Hidden Order State Research Articles

Spin-orbit density wave: a new phase of matter applicable to the hidden order state of URu2Si2

We provide a brief review and detailed analysis of the spin-orbit density wave (SODW) proposed as a possible explanation to the ‘hidden order’ phase of URuSi. Due to the interplay between inter-orbital Coulomb interaction and spin-orbit coupling (SOC) in this compound, the SODW is shown to arise from Fermi surface nesting instability between two spin-orbit split bands. An effective low-energy Hamiltonian including single-particle SOC and two-particle SODW is derived, while the numerical results are calculated using density-functional theory (DFT)-based band-structure input. Computed gapped quasiparticle spectrum, entropy loss and spin-excitation spectrum are in detailed agreement with experiments. Interestingly, despite the fact that SODW governs dynamical spin-excitations, the static magnetic moment is calculated to be zero, owing to the time-reversal invariance imposed by SOC. As a consequence, SODW can be destroyed by finite magnetic field even at zero temperature. Our estimation of the location of the quantum critical point is close to the experimental value of 35 T. Finally, we extend the idea of SODW to other SOC systems including iridium oxides (iridates) and two-dimensional electronic systems such as BiAg surface and LaAlO/SrTiO interface. We show hint of quasiparticle gapping, reduction of pre-existing magnetic moment, large magneto-resistance, etc. which can be explained consistently within the SODW theory.

Optical study of hybridization and hidden order in URu2Si2

We summarize existing optical data of URu2Si2 to clarify the nature of the hidden order transition in this heavy fermion metal. Hybridization develops between 50 K and 17.5 K, and a coherent Drude peak emerges which mirrors the changes in the dc resistivity. The Drude weight indicates that there is little change in the effective mass of these carriers in this temperature range. In addition, there is a flat background conductivity that develops a partial hybridization gap at 10 meV as the temperature is lowered, shifting spectral weight to higher frequencies above 300 meV. Below 30 K the carriers become increasingly coherent and Fermi-liquid-like as the hidden order transition is approached. The hidden order state in URu2Si2 is characterized by multiple anisotropic gaps. The gap parameter meV in the ab-plane. In the c-direction, there are two distinct gaps with magnitudes of meV and meV. These observations are in good agreement with other spectroscopic measurements. Overall, the spectrum can be fit by a Dynes-type density of states model to extract values of the hidden order gap. The transfer of spectral weight strongly resembles what one sees in density wave transitions.

Spin excitons in the unconventional superconducting and hidden order state of strongly correlated electrons

The formation of collective spin excitons below the single particle continuum is observed in numerous unconventional superconductors. CeCoIn5 is the most well established case for heavy fermion compounds. It is also the first example where the splitting of magnetic excitons by a magnetic field is observed for fields within the tetragonal plane. Contrary to expectations it is revealed as a doublet excitation. We explain the splitting as the result of a strongly anisotropic spin response described within the context of an Anderson lattice type model. Recently it was shown that collective spin excitations also appear within the hidden order phase of non- superconducting CeB6. It is a signature of the itinerant nature of spin response as opposed to the commonly used localized 4f approach in this compound. We show that the salient features of the spin exciton can be explained in an itinerant quasiparticle model supplemented by hidden and antiferromagnetic order.

Polarized Neutron on URu2Si2

Abstract Polarized neutron scattering has shed a new light on URu 2 Si 2 . This compound studied for almost thirty years presents two tran- sitions: a superconducting state below 1.2K (T sc ) and a well-defined bulk transition at 17.8K (T 0 ). In spite of intensive research, no local probe has defined the order parameter associated with this transition (the famous Hidden Order (HO)). Neutron Larmor diffraction measurements combined with uniaxial stress experiments have shown that the relevant parameter that governs the magnetic properties is the a -lattice parameter. Induced magnetization distribution measured by elastic polarized neutron scattering shows a subtle change when entering the HO state that suggests a freezing of rank 5 multipoles (i.e. dotriacontapole). Polarized inelastic neutron measurements have shown the existence of two well defined excitations on the top of a broad continuum. How- ever only the AF excitation vanishes at T 0 and as well as when URu 2 Si 2 switches between HO to AF state under pressure. These excitations seem to correspond also to transitions between singlet levels.

