Dragon-kings: mechanisms, statistical methods and empirical evidence

This introductory article presents the special Discussion and Debate volume "From black swans to dragon-kings, is there life beyond power laws?" published in Eur. Phys. J. Special Topics in May 2012. We summarize and put in perspective the contributions into three main themes: (i) mechanisms for dragon-kings, (ii) detection of dragon-kings and statistical tests and (iii) empirical evidence in a large variety of natural and social systems. Overall, we are pleased to witness significant advances both in the introduction and clarification of underlying mechanisms and in the development of novel efficient tests that demonstrate clear evidence for the presence of dragon-kings in many systems. However, this positive view should be balanced by the fact that this remains a very delicate and difficult field, if only due to the scarcity of data as well as the extraordinary important implications with respect to hazard assessment, risk control and predictability.Comment: 20 page

The ground state of metallic nano-structures in heavily irradiated NaCl–KBF4

ESR, NMR and static magnetic susceptibility measurements of heavily irradiated NaCl–K and NaCl–KBF4 are reported. Up to 10% of the NaCl-molecules are transformed into metallic Na nanoparticles and Cl2 precipitates. In addition, there are paramagnetic F- and F-aggregates, which are coupled by exchange interactions to the conduction electrons in the nanoparticles. Above 160 K the NMR and ESR signals of NaCl–K and NaCl–KBF4 show Pauli paramagnetism and the properties of the Na nanoparticles are similar to bulk sodium. A single ESR line is observed revealing exchange interaction between conduction electrons in the nano-particles and F-aggregates. The observed decrease of the ESR susceptibility with decreasing temperature is due to a metal-insulator transition. The conduction electrons are localized below 40K and the above mentioned F-aggregate centers contribute significantly to the overall ESR signal. For NaCl–KBF4 we observed that with decreasing temperature the ESR line shifts towards lower fields due to antiferromagnetic ordering and internal magnetic fields.

Metal–insulator and magnetic transitions in heavily irradiated NaCl–KBF4

We have performed electron spin resonance (ESR), nuclear magnetic resonance (NMR) and static magnetic susceptibility measurements on heavily irradiated NaCl–KBF4 single crystals in the temperature range 4.2 < T < 350 K. In these samples, up to about 10% of the NaCl molecules are transformed into extremely small metallic Na particles and Cl2 precipitates. At high temperatures a one-line ESR signal, i.e. common mode due to strong exchange interaction between conduction electrons and F-aggregate centres, is observed. We propose that the smooth decrease of the ESR spin susceptibility with decreasing temperature, which can be as large as 50%, is due to a metal–insulator transition, taking place at about 40 K. In the same temperature range, the linewidth increases by 18±2 G with decreasing temperature. This anomalous broadening is explained by a reduction of the exchange narrowing at low temperatures. NMR spin–lattice relaxation on 23Na shows a Korringa-type behaviour down to 10 K, which suggests that the conducting phase in heavily irradiated NaCl–KBF4 behaves as a three-dimensional metal. SQUID experiments have revealed antiferromagnetic ordering at 40 K and a ferromagnetic phase below 20 K. The nature of the observed effects is discussed.

Electron spin resonance and nuclear magnetic resonance of sodium macrostructures in strongly irradiated NaCl–K crystals: Manifestation of quasi-one-dimensional behavior of electrons

Data from an investigation of electron spin resonance and nuclear magnetic resonance of NaCl–K (~1 mole%) crystals strongly irradiated with electrons imply the observation of a metal-insulator transition with decreasing temperature and the manifestation of quasi-one-dimensional electron motion in sodium macrostructures.

Formation of the sodium 1-D structures in doped NaCl by high energy electron irradiation

An investigation of the formation and properties of linear sodium structures in electron-irradiated potassium doped NaCl crystals was carried out by means of electron spin resonance (ESR) and nuclear magnetic resonance (NMR). It has been found that the behavior of ESR and NMR signals depends on the dose and temperature. The most interesting properties were observed in heavily irradiated samples. The magnetic spin susceptibility determined by ESR signal intensity showed temperature insensitive Pauli paramagnetism at high temperature and then decreased below 160 K, indicating metal-insulator transition (MIT). The nuclear spin-lattice relaxation rate T1^-1 showed a remarkable (root) frequency dependence, which is due to the one-dimensional diffusive motion of electrons. The influence of some impurities on the formation of microstructures has been studied too and the nature of the MIT at low temperatures in heavily irradiated NaCl:K crystals is discussed.