A comparison between advanced time–frequency analyses of non-stationary magnetization dynamics in spin-torque oscillators
Introduction
It has been discovered how a spin-polarized current flowing throw a nanomagnet can excite several different types of magnetization dynamics [1], [2]. Such phenomenon has powered research on the applied spintronic technology which have been studied extensively both theoretically and experimentally [3], [4], [5], [6], [7]. Frequency [3] and time [7] domain measurements of magnetoresistance signal show strong non-linear and non-stationary behavior, for instance transition between static magnetic states and different steady-state precessions characterized by uniform and non-uniform magnetization patterns. In addition, the frequency, the linewidth, and the microwave output power of the precessions show strong dependence on external field and current [8], [9].
In particular, exchange bias nanoscale spin-valves with a Py-free layer (Py=Ni80Fe20) of elliptical cross-sectional area exhibit dynamics with series of frequency jumps, as function of bias current, between stationary nonlinear modes with different spatial distribution [10], [11].
As can be noted, those measurements also show a non-stationary magnetization dynamics related to nanosecond switching between a dynamical mode and a static magnetic configuration or between different dynamical modes [11]. In the latter case, this non-stationary regime is characterized by a spectrum with two well-defined peaks in frequency, and it is observed before that large-amplitude magnetic precession is excited [10].
In [12], we demonstrated how a continuous wavelet analysis (WA) is able to systematically reveal the non-stationary regime of experimental time-domain data [11]. We also predicted that, by combining micromagnetic simulations and WA, the excited modes of a spin-torque oscillator (STO) show together to a frequency modulation [13] a nanosecond intermittent disappearing and reappearing of the instantaneous microwave output power. In our present work, we introduce the use of the HHT (Hilbert–Huang Transform) in order to extract these modal components.
Concerning the same kind of devices, experimental data published in Ref. [11] show that non-stationary magnetization dynamics is driven before of the large-amplitude magnetization precession. In particular, for I=4.5 mA and H=600 Oe, the power spectrum of the real-time voltage signal (for a signal of 20 ns see Fig. 6(e) in Ref. [11]), captured via microwave single-shot storage-oscilloscope at which frequency jumps have been observed as shown in Fig. 6(a) of Ref. [11], reveals two excited modes P1 and P2 (where and ). The origin of such dynamics has been studied in our previous work [11] and a tool for computing the MWS (Micromagnetic Wavelet Scalogram) has been presented to systematically give information of the excitations in the time–frequency space.
In the present work, we propose the use of an emerging technique in order to extract independent modal information from the time domain signal. Our technique applied to the voltage signal of the STO demonstrates that can completely characterize the origin of the excited modes, furnishing information which is complementary to the one of the WA.
Section snippets
Description of the experimental setup
The experimental framework is the same as depicted in Ref. [10] and is composed by a magnetic multilayer consisting of Cu (80 nm)/Ir20Mn80 (8 nm)/Py (4 nm)/Cu (8 nm)/Py (4 nm)/Cu (20 nm)/Pt (30 nm) onto an oxidized Si wafer (Py=Ni80Fe20). Measurements are shown in the voltage trace of Fig. 6(c) of Ref. [11] and have been performed under the bias conditions (applied current I=4.5 mA and under H=600 Oe), while the sampling frequency was 20 GHz.
Wavelet analysis
In our study, in order to identify the non-stationary behavior of the STO, we adopted the Wavelet-based method developed in Ref. [14], in particular we computed the MWS of , using , with as the scale set dimension for the wavelet transform. The use of this WA allows to characterize a signal in the time–frequency space and to study eventual non-stationary behaviors.
Hilbert–Huang transform
HHT [15], [16] is a recently developed method which has proven successful in the study of the
Combined wavelet and HHT-based analysis
Fig. 1(a) shows the time trace of the voltage signal for a nanosecond window of 0–20 ns as in Fig. 6(c) of Ref. [11], whereas in the inset displays its normalized Fourier spectrum (equivalent to the plot in Fig. 6(e) of Ref. [11]) where the two peaks P1 and P2 (fP1=3.9 GHz and fP2≈4.6 GHz) can be identified, indicating the excitation of two modes for a wide nanosecond interval. The intensities of the two peaks are of the same order, suggesting that the excited modes are independent components
Conclusions
We studied spin wave dynamics excited in STOs through different analysis techniques. By means of the WA, we are able to enlighten the existence of time windows where either only one mode is excited or the absence of excitation. Simultaneous existence of the two modes is not detected indicating their non-stationary origin. The key results of this paper are the use of HHT to efficiently decompose and identify the time traces associated to each of these components. The tool we developed supports
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