This Topical Review describes the multitude of unconventional behaviors in the hidden order, heavy fermion, antiferromagnetic and superconducting phases of the intermetallic compound URu$_2$Si$_2$ when tuned with pressure, magnetic field, and substitutions for all three elements. Such `perturbations' result in a variety of new phases beyond the mysterious hidden order that are only now being slowly understood through a series of state-of-the-science experimentation, along with an array of novel theoretical approaches. Despite all these efforts spanning more than 30 years, hidden order (HO) remains puzzling and non-clarified, and the search continues in 2019 into a fourth decade for its final resolution. Here we attempt to update the present situation of URu$_2$Si$_2$ importing the latest experimental results and theoretical proposals. First, let us consider the pristine compound as a function of temperature and report the recent measurements and models relating to its heavy Fermi liquid crossover, its HO and superconductivity (SC). Recent experiments and theories are surmized that address four-fold symmetry breaking (or nematicity), Isingness and unconventional excitation modes. Second, we review the pressure dependence of URu$_2$Si$_2$ and its transformation to antiferromagnetic long-range order. Next we confront the dramatic high magnetic-field phases requiring fields above 40 T. And finally, we attempt to answer how does random substitutions of other $5f$ elements for U, and $3d$, $4d$, and $5d$ elements for Ru, and even P for Si affect and transform the HO. Commensurately, recent theoretical models are summarized and then related to the intriguing experimental behavior.

Hidden order and beyond: an experimental-theoretical overview of the multifaceted behavior of URu$_2$Si$_2$

The multipole concept, which characterizes the spacial distribution of scalar and vector objects by their angular dependence, has already become widely used in various areas of physics In recent years it has become employed to systematically classify the anisotropic distribution of electrons and magnetization around atoms in solid state materials This has been fuelled by the discovery of several physical phenomena that exhibit unusual higher rank multipole moments, beyond that of the conventional degrees of freedom as charge and magnetic dipole moment Moreover, the higher rank electric/magnetic multipole moments have been suggested as promising order parameters in exotic hidden order phases While the experimental investigations of such anomalous phases have provided encouraging observations of multipolar order, theoretical approaches have developed at a slower pace In particular, a materials' specific theory has been missing The multipole concept has furthermore been recognized as the key quantity which characterizes the resultant configuration of magnetic moments in a cluster of atomic moments This cluster multipole moment has then been introduced as macroscopic order parameter for a noncollinear antiferromagnetic structure in crystals that can explain unusual physical phenomena whose appearance is determined by the magnetic point group symmetry It is the purpose of this review to discuss the recent developments in the first-principles theory investigating multipolar degrees of freedom in condensed matter systems These recent developments exemplify that ab initio electronic structure calculations can unveil detailed insight in the mechanism of physical phenomena caused by the unconventional, multipole degree of freedom

First-principles theory of magnetic multipoles in condensed matter systems

Diffraction Anomalous Fine Structure (DAFS) combines the long-range, crystallographic sensitivity of X-ray diffraction with the short-range sensitivity of X-ray Absorption Spectroscopy (XAS). In comparison to other spectroscopic methods, DAFS can additionally distinguish phases of different translational symmetry by choice of momentum transfer, or isolate spectra from chemically identical atoms on various Wyckoff sites of a crystal's structure using crystallographic weights. The Anisotropy of Anomalous Scattering (AAS) extends the concept of isotropically scattering atoms to a more general case, where the atom's scattering characteristics depend on the polarization as well as the wavevector of the incident and scattered X-rays. These can be written as tensors that reflect the local site symmetries of the resonant atom. Forbidden Reflection Near-Edge Diffraction (FRED) is an elegant way to measure AAS by using reflections that are extinguished in the special case of isotropically scattering atoms. They can only be observed due to the non-isotropic contributions at photon energies in the vicinity of an absorption edge where electronic transitions occur. Combining the site selectivity of DAFS with the information accessible through AAS allows probing the short-range order and local orbitals of selected atoms in a crystal structure of a chosen phase. The present condensed review gives a brief overview on the pioneer work, the theory and sensitivities as well as selected recent applications of these powerful and promising Resonant X-ray Diffraction (RXD) methods. Additionally, some recent work of the authors is included exemplarily for the model structure rutile TiO2 presenting the progress in measurement and interpretation.

