Possible phase transition deep inside the hidden order phase of ultraclean URu2Si2

Hidden order and beyond: an experimental-theoretical overview of the multifaceted behavior of URu2Si2

This topical review describes the multitude of unconventional behaviors in the hidden order, heavy fermion, antiferromagnetic and superconducting phases of the intermetallic compound URu₂Si₂ 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 URu₂Si₂ 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 URu₂Si₂ 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.

Phase diagram of URu2-x Fe x Si2 in high magnetic fields

Electrical transport measurements were performed on URu_{2 - x} Fe _x Si₂ single-crystal specimens in high magnetic fields up to 45 T (DC fields) and 60 T (pulsed fields). We observed a systematic evolution of the critical fields for both the hidden-order (HO) and large-moment antiferromagnetic (LMAFM) phases and established the 3D phase diagram of T-H-x In the HO phase, H/H₀ scales with T/T₀ and collapses onto a single curve. However, in the LMAFM phase, this single scaling relation is not satisfied. Within a certain range of x values, the HO phase reenters after the LMAFM phase is suppressed by the magnetic field, similar to the behavior observed for URu₂Si₂ within a certain range of pressures.

Emergent antiferromagnetism out of the "hidden-order" state in URu2Si2: high magnetic field nuclear magnetic resonance to 40 T

Very high field (29)Si-NMR measurements using a fully (29)Si-enriched URu(2)Si(2) single crystal were carried out in order to microscopically investigate the "hidden order" (HO) state and adjacent magnetic phases in the high field limit. At the lowest measured temperature of 0.4 K, a clear anomaly reflecting a Fermi surface instability near 22 T inside the HO state is detected by the (29)Si shift, (29)K(c). Moreover, a strong enhancement of (29)K(c) develops near a critical field H(c) ≃ 35.6 T, and the ^{29}Si-NMR signal disappears suddenly at H(c), indicating the total suppression of the HO state. Nevertheless, a weak and shifted (29)Si-NMR signal reappears for fields higher than H(c) at 4.2 K, providing evidence for a magnetic structure within the magnetic phase caused by the Ising-type anisotropy of the uranium ordered moments.

Formation of the coherent heavy fermion liquid at the hidden order transition in URu2Si2

We present high-resolution angle-resolved photoemission spectra of the heavy-fermion superconductor URu2Si2. Detailed measurements as a function of both photon energy and temperature allow us to disentangle a variety of spectral features, revealing the evolution of the low-energy electronic structure across the "hidden order" transition. Above the transition, our measurements reveal the existence of weakly dispersive states that exhibit a large scattering rate and do not appear to shift from above to below the Fermi level, as previously reported. Upon entering the hidden order phase, these states rapidly hybridize with light conduction band states and transform into a coherent heavy fermion liquid, coincident with a dramatic drop in the scattering rate. This evolution is in stark contrast with the gradual crossover expected in Kondo lattice systems, which we attribute to the coupling of the heavy fermion states to the hidden order parameter.

High-magnetic-field lattice length changes in URu2Si2

We report high-magnetic-field (up to 45 T) ĉ-axis thermal-expansion and magnetostriction experiments on URu(2)Si(2) single crystals. The sample length change ΔL(c)(T(HO))/L(c) associated with the transition to the "hidden order" phase becomes increasingly discontinuous as the magnetic field is raised above 25 T. The reentrant ordered phase III is clearly observed in both the thermal expansion ΔL(c)(T)/L(c) and magnetostriction ΔL(c)(B)/L(c) above 36 T, in good agreement with previous results. The sample length is also discontinuous at the boundaries of this phase, mainly at the upper boundary. A change in the sign of the coefficient of thermal expansion α(c)=1/L(c)(∂ΔL(c)/∂T) is observed at the metamagnetic transition (B(M) ~ 38 T), which is likely related to the existence of a quantum critical end point.

Cyclotron resonance in the hidden-order phase of URu2Si2

We report the first observation of cyclotron resonance in the hidden-order phase of ultraclean URu2Si2 crystals, which allows the full determination of angle-dependent electron-mass structure of the main Fermi-surface sheets. We find an anomalous splitting of the sharpest resonance line under in-plane magnetic-field rotation. This is most naturally explained by the domain formation, which breaks the fourfold rotational symmetry of the underlying tetragonal lattice. The results reveal the emergence of an in-plane mass anisotropy with hot spots along the [110] direction, which can account for the anisotropic in-plane magnetic susceptibility reported recently. This is consistent with the "nematic" Fermi liquid state, in which itinerant electrons have unidirectional correlations.

Sequential spin polarization of the Fermi surface pockets in URu2Si2 and its implications for the hidden order

Using Shubnikov-de Haas oscillations measured in URu2Si2 over a broad range in a magnetic field of 11-45 T, we find a cascade of field-induced Fermi surface changes within the hidden order phase I and further signatures of oscillations within field-induced phases III and V [previously discovered by Kim et al., [Phys. Rev. Lett. 91, 256401 (2003)]. A comparison of kinetic and Zeeman energies indicates a pocket-by-pocket polarization of the Fermi surface leading up to the destruction of the hidden order phase I at ≈35  T. The anisotropy of the Zeeman energy driving the transitions in URu2Si2 points to an itinerant hidden order parameter involving quasiparticles whose spin degrees of freedom depart significantly from those of free electrons.