Line Shape Distortion in a Nonlinear Auto-Oscillator Near Generation Threshold: Application to Spin-Torque Nano-Oscillators

Abstract

The lineshape in an auto-oscillator with a large nonlinear frequency shift in the presence of thermal noise is calculated. Near the generation threshold, this lineshape becomes strongly non-Lorentzian, broadened, and asymmetric. A Lorentzian lineshape is recovered far below and far above threshold, which suggests that lineshape distortions provide a signature of the generation threshold. The theory developed adequately describes the observed behavior of a strongly nonlinear spin-torque nano-oscillator.PACS numbers: 75.30.Ds, 75.40.Gb, 05.10.Gg Thermal noise plays a key role in the dynamics of autooscillatory systems, especially for the nano-sized systems in which the characteristic energy of auto-oscillation is comparable with the thermal noise energy k B T . One important consequence of noise is the broadening of the power spectrum. It is well-established, for example, that white Gaussian noise leads to a broadened Lorentzian shape of the power spectrum both far below and far above the generation threshold in conventional auto-oscillators (for which the frequency is weakly dependent on the amplitude) [1]. In addition, the presence of noise also blurs the threshold between the damped and auto-oscillatory states.In the immediate vicinity of the auto-oscillation threshold, a non-Lorentzian spectrum appears: the lineshape can be described by a sum of several Lorentzian profiles corresponding to several simultaneously excited statistical modes. These modes have the same central frequency for a conventional auto-oscillator and, therefore, the contributions of higher-order modes do not lead to large qualitative changes in the overall spectral line profile [1]. In contrast, the central frequencies of the partial Lorentzian profiles are shifted in frequency by different amounts in a nonlinear auto-oscillator in which the frequency is strongly dependent on the amplitude. In the vicinity of the auto-oscillation threshold at which these shifts are of the order of the oscillation linewidth, the frequency nonlinearity leads to important qualitative changes in the lineshape: the spectral line is asymmetric and significantly broadened.An example of an auto-oscillating system with strong frequency nonlinearity is the spin-torque nano-oscillator (STNO), which is of considerable interest at present. This oscillator consists of two ("free" and "fixed") ferromagnetic layers separated by a nonmagnetic (metallic or dielectric) spacer. When driven by a spin-polarized direct current, an effective negative damping results in the "free" layer due to the spin-transfer effect [2,3].For a sufficiently large direct current, the induced negative damping overcomes the natural positive damping of the "free" layer, and auto-oscillations of magnetization of this layer result [4,5,6]. These and related phenomena are subjects of intensive research at present due to their possible applications in microwave nano-electronics.In this Letter, we present a theory of lineshape distortion in auto-oscillators with a strong nonlinear frequency shift in t...

Linewidth of higher harmonics in a nonisochronous auto-oscillator: Application to spin-torque nano-oscillators

“…lasers) are isochronous, in a sense that their auto-oscillation frequency is independent of the amplitude, but there is an important class of non-isochronous auto-oscillators where generated frequencies depend on the auto-oscillation amplitude [3][4][5]. For example, the human heart, all the auto-oscillators exploiting ferromagnetic resonance and, in particular, the recently developed spin-torque nano-oscillators (STNO) [3][4][5][6][7][8][9][10][11] belong to this class.…”

“…In contrast with [2], in the case of a non-isochronous auto-oscillator [3] the shape of the generation line becomes non-Lorentzian [6], and the phase variance of the main frequency is a non-linear function of τ (see Eq. in [5]):…”

“…A relevant example of a non-isochronous autooscillator that currently attracts a lot of attention from researchers is the STNO [3][4][5][6][7][8][9][10][11]. For STNOs multiharmonic spectra of the steady-state oscillations were observed both in experiment and in simulations [11,17].…”

Coupling Efficiency for Phase Locking of a Spin Transfer Nano-Oscillator to a Microwave Current

“…Among them, a strong interest of spin transfer effects is the observation of a steady precession of a magnetization, generating a microwave power due to the magnetoresistive response of the devices [3,4,5]. Numerous efforts were made to understand the microwave emission under magnetic field and current bias in a single spin transfer nanooscillator (STNO) [6,7,8,9,10,11]. Most of the characteristics presently observed in STNOs are indeed very attractive for future applications in telecommunication devices.…”

Measurement of nonlinear frequency shift coefficient in spin-torque oscillators based on MgO tunnel junctions

“…On the black line shown in Fig. 1, the frequency nonlinearity vanishes (the nonlinearity due to the demagnetizing effect cancels out that due to the in-plane anisotropy), where remarkable reduction of linewidth is expected 12,14,15 .To estimate the value of ν from experiment, we have used the spectrum analysis method based on the theories of spectrum linewidth of STO under thermal fluctuations 7,8,9,10,11,12 . The method is similar to the one often used to measure the linewidth enhancement factor (α-factor) in lasers 16 .…”