1/f thermally excited noise in asymmetric oscillators

Many physical systems and devices operate in a (quasi)static regime in contact with a thermal bath, which leads to fluctuating oscillations around the energy minimum. For linear systems, the spectrum of these oscillations replicates the resonance curve of a damped oscillator [1]. In particular, power spectral density grows monotonically with frequency in the low frequency range, until reaching a maximum at the resonant frequency. Small sizes of contemporary magneto-resistive readers and other MEMS/NEMS devices pushes oscillations to non-linear regimes, which may lead to resonance line broadening, bifurcations, etc. [2]. However, non-linearity does not change the monotonicity of thermal fluctuations in the low frequency range, until the energy profile is symmetric around the minimum. Asymmetry of the energy profile around the stable point leads to low frequency thermal noise, with 1/f-like spectral profile. This phenomenon results in M-shape low frequency noise dependence vs magnetic field in magnetic tunneling readers [3]. This provides the motivation for the detailed study about the relationship between low frequency noise and asymmetric oscillations presented below. In magneto-resistive readers, it has been shown that the magnetic precession can be described in term of a 1D damped oscillator [4]. This serves as the primary basis for this investigation. 5 GHz asymmetric oscillators (which is the typical resonant frequency for the reader free layer) in contact with a thermal bath is analyzed using the Langevin equation. Potential energy profiles were generated using bi-harmonic and skew normal approximations [5], providing the ability to generate symmetric and asymmetric potentials using a single adjustable parameter. Asymmetric oscillations will introduce a DC shift, but the presence of random fluctuations in this asymmetric potential produces a broadening of the DC frequency spike leading to a pronounced 1/f-like low-frequency shape to the spectral density. Fig.1 depicts the simulated oscillation spectra for the bi-harmonic oscillator potential and shows the increasing power spectral density at low frequencies as asymmetry is introduced. In order to further characterize the nature of this 1/f-like low frequency noise profile, the time domain signal for the asymmetric oscillator was decomposed into low and high frequency components as shown in Fig. 2a. Fig. 2b shows the two dimensional histogram of the low frequency noise and the high frequency instantaneous amplitude. The strong correlation seen confirms that the 1/f-like low frequency noise originates from the fluctuations of the asymmetric oscillations. This model demonstrates a new mechanism of 1/f noise generation, which in many practical cases have been classified as being of unknown origin [6]. Experimental evidence for this behavior in the context of magnetic tunnel junction readers used in magnetic recording has been reported as well [7].