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Hidden order in URu$_2$Si$_2$ has remained a mystery now entering its 4th decade. The importance of resolving the nature of the hidden order has stimulated extensive research. Here we present a detailed characterization of different surface terminations in URu$_2$Si$_2$ by angle-resolved photoemission spectroscopy, in conjunction with scanning tunneling spectroscopy and DMFT calculations that may unveil a new piece of this puzzle. The U-terminated surface is characterized by an electron-like band around the $bar{X}$ point, while a hole-like band for the Si-terminated surface. We also investigate temperature evolution of the electronic structure around the $bar{X}$ point from 11 K up to 70 K, and did not observe any abrupt change of the electronic structure around the coherence temperature (55 K). The $f$ spectral weight gradually weakens upon increasing temperature, still some $f$ spectral weight can be found above this temperature. Our results suggest that surface terminations in URu$_2$Si$_2$ are an important issue to be taken into account in future work.
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Electrical resistivity measurements were performed on single crystals of URu$_2-x$Os$_x$Si$_2$ up to $x$ = 0.28 under hydrostatic pressure up to $P$ = 2 GPa. As the Os concentration, $x$ , is increased, (1) the lattice expands, creating an effective negative chemical pressure $P_{ch}$($x$), (2) the hidden order (HO) phase is enhanced and the system is driven toward a large-moment antiferromagnetic (LMAFM) phase, and (3) less external pressure $P_{c}$ is required to induce the HO to LMAFM phase transition. We compare the $T(x)$, $T(P)$ phase behavior reported here for the URu$_2-x$Os$_x$Si$_2$ system with previous reports of enhanced HO in URu$_2$Si$_2$ upon tuning with $P$, or similarly in URu$_2-x$Fe$_x$Si$_2$ upon tuning with positive $P_{ch}$($x$). It is noted that pressure, Fe substitution, and Os substitution are the only known perturbations that enhance the HO phase and induce the first order transition to the LMAFM phase in URu$_2$Si$_2$. We present a scenario in which the application of pressure or the isoelectronic substitution of Fe and Os ions for Ru results in an increase in the hybridization of the U-5$f$- and transition metal $d$-electron states which leads to electronic instability in the paramagnetic phase and a concurrent stability of HO (and LMAFM) in URu$_2$Si$_2$. Calculations in the tight binding approximation are included to determine the strength of hybridization between the U-5$f$ electrons and each of the isoelectronic transition metal $d$-electron states of Fe, Ru, and Os.
The $g$-factor anisotropy of the heavy quasiparticles in the hidden order state of URu$_2$Si$_2$ has been determined from the superconducting upper critical field and microscopically from Shubnikov-de Haas (SdH) oscillations. We present a detailed analysis of the $g$-factor for the $alpha$, $beta$ and $gamma$ Fermi-surface pockets. Our results suggest a strong $g$-factor anisotropy between the $c$ axis and the basal plane for all observed Fermi surface pockets. The observed anisotropy of the $g$-factor from the quantum oscillations is in good agreement with the anisotropy of the superconducting upper critical field at low temperatures, which is strongly limited by the paramagnetic pair breaking along the easy magnetization axis $c$. However, the anisotropy of the initial slope of the upper critical field near $T_c$ cannot be explained by the anisotropy of the effective masses and Fermi velocities derived from quantum oscillations.
Identifying the nature of magnetism, itinerant or localized, remains a major challenge in condensed-matter science. Purely localized moments appear only in magnetic insulators, whereas itinerant moments more or less co-exist with localized moments in metallic compounds such as the doped-cuprate or the iron-based superconductors, hampering a thorough understanding of the role of magnetism in phenomena like superconductivity or magnetoresistance. Here we distinguish two antiferromagnetic modulations with respective propagation wave vectors of $Q_{pm}$ = ($H pm 0.557(1)$, 0, $L pm 0.150(1)$) and $Q_text{C}$ = ($H pm 0.564(1)$, 0, $L$), where $left(H, Lright)$ are allowed Miller indices, in an ErPd$_2$Si$_2$ single crystal by neutron scattering and establish their respective temperature- and field-dependent phase diagrams. The modulations can co-exist but also compete depending on temperature or applied field strength. They couple differently with the underlying lattice albeit with associated moments in a common direction. The $Q_{pm}$ modulation may be attributed to localized 4emph{f} moments while the $Q_text{C}$ correlates well with itinerant conduction bands, supported by our transport studies. Hence, ErPd$_2$Si$_2$ represents a new model compound that displays clearly-separated itinerant and localized moments, substantiating early theoretical predictions and providing a unique platform allowing the study of itinerant electron behavior in a localized antiferromagnetic matrix.
We studied the physical properties of two Kondo-lattice compounds, CeRu$_2$As$_2$ and CeIr$_2$As$_2$, by a combination of electric transport, magnetic and thermodynamic measurements. They are of ThCr$_2$Si$_2$-type and CaBe$_2$Ge$_2$-type crystalline structures, respectively. CeRu$_2$As$_2$ shows localized long-range antiferromagnetic ordering below $T_N$=4.3 K, with a moderate electronic Sommerfeld coefficient $gamma_0$=35 mJ/mol$cdot$K$^2$. A field-induced metamagnetic transition is observed near 2 T below $T_N$. Magnetic susceptibility measurements on aligned CeRu$_2$As$_2$ powders suggest that it has an easy axis and that the cerium moments align uniaxially along $mathbf{c}$ axis. In contrast, CeIr$_2$As$_2$ is a magnetically nonordered heavy-fermion metal with enhanced $gamma_0$$>$300 mJ/mol$cdot$K$^2$. The initial onset Kondo temperatures of the two compounds are respectively 6 K and 30 K. We discuss the role of the crystal structure to the strength of Kondo coupling. This work provides two new dense Kondo-lattice materials for further investigations on electronic correlation, quantum criticality and heavy-electron effects.
The observation of Ising quasiparticles is a signatory feature of the hidden order phase of URu$_2$Si$_2$. In this paper we discuss its nature and the strong constraints it places on current theories of the hidden order. In the hastatic theory such anisotropic quasiparticles are naturally described described by resonant scattering between half-integer spin conduction electrons and integer-spin Ising moments. The hybridization that mixes states of different Kramers parity is spinorial; its role as an symmetry-breaking order parameter is consistent with optical and tunnelling probes that indicate its sudden development at the hidden order transition. We discuss the microscopic origin of hastatic order, identifying it as a fractionalization of three body bound-states into integer spin fermions and half-integer spin bosons. After reviewing key features of hastatic order and their broader implications, we discuss our predictions for experiment and recent measurements. We end with challenges both for hastatic order and more generally for any theory of the hidden order state in URu$_2$Si$_2$.
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