(1)/ Co40Fe40B20(2.5) bilayer. The devices investigated here have NC radii, r, ranging from 40–130 nm (±10 nm). The radius values have been extracted from scanning electron microscopy (SEM) images (see inset in Fig. 1(c)).
The total device resistance, Rt ranges from 10 Ω to 20 Ω and is given by the sum of the electrode resistance, Rel and the NC resistance, Rnc. From the fitting of Rt versus r we extract Rel ≈ 9 Ω. Characteristic easy-axis magnetization switching loops of the devices are presented in Fig. 1(a), measured at low current, I (∼1 mA). Both stacks show clear switching between parallel (P) and antiparallel (AP) states for all realized radii. The NCs in Fig. 1(a) present a giant magnetoresistance (GMR) of ΔR = 35 mΩ for the CoFeB FL and 65 mΩ for the CoFe/CoFeB FL, respectively. The switching field (HS) of the CoFeB FL is 2–3 times smaller than the one of the CoFe/CoFeB FL.
In Fig. 1(b) two typical dV /dI versus I curves are presented for a r = 85 nm CoFeB and a r = 65 nm CoFe/ CoFeB contact. Negative current corresponds to electrons flowing from the free towards the fixed magnetic layer. The typical parabolic Joule heating contribution has been subtracted from the raw data. Both measurements show, for negative current polarity, a similar sequence of resistance features, but of different amplitude. The dynamic resistance change is ΔRdyn = 7 mΩ for the CoFeB NC, i.e. only 20% of the total GMR. On the other hand, the resistance change for the CoFe/CoFeB NC corresponds to the full GMR amplitude. This means that the current induces an inhomogeneous magnetization state in the CoFeB NC, whereas the magnetization of the CoFe/CoFeB FL under the NC has switched completely to a uniform state. Excitation spectra in the sub-GHz regime, as the ones shown in Fig. 1(c) and attributed to vortex dynamics could only be measured for the CoFeB stack and only for negative current polarity, where the FL magnetization is excited by spin-polarized electrons reflected from the fixed magnetic layer. This is in accordance to other experimental findings 5, 10 and theoretical predictions in the Refs. 8, 11. The upward dV /dI jump for increasing |I | (Fig. 1(b)) marks the excitation onset. In the way back, the excitation collapses almost at the same current (see dashed lines in Fig. 1(b)). For the CoFe/CoFeB NCs, where a complete magnetization switching is assumed to have taken place, no excitation could be observed for frequencies (f) between 0.1 GHz and 18 GHz, for |I | up to 45 mA and applied fields up to the FL switching field. This shows that a pre-requirement for magnetic excitations is the establishment of a non-uniform magnetic state in the FL, which is fulfilled only in the case of the CoFeB NC.
Additionally for the CoFeB FL, no excitation was observed for r > 100 nm. This result is in agreement with 7 where, for NC radii above 100 nm, the Oersted field contribution is expected to be much stronger than the STT force, prohibiting any STT-driven oscillation. Figure 2 presents characteristic power spectra for r between 40 nm and 100 nm, at zero applied field. For some NCs two spectral peaks can be clearly distinguished that are not harmonically correlated (see Fig. 2(d)). This particularity of our system was already underlined in our previous publication 6, where it was evidenced for hard axis, in-plane fields.
All spectra show a quasi-linear correlation between f and I. This is in qualitative agreement with models for vortex excitation in NCs 8, 9. We note here that in 3, 4 and 10 the presence of excitation is hysteretic with the current, i.e. the vortex has to be nucleated at a high current and then it persists for decreasing current much below the nucleation threshold. In our case, the nucleation current is particularly low and almost coincides with the current where the excitation collapses (Fig. 1(b)). As a result, an excitation spectrum is determined by the current amplitude and is practically independent of whether the current is increasing or decreasing, in accordance with the predictions of Ref. 9. Further, the excitation is located within a current window, where the dV /dI (I) curve is not hysteretic. Figure 3 summarizes the main results at 0 Oe. In Fig. 3(a) the excitation onset current, I0, is found to scale linearly with r2, i.e. the dynamics are initiated at a constant current density of j0= 6.5 × 1011 A/m2, as extracted from the linear fit of I0 versus r2. Open symbols in the graphs correspond to excitation modes appearing in pair, as the one in Fig. 2(d). Not only I0 but also the current corresponding to the maximum excitation power, IPM, shows a quasi-linear dependence on r2 (Fig. 3(b)), i.e. to achieve maximum power, a defined current density is required, in this case jPM= 8 × 1011 A/m2, irrespective of the NC size. On the other hand, the maximum power is not emanated at the same frequency, fPM, for all NCs. Indeed, fPM decreases with the NC radius, as shown in Fig. 3(c). Also the slope, df /dI, decreases with r (Fig. 3(d)). This disagrees with Ref. 8, where df /dI is predicted to be independent of the NC radius.
Another important aspect is the appearance of multiple oscillation modes for NC radii between 75 nm and 85 nm. The relative amplitude and position of these modes in the I –f space changes with the application of small, in-plane magnetic fields. In our previous work 6 we have demonstrated such mode metastability for hard axis, in-plane fields. In Fig. 4(a)–(c) we show a similar effect for easy axis fields.
In the spectra obtained at H = –20 Oe and 0 Oe, two modes are clearly distinguished. These merged into one at H = +20 Oe. The existence of multiple localized modes has been predicted by Berkov and Gorn 9 as a demonstration of the strongly inhomogeneous and spatially extended magnetic configurations in these relatively large NCs. The influence of the easy-axis (EA) field on the excitation characteristics can only be observed in the vicinity of HS. The frequency at specific current, fI, increases with the application of negative fields (favors AP alignment) and decreases for positive fields (favors P alignment). In Fig. 4(d)–(h) we present the dependence of the frequency on the EA magnetic field for different NCs. Slopes varying between –0.2 MHz/Oe and –1.5 MHz/Oe are extracted. Different slopes represent different degrees of uniformity in the vortex-like magnetization profile since the force exercised by the external field depends on the magnetic state uniformity.
The maximum power spectra density value of the devices at zero field is in the order of several nV2/Hz and is correlated with the ΔR value of the element. Close to HS the PSD can increase over 250 nV2/Hz. The linewidth ranges between 4 MHz and 48 MHz. The smallest linewidth is found at Pmax, here the dynamics is expected to become less sensitive to thermal fluctuations in frequency and amplitude 6.
In summary, we have investigated the size and magnetic free layer dependence of the vortex dynamics in relatively large spin-valve NCs, incorporating an unpinned AAF. STT induced switching was observed for both CoFeB and CoFe/CoFeB FLs but only the first showed sub-GHz vortex excitation for r ≤ 100 nm. The excitation onset current as well as the current at maximum power scale with the NC area, while the excitation frequency and its slope decrease with increasing NC radius. The strongly inhomogeneous magnetic state in these large NCs at small magnetic fields is demonstrated by the appearance of multiple excitation modes, the frequency of which can be manipulated by small easy axis magnetic fields.