This Colloquium reviews the 25 year quest for understanding the continuous (2 nd ) order, meanfield-like phase transition occurring at 17.5 K in URu 2 Si 2 . Since ca. ten years the term hidden order (HO) has been coined and utilized to describe the unknown ordered state, whose origin cannot be disclosed by conventional solid-state probes, such as x-rays, neutrons, or muons. HO is able to support superconductivity at lower temperatures (Tc ≈ 1.5 K) and when magnetism is developed with increasing pressure both the HO and the superconductivity are destroyed. Other ways of probing the HO are via Rh-doping and very large magnetic fields. During the last few years a variety of advanced techniques have been tested to probe the HO state and their attempts will be summarized. A digest of recent theoretical developments is also included. It is the objective of this survey to shed additional light on the HO state and its associated phases in other materials.
VII. Present State of HO 12Acknowledgments 16 References 17Figures 21
I. HISTORICAL BACKGROUNDUranium is a most intriguing element, not only in itself but also as a basis for forming a variety of compounds and alloys with unconventional or puzzling physics properties (for recent reviews, see Sechovský and Havela (1998), Santini et al. (1999), Stewart (2006)). Natural or depleted uranium, i.e. containing 99.5 percent 238 U has a * Electronic address: mydosh@physics.leidenuniv.nl † Electronic address: peter.oppeneer@physics.uu.se mild alpha radioactivity of 25 kBq/g, which allows Ubased samples to be fabricated and studied in university laboratories with a minimum of safety precautions. Following initial discoveries of unexpected superconductivity and heavy-fermion behavior in uranium-based compounds as UBe 13 (Ott et al., 1983) and UPt 3 (Stewart et al., 1984) it has become popular to synthesize uranium compounds and to cool these in search for exotic ground states. Over the past 50 or so years many conducting and insulating systems were synthesized, analyzed and structurally characterized (Sechovský and Havela, 1998;Stewart, 2001Stewart, , 2006. The usual classification of the metallic samples at low temperature is superconducting and/or magnetic or with some of the modern compounds designated as "exotic" (Pfleiderer, 2009).Why are uranium-based materials so interesting? The observed variety of unusual behaviors derive directly from the U open 5f shell. Several defining electronic structure quantities of the U f electrons are all on the same energy scale: the exchange interaction, 5f bandwidth, the spin-orbit interaction, and intra-atomic f − f Coulomb interaction. As a consequence, i) elemental uranium displays intermediate behavior between the transition metals and the rare-earths in their characteristic bandwidths, yet it generates the largest spin-orbit coupling. ii) U lies directly on the border between localized and itinerant (or overlapping) 5f wavefunctions. iii) The WignerSeitz radii R WS of comparative elements places U near the minimum between metallic and...
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