Shortly after the seminal paper "Self-Organized Criticality: An explanation of 1/f noise" by Bak et al. (1987), the idea has been applied to solar physics, in "Avalanches and the Distribution of Solar Flares" by Lu and Hamilton (1991). In the following years, an inspiring cross-fertilization from complexity theory to solar and astrophysics took place, where the SOC concept was initially applied to solar flares, stellar flares, and magnetospheric substorms, and later extended to the radiation belt, the heliosphere, lunar craters, the asteroid belt, the Saturn ring, pulsar glitches, soft X-ray repeaters, blazars, black-hole objects, cosmic rays, and boson clouds. The application of SOC concepts has been performed by numerical cellular automaton simulations, by analytical calculations of statistical (powerlaw-like) distributions based on physical scaling laws, and by observational tests of theoretically predicted size distributions and waiting time distributions. Attempts have been undertaken to import physical models into the numerical SOC toy models, such as the discretization of magneto-hydrodynamics (MHD) processes. The novel applications stimulated also vigorous debates about the discrimination between SOC models, SOC-like, and non-SOC processes, such as phase transitions, turbulence, random-walk diffusion, percolation, branching processes, network theory, chaos theory, fractality, multi-scale, and other complexity phenomena. We review SOC studies from the last 25 years and highlight new trends, open questions, and future challenges, as discussed during two recent ISSI workshops on this theme
In this work we present electrical resistivity, magnetic susceptibility, and electron spin resonance data at high temperature of the Sr 2 FeMoO 6 double perovskite. We found between 300 K and 900 K two metalinsulator transition temperatures at T c Ϸ405 K and Ϸ590 K respectively. Below the first transition, the material is metallic and magnetically ordered. Above 590 K, shows a metallic behavior again, while in the range 405 KрTр590 K we observed a weak localization. The magnetic susceptibility can be described taking into account localized and itinerant electrons. The paramagnetic resonance of Fe 3ϩ ions with gϭ2.009(5) can be studied in temperature. Above T c the linewidth data present similar behavior to that of manganese perovskites, with a relaxation mechanism related to spin-spin interactions. The intensity of the resonance line decreases with T faster than a Curie law expected, due to a reduction in the number of localized spins of the Fe 3ϩ ions. At high temperatures (Tу520 K͒ we observe a second paramagnetic resonance line with gϭ1.995(1) associated with a small amount of Mo 5ϩ ions.
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