Probing a crystal's short‐range structure and local orbitals by Resonant X‐ray Diffraction methods

Resonant Elastic X-Ray Scattering (REXS) has played a fundamental role in understanding electronic properties and in revealing hidden order, local symmetries and exotic states realized in correlated solids This article reports on some of the relevant scientific contributions and technical advances over the last 20 years, by providing a list of related publications produced by various groups all around the world The given perspective is that of a group of young scientists involved at various times in the investigation of the beauty of electronic ordering by the REXS technique

https://link.springer.com/content/pdf/10.1140%2Fepjst%2Fe2012-01609-0.pdf

REXS contribution to electronic ordering investigation in solids

Here, a neutron powder diffraction (NPD) study of LnMnSbO (Ln = La or Ce) reveals differences between the magnetic ground state of the two compounds due to the strong Ce-Mn coupling compared to La-Mn. The two compounds adopt the P4/nmm space group down to 2 K, and whereas magnetization measurements do not show obvious anomaly at high temperatures, NPD reveals a C-type antiferromagnetic (AFM) order below TN = 255K for LaMnSbO and 240 K for CeMnSbO. While the magnetic structure of LaMnSbO is preserved to base temperature, a sharp transition at TSR = 4.5K is observed in CeMnSbO due to a spin-reorientation (SR) transition of the Mn2+ magnetic moments from pointing along the c axis to the ab plane. The SR transition in CeMnSbO is accompanied by a simultaneous long-range AFM ordering of the Ce moments, which indicates that the Mn SR transition is driven by the Ce-Mn coupling. The ordered moments are found to be somewhat smaller than those expected for Mn2+ (S = 5/2) in insulators, but large enough to suggest that these compounds belong to the class of local-moment antiferromagnets. The lower TN found in these two compounds compared to the As-based counterparts (TN = 317 formore » LaMnAsO, TN = 347K for CeMnAsO) indicates that the Mn-Pn (Pn=As or Sb) hybridization that mediates the superexchange Mn-Pn-Mn coupling is weaker for the Sb-based compounds.« less

Structure and magnetic properties of LnMnSbO ( Ln=La and Ce)

We have made an extensive study of ${\text{PrB}}_{6}$ using x-ray resonant scattering to investigate both the lattice and magnetic properties. We have identified a structural distortion associated with the incommensurate to commensurate magnetic phase transition at $T=4.5\text{ }\text{K}$. Magnetic satellite reflections have been observed in the incommensurate and commensurate phases. The azimuthal dependence of the scattered intensity from the commensurate magnetic satellite reflection at $(\frac{1}{2},\frac{5}{4},\frac{5}{4})$ is consistent with the model for the magnetic structure deduced from earlier neutron-diffraction results. Evidence for possible quadrupolar ordering is discussed.

X-ray resonant scattering study of the structural and magnetic transitions in PrB 6

We have made an extensive study of PrB6 using x-ray resonant scattering to investigate both the lattice and magnetic properties. We have identified a structural distortion associated with the incommensurate to commensurate magnetic phase transition at T=4.5 K. Magnetic satellite reflections have been observed in the incommensurate and commensurate phases. The azimuthal dependence of the scattered intensity from the commensurate magnetic satellite reflection at (1/2, 5/4, 5/4) is consistent with the model for the magnetic structure deduced from earlier neutron-diffraction results. Evidence for possible quadrupolar ordering is discussed.

X-ray resonant scattering study of the structural and magnetic transitions in PrB6

We present bulk magnetic and transport measurements and x-ray resonant scattering measurements on U(Pd${}_{1\ensuremath{-}x}$Pt${}_{x}$)${}_{3}$ for $x=0.005$ and $0.01$, which demonstrate the high sensitivity of the quadrupolar order in the canonical antiferroquadrupolar ordered system UPd${}_{3}$ to doping with platinum. Bulk measurements for $x=0.005$ reveal behavior similar to that seen in UPd${}_{3}$, albeit at a lower temperature, and x-ray resonant scattering provides evidence of quadrupolar order described by the ${Q}_{xy}$ order parameter. In contrast, bulk measurements reveal only an indistinct transition in $x=0.01$, consistent with the observation of short-range quadrupolar order in our x-ray resonant scattering results.

/pdf/5-f-delocalization-induced-suppression-of-quadrupolar-order-3zeomscvrw.pdf

5 f delocalization-induced suppression of quadrupolar order in U(Pd 1 − x Pt x ) 3

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X-ray resonant scattering study of the structural and magnetic transitions in PrB 6

X-ray resonant scattering study of the structural and magnetic transitions in PrB6

5 f delocalization-induced suppression of quadrupolar order in U(Pd 1 − x Pt x ) 3