Γ3-Type Lattice Instability and the Hidden Order of URu2Si2

We have performed ultrasonic measurements on single-crystalline URu2Si2 with pulsed magnetic fields, in order to check for possible lattice instabilities due to the hybridized state and the hidden-order state of this compound. The elastic constant (C11-C12)/2, which is associated with a response to the {\Gamma}3-type symmetry-breaking (orthorhombic) strain field, shows a three-step increase at H > 35 T for H || c at low temperatures, where successive meta-magnetic transitions are observed in the magnetization. We discovered a new fact that the absolute change of the softening of (C11-C12)/2 in the temperature dependence is quantitatively recovered at the suppression of hybridized-electronic state and the hidden order in high-magnetic field for H \perp c associated with the successive transitions. The present results suggest that the {\Gamma}3-type lattice instability, is related to both the emergence of the hybridized electronic state and the hidden-order parameter of URu2Si2. On the other hand, magnetic fields H || [100] and [110] enhance the softening of (C11-C12)/2 in the hidden order phase, while no step-like anomaly is observed up to 68.7 T. We discuss the limitation of the localized-electron picture for describing these features of URu2Si2 by examination of a crystalline electric field model in terms of mean-field theory.

Observation of two fine structures related to the hidden order in the spectral functions of URu2Si2

We studied the spectral functions of URu${}_{2}$Si${}_{2}$ in the hidden-order state by means of ultrahigh-resolution angle-resolved photoemission spectroscopy. High signal-to-noise ratio data uncover the existence of two anomalous fine structures, namely a ``splitting'' in the previously reported narrow dispersive band, and a small, dispersionless ``satellite'' structure. These structures can be explained by neither ordinary bands nor the development of a hybridization of two states; thus our observation should evoke the consideration of complicated many-body effects. As a possible origin, we suggest the existence of electron-mode coupling in the ordered state.

Interplay of magnetism, Fermi surface reconstructions, and hidden order in the heavy-fermion material URu2Si2

URu$_2$Si$_2$ is surely one of the most mysterious of the heavy-fermion compounds. Despite more than twenty years of experimental and theoretical works, the order parameter of the transition at $T_0 = 17.5$ K is still unknown. The state below $T_0$ remains called "hidden-order phase" and the stakes are still to identify the energy scales driving the system to this phase. We present new magnetoresistivity and magnetization measurements performed on very-high-quality single crystals in pulsed magnetic fields up to 60 T. We show that the transition to the hidden-order state in URu$_2$Si$_2$ is initially driven by a high-temperature crossover at around 40-50 K, which is a fingerprint of inter-site electronic correlations. In a magnetic field $\mathbf{H}$ applied along the easy-axis $\bf{c}$, the vanishing of this high-temperature scale precedes the polarization of the magnetic moments, as well as it drives the destabilization of the hidden-order phase. Strongly impurity-dependent magnetoresistivity confirms that the Fermi surface is reconstructed below $T_0$ and is strongly modified in a high magnetic field applied along $\mathbf{c}$, i.e. at a sufficiently-high magnetic polarization. The possibility of a sharp crossover in the hidden-order state controlled by a field-induced change of the Fermi surface is pointed out.

Magnetic properties of URu2Si2under uniaxial stress by neutron scattering

The aim of this study is to compare the magnetic behavior of URu2Si2 under uniaxial stress along the a-axis with the behavior under hydrostatic pressure. Both are very similar, but uniaxial stress presents a critical stress {\sigma}xa smaller (0.33(5)GPa) than the hydrostatic critical pressure px =0.5 GPa where the ground state switches from HO (hidden order) to AF (antiferromagnetic) ground state. From these critical values and from Larmor neutron diffraction (LND), we conclude that the magnetic properties are governed by the shortest U-U distance in the plane (a lattice parameter). Under stress, the orthorhombic unit cell stays centered. A key point shown by this study is the presence of a threshold for the uniaxial stress along the a-axis before the appearance of the large AF moment which indicates no-mixture of order parameter (OP) between the HO ground state and the AF one as under hydrostatic pressure. The two most intense longitudinal magnetic excitations at Q0=(1,0,0) and Q1=(0.6,0,0) were measured in the HO state: the excitation at Q0 decreases in energy while the excitation at Q1 increases in energy with the uniaxial stress along the a-axis. The decrease of the energy of the excitation at Q0 seems to indicate a critical energy gap value of 1.2(1) meV at {\sigma}xa. A similar value was derived from studies under hydrostatic pressure at px.

Local suppression of the hidden-order phase by impurities in URu2Si2

We consider the effects of impurities on the enigmatic hidden order (HO) state of the heavy-fermion material ${\mathrm{URu}}_{2}{\mathrm{Si}}_{2}$. In particular, we focus on local effects of Rh impurities as a tool to probe the suppression of the HO state. To study local properties, we introduce a lattice free energy, where the time invariant HO order parameter $\ensuremath{\Psi}$ and local antiferromagnetic (AFM) order parameter $M$ are competing orders. Near each Rh atom, the HO order parameter is suppressed, creating a hole in which local AFM order emerges as a result of competition. These local holes are created in the fabric of the HO state like in a Swiss cheese and ``filled'' with droplets of AFM order. We compare our analysis with recent NMR results on U(Rh${}_{x}$Ru${}_{1\ensuremath{-}x}$)${}_{2}$Si${}_{2}$ and find good agreement with the data.

Electronic structure of U(Ru1−xRhx)2Si2 studied by laser angle-resolved photoemission spectroscopy

We have studied electronic structures of U(Ru1-xRhx)2Si2 employing ultrahigh-resolution laser angle-resolved photoemission spectroscopy to understand the effect of Rh substitution. A hole-like dispersive feature, which presumably has Rh d-band character, was observed in U(Ru1-xRhx)2Si2 for both x = 0 and x = 0.03. However, although a heavy quasiparticle band appears in the hidden-order state of URu2Si2 (x = 0), it was not observed for x = 0.03 over the temperature range studied. In addition, it was found that energy-distribution curves at the Fermi vector of the hole-like band for x = 0.03 behave similarly to the Fermi-Dirac function. We also present the mapping of Fermi surfaces formed by the hole-like band, which stay nearly unaffected by Rh substitution.

The emergent and hidden unveiled

The appearance of an unexplained electronic state in the uranium metal URu2Si2 at low temperatures has long puzzled condensed-matter physicists. The latest experiment on the material sheds light on the process. A long-standing mystery in condensed matter physics is that of the appearance of a 'hidden order' state in URu2Si2 at low temperature, an unexpected phase change that is accompanied by a sharp change in bulk properties of the material. The problem is related to the appearance of a 'heavy fermion' state (already at a higher temperature) where electron-like charge carriers propagate through the solid with an effective mass thousands of times larger than that of a free electron. Schmidt et al. have now used scanning tunnelling microscopy and spectroscopy to visualize the electronic structure of URu2Si2 with subatomic resolution. In the process, they observe the electronic structure associated with a magnetic 'Kondo' lattice, which was assumed to cause heavy fermion effects, but never observed directly. Further, the spectroscopic findings show how the hidden order state evolves with decreasing temperature from this lattice.

Visualizing the formation of the Kondo lattice and the hidden order in URu 2 Si 2

Heavy electronic states originating from the f atomic orbitals underlie a rich variety of quantum phases of matter. We use atomic scale imaging and spectroscopy with the scanning tunneling microscope to examine the novel electronic states that emerge from the uranium f states in URu(2)Si(2). We find that, as the temperature is lowered, partial screening of the f electrons' spins gives rise to a spatially modulated Kondo-Fano resonance that is maximal between the surface U atoms. At T = 17.5 K, URu(2)Si(2) is known to undergo a second-order phase transition from the Kondo lattice state into a phase with a hidden order parameter. From tunneling spectroscopy, we identify a spatially modulated, bias-asymmetric energy gap with a mean-field temperature dependence that develops in the hidden order state. Spectroscopic imaging further reveals a spatial correlation between the hidden order gap and the Kondo resonance, suggesting that the two phenomena involve the same electronic states.

Arrested Kondo effect and hidden order in URu2Si2

Complex electronic matter shows subtle forms of self-organization, which are almost invisible to the available experimental tools. One prominent example is provided by the heavy-fermion material URu2Si2. At high temperature, the 5f electrons of uranium carry a very large entropy. This entropy is released at 17.5 K by means of a second-order phase transition1 to a state that remains shrouded in mystery, termed a ‘hidden order’ state2. Here, we develop a first-principles theoretical method to analyse the electronic spectrum of correlated materials as a function of the position inside the unit cell of the crystal and use it to identify the low-energy excitations of URu2Si2. We identify the order parameter of the hidden-order state and show that it is intimately connected to magnetism. Below 70 K, the 5f electrons undergo a multichannel Kondo effect, which is ‘arrested’ at low temperature by the crystal-field splitting. At lower temperatures, two broken-symmetry states emerge, characterized by a complex order parameter ψ. A real ψ describes the hidden-order phase and an imaginary ψ corresponds to the large-moment antiferromagnetic phase. Together, they provide a unified picture of the two broken-symmetry phases in this material.

Low-frequency excitation in the optical properties of superconductingCeCoIn5

The far-infrared optical response of ${\text{CeCoIn}}_{5}$, a superconducting heavy fermion metal with a ${T}_{C}$ of 2.3 K, was investigated from $5--40\text{ }{\text{cm}}^{\ensuremath{-}1}$ at temperatures from 0.5--2.5 K using a polarizing interferometer and a ${\text{He}}^{3}$ cryostat. A strong absorption feature is revealed at low temperatures which appears to be a gap in the density of states, reminiscent of the energy gap seen in the hidden order state in $U{\text{Ru}}_{2}{\text{Si}}_{2}$. The depth of the spectral structure decreases with increasing temperature from 0.5 to 2.5 K indicating that the characteristic temperature for this behavior is close to the superconducting ${T}_{C}$. A peak in the superconducting state Kramers-Kronig-derived optical conductivity occurs just above the gap at 1.5 meV.

Incommensurate spin resonance inURu2Si2

The nature of the hidden order (HO) in ${\text{URu}}_{2}{\text{Si}}_{2}$ below ${T}_{\text{HO}}=17.5\text{ }\text{K}$ has been a puzzle for a long time. Neutron-scattering studies of this material reveal a rich spin dynamics. We focus on the inelastic neutron scattering in ${\text{URu}}_{2}{\text{Si}}_{2}$ and argue that the observed gap in the fermion spectrum naturally leads to the spin feature observed at energies ${\ensuremath{\omega}}_{\text{res}}=4--6\text{ }\text{meV}$ at momenta at ${\mathbf{Q}}^{\ensuremath{\ast}}=(\mathbf{1}\ifmmode\pm\else\textpm\fi{}\mathbf{0}.\mathbf{4},\mathbf{0},\mathbf{0})$. We discuss how spin features seen in ${\text{URu}}_{2}{\text{Si}}_{2}$ can indeed be thought of in terms of the spin resonance that develops in HO state and is not related to the superconducting transition at 1.5 K. In our analysis, we assume that the HO gap is due to a particle-hole condensate that connects nested parts of the Fermi surface with nesting vector ${\mathbf{Q}}^{\ensuremath{\ast}}$. Within this approach, we can predict the behavior of the spin susceptibility at ${\mathbf{Q}}^{\ensuremath{\ast}}$ and find it to be strikingly similar to the phenomenology of resonance peaks in high ${T}_{c}$ and heavy fermion superconductors. The energy of the resonance peak scales with ${T}_{\text{HO}}$ ${\ensuremath{\omega}}_{\text{res}}\ensuremath{\simeq}4{k}_{B}{T}_{\text{HO}}$. We discuss observable consequences that spin resonance will have on neutron scattering and local density of states. Moreover, we argue how the establishment of spin resonance in ${\text{URu}}_{2}{\text{Si}}_{2}$ and better characterization of susceptibility, temperature, pressure, and Rh-doping dependence would elucidate the nature of the HO.

Suppression of Hidden Order and Emergence of Ferromagnetism in URu2-xRexSi2

AbstractMeasurements on URu2-xRexSi2 single crystals indicate that substitution of Re for Ru in URu2Si2 reduces the transition temperature of the hidden order state and quickly destroys superconductivity. At intermediate Re concentrations, weak ferromagnetism emerges and non Fermi liquid (NFL) behavior is observed in the low-temperature specific heat and electrical resistivity. A scaled Arrott analysis of the magnetization indicates the onset of ferromagnetism at x =0.15, where the hidden order disappears, and that the quantum phase transition is associated with novel critical exponents.

Field-Induced Fermi Surface Reconstruction and Adiabatic Continuity between Antiferromagnetism and the Hidden-Order State inURu2Si2

Shubnikov-de Haas oscillations reveal at high fields an abrupt reconstruction of the Fermi surface within the hidden-order (HO) phase of URu2Si2. Taken together with reported Hall effect results, this implies an increase in the effective carrier density and suggests that the field suppression of the HO state is ultimately related to destabilizing a gap in the spectrum of itinerant quasiparticles. While hydrostatic pressure favors antiferromagnetism in detriment to the HO state, it has a modest effect on the complex H-T phase diagram. Instead of phase separation between HO and antiferromagnetism our observations indicate adiabatic continuity between both orderings with field and pressure changing their relative weight.