Memory effect and generation-recombination noise of magnetic monopoles in spin ice

Abstract

We theoretically investigate the generation-recombination processes of magnetic monopoles in spin ices. We calculate the spectrum of the relative fluctuations of the numbers of pairs of magnetic monopoles, directly related to that measurable of the magnetic flux noise, using the Langevin approach, previously proposed. Measurements of spectral density of magnetic-flux noise, recently, gave an experimental confirmation of our theoretical results. The agreement with the experimental results is obtained by suggesting a model for the total spectrum of relative fluctuations, which consists in superimposing the spectra of a set of generation-recombination processes, characterized by dierent time constants and a given probability density function.

Field-Induced Magnetic Monopole Plasma in Artificial Spin Ice

“…Per the fluctuation-dissipation theorem, the corresponding noise spectrum then exhibits a Lorentzian lineshape (β = 2) and is said to be Brownian. Noise exhibiting β = 2 therefore implies simple diffusive Brownian kinetics, such as from a trivial random walk with independent increments, or from monopole creation and annihilation models described, e.g., by Ryzhkin [24] and Klyuev [25]. In contrast, noise exhibiting β < 2 indicates kinetics that cannot be described by a single exponential time scale [26].…”

“…In particular, when temporal fluctuations are no longer independent but instead exhibit negative correlations (e.g., if prior fluctuations increased the magnetization, then the next fluctuation is more likely to decrease it), then monopoles will exhibit sub-diffusive behavior. Such processes are related to "fractional" Brownian motion [27] and can be said to retain a memory [25]. Noise following Eq.…”

New trends in nonequilibrium statistical mechanics: classical and quantum systems

“…The out-of-equilibrium aspects of single strands in a DNA folding hairpin structure and the main features of DNA G4 thermal and mechanical stability have been analyzed in [82,83]. Finally, in the paper [84] the generation-recombination processes of magnetic monopoles in spin ices have been theoretically investigated. Interestingly, the measurements of the spectral density of the magnetic flux noise in reference [85] gave experimental confirmation of the theoretical results obtained by the authors in [84].…”

The color of magnetic monopole noise

“…While recent studies have concentrated on the relaxation time [17,18,21,22] and on variations of the power intensity under temperature and field [18], the anomalous color of the noise has perhaps not been properly appreciated.…”

“…Linear approximations then necessarily lead to a Lorentzian power spectrum, or β = 2 in (1), i.e., brown (or Brownian) noise. To color the noise, Klyuev et al [22] had postulated a continuous superposition of different Brownian spectra, an idea that dates back to early attempts at explaining pink flickering in triodes [23]. In more recent times, however, an evolving framework spanning from quantitative finance to complex systems to biology has tied colored noise to memory, incremental (anti)correlations, fractional Brownian motion [24][25][26][27], and anomalous diffusion for a broad phenomenology of random walks on disordered substrates, percolation clusters, fractals, etc.…”