Spin and orbital hybridization at specifically nested Fermi surfaces in URu2Si2

Abstract

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...

Direct observation of lattice symmetry breaking at the hidden-order transition in URu2Si2

“…Among the allowed irreducible representations for the hidden order (four non-degenerate A 1 , A 2 , B 1 and B 2 , and one degenerate E symmetries), the orthorhombic Fmmm-type space group symmetry pins down that the hidden order belongs to the E-type, more specifically E(Z a ,Z b ) with Z a ,Z b ¼ ± 1, in which the sign of Z a Z b determines the nematic direction of the domain 23 . Our results are consistent with the recently proposed orders that are compatible with this E-type symmetry 19,[23][24][25][26][27][28][29] . Multipole orders with odd 19,24,28 (even 23 ) ranks with (without) timereversal symmetry breaking should belong to E À (E þ ) symmetry, where the superscript sign represents the parity with respect to time reversal.…”

“…These results lead us to conclude that the hidden-order transition is a weak first-order phase transition accompanied by lattice symmetry breaking from the fourfold tetragonal to twofold orthorhombic structure. The present result is consistent with the 29 Si NMR measurements under in-plane magnetic fields 8,18 , which reveal very similar temperature dependence of the spectral width having a clear jump at T HO (Fig. 3d).…”

“…Multipole orders with odd 19,24,28 (even 23 ) ranks with (without) timereversal symmetry breaking should belong to E À (E þ ) symmetry, where the superscript sign represents the parity with respect to time reversal. More exotic orders, such as spin nematic 26,27 , hastatic 25 and dynamical circulating current orders 29 , are also consistent with the rotational symmetry breaking.…”

Unusual Magnetic Field-Dependence of the Electronic Dispersion Relations in a Hidden Ordered Phase.

“…The transition results in a folding of the Brillouin zone through a commensurate vector Q which is consistent with Angle Resolved Photoemission [12], de Haasvan Alphen [13] and neutron scattering measurements [14]. Similar nesting conditions have been found to be satisfied in LDA calculations [15,16] of the electronic structure of URu 2 Si 2 . We have shown [9] that the transition in the underscreened Anderson Lattice Model can be considered as resulting in a coupled spin and orbital density wave such that the orbital density wave for the spin-up is exactly out of phase with the orbital density wave for the spin-