Spontaneous, collective ordering of electronic degrees of freedom leads to second-order phase transitions that are characterized by an order parameter driving the transition. The notion of a 'hidden order' has recently been used for a variety of materials where a clear phase transition occurs without a known order parameter. The prototype example is the heavy-fermion compound URu(2)Si(2), where a mysterious hidden-order transition occurs at 17.5 K. For more than twenty years this system has been studied theoretically and experimentally without a firm grasp of the underlying physics. Here, we provide a microscopic explanation of the hidden order using density-functional theory calculations. We identify the Fermi surface 'hot spots' where degeneracy induces a Fermi surface instability and quantify how symmetry breaking lifts the degeneracy, causing a surprisingly large Fermi surface gapping. As the mechanism for the hidden order, we deduce spontaneous symmetry breaking through a dynamic mode of antiferromagnetic moment excitations.

We report a comprehensive electronic structure investigation of the paramagnetic ͑PM͒, the large moment antiferromagnetic ͑LMAF͒, and the hidden order ͑HO͒ phases of URu 2 Si 2 . We have performed relativistic full-potential calculations on the basis of the density-functional theory, employing different exchangecorrelation functionals to treat electron correlations within the open 5f shell of uranium. Specifically, we investigate-through a comparison between calculated and low-temperature experimental properties-whether the 5f electrons are localized or delocalized in URu 2 Si 2 . The local spin-density approximation ͑LSDA͒ and generalized gradient approximation ͑GGA͒ are adopted to explore itinerant 5f behavior, the GGA plus additional strong Coulomb interaction ͑GGA+ U approach͒ is used to approximate moderately localized 5f states, and the 5f-core approximation is applied to probe potential properties of completely localized uranium 5f states. We also performed local-density approximation plus dynamical mean-field theory calculations ͑DMFT͒ to investigate the temperature evolution of the quasiparticle states at 100 K and above, unveiling a progressive opening of a quasiparticle gap at the chemical potential when temperature is reduced. A detailed comparison of calculated properties with known experimental data demonstrates that the LSDA and GGA approaches, in which the uranium 5f electrons are treated as itinerant, provide an excellent explanation of the available low-temperature experimental data of the PM and LMAF phases. We show furthermore that due to a materialspecific Fermi-surface instability a large, but partial, Fermi-surface gapping of up to 750 K occurs upon antiferromagnetic symmetry breaking. The occurrence of the HO phase is explained through dynamical symmetry breaking induced by a mode of long-lived antiferromagnetic spin fluctuations. This dynamical symmetry breaking model explains why the Fermi-surface gapping in the HO phase is similar but smaller than that in the LMAF phase and it also explains why the HO and LMAF phases have the same Fermi surfaces yet different order parameters. A suitable order parameter for the HO is proposed to be the Fermi-surface gap, and the dynamic spin-spin correlation function is further suggested as a secondary order parameter.

The Fermi surface (FS) nesting properties of URu2Si2 are analyzed with particular focus on their implication for the mysterious hidden order phase. We show that there exist two Fermi surfaces that exhibit a strong nesting at the antiferromagnetic wavevector, Q0=(0, 0, 1). The corresponding energy dispersions fulfill the relation 1(k)=− 2(k ± Q0) at eight FS hotspot lines. The spin-orbital characters of the involved 5f states are distinct (jz=±5/2 vs. ±3/2) and hence the degenerate Dirac crossings are symmetry protected in the nonmagnetic normal state. Dynamical symmetry breaking through an Ising-like spin and orbital excitation mode with ∆jz=±1 induces a hybridization of the two states, causing substantial FS gapping. Concomitant spin and orbital currents in the uranium planes give rise to a rotational symmetry breaking.PACS numbers: 71.27.+a, 74.70.Tx At temperatures below T o =17.5 K a mysterious hidden order (HO) phase develops 1-3 in the heavy-fermion uranium compound URu 2 Si 2 , the origin of which could not be definitely established despite intensive investigations. 4The occurrence of the new, ordered phase below T o is clearly witnessed by a sharp, second order phase transition appearing in the thermodynamic and transport quantities.1,2,5,6 The appearing new electronic order is not long-range ordered (dipolar) magnetism, although a small pressure of about 0.5 GPa suffices to stabilize longrange antiferromagnetic (AF) order.7,8 Recent experimental progress succeeded to reveal particular features of the HO state, thus providing a mosaic of pieces for unraveling the HO.9-17 To explain the origin of the HO a large number of sometimes exotic theories have been proposed over a period of more than twenty years 18-27 which however could not yet provided a complete understanding (see Ref. 4 for a survey of theories).A central question concerning the nature of the HO phase is which symmetry is spontaneously broken at the HO transition. A recent torque experiment performed on very small (µm-size) single crystals measured the magnetic susceptibility in the basal a-a plane of the tetragonal unit cell.28 Okazaki et al. 28 observe rotational symmetry breaking, i.e., the off-diagonal susceptibility χ xy is nonzero in the HO phase, unlike in the normal nonmagnetic phase above T o where χ xy =0. To explain the nonzero off-diagonal susceptibility several novel models 29-31 for the HO phase have been put forward recently. The non-vanishing off-diagonal susceptibility has been ascribed to a certain type of quadrupolar order, 29 a modulated spin liquid, 30 and a spin nematic state. 31Apart from breaking of xy-symmetry in the basal plane, it recently became clear that the lattice periodicity along the c -axis in the Brillouin zone (BZ) is modified, too, in the HO phase.14,15 The body-centered tetragonal (bct) unit cell of URu 2 Si 2 in the normal state becomes doubled in the HO state, and thus becomes simple tetragonal (st), consistent with a recent prediction.23 A complete understanding of the HO state obviously require...

The crystal and electronic structures of the orthorhombic compound UCoGe are presented and discussed. It has been either refined by the x-ray diffraction on a single crystal or computed within the local spin density functional theory, employing the fully relativistic version of the full-potential local-orbital band structure code, respectively. We particularly give our attention to investigating the Fermi surface and de Haas-van Alphen quantities of UCoGe. The calculated electronic density is then examined by x-ray photoelectron spectroscopy (XPS). Fairly good agreement is achieved between theoretical and experimental XPS results in the paramagnetic state. A small difference in the position (in energy scale) of the U 5f bands is caused by the electron localization effect observed in the experimental XPS. There is also some discrepancy for the Co 3d electron contributions below E(F). The Fermi surface in the non-magnetic state is of a semimetallic type while that in the ferromagnetic state, with the ordered moment of -0.47 μ(B)/f.u. along the c axis, is more metallic, with nesting properties that may favour superconductivity.