Colloquium: Hidden order, superconductivity, and magnetism: The unsolved case ofURu2Si2

Abstract

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...

Single Crystal Growth of URu2Si2 by the Modified Bridgman Technique

“…Single-crystal X-ray diffraction measurements revealed the expected ThCr 2 Si 2 type structure with lattice constants a U = 4.133 (3) Å and c U = 9.58 (1) Å and a Th = 4.189 (2) Å and c Th = 9.745 (6) Å for URu 2 Si 2 and ThCr 2 Si 2 , respectively. These values are similar to those reported earlier [1][2][3][4]16,26]. For both materials, the direction perpendicular to the crystal surface is the c-axis, in agreement with earlier results from molten indium flux growth of URu 2 Si 2 ( Figure 1f) [16].…”

“…χ(T) shows pronounced anisotropy where the c-axis is the easy axis, which is characteristic of the paramagnetism in URu 2 Si 2 [3,4]. The inverse magnetic susceptibility χ −1 reveals a Curie-Weiss temperature dependence χ(T) = C/(T−θ), and a fit to the data yields µ eff = 3.72 µ B and θ = −90.5 K. Near T coh,Ø ≈ 55 K, χ(T) evolves through a broad hump that may be associated with the onset of Kondo coherence [1][2][3][4]. At the "hidden-order" temperature T 0 , χ(T) is abruptly reduced.…”

“…Research into URu 2 Si 2 has been fueled by interest in an unusual amalgam of phenomena that are believed to originate from a blend of local and itinerant electron behavior, including a peculiar non-magnetic low temperature broken symmetry state ("hidden order"), for which the order parameter has yet to be identified [1][2][3][4]. The fact that it also hosts unconventional superconductivity makes this material even more attractive.…”

Unusual Magnetic Field-Dependence of the Electronic Dispersion Relations in a Hidden Ordered Phase.

“…Despite the intensive investigation that followed its discovery nearly thirty years ago, the nature of the order parameter is still unknown. The phase is now known as a Hidden Ordered Phase [7]. Recently, Okazaki et al have measured the magnetic susceptibility [8] of ultra-small samples using highly sensitive magnetic torque measurements and have reported that, below the transition, the susceptibility becomes anisotropic in the a − b plane.…”

SCES2013 Summary: Experiment

“…During the past 25 years, virtually every imaginable experimental technique has been applied in attempts to reveal the nature of this state, but its origin remains an open question. [28,29] The coupling of 'something' to charge degrees of freedom clearly opens a gap in the electronic spectrum below 17.5 K, but the unanswered question is what is that 'something' The development of significantly improved resolution in angle-resolved photoemission spectroscopy and the application of new resonant x-ray and scanning tunneling techniques, among others, are ruling out some of the many theoretical suggestions for its origin and maybe are giving clues to what it might be. Perhaps, the answer lies in the simultaneous coupling among multiple degrees of freedom that compete or cooperate in such a way that the coupling to a single degree of freedom is not dominant.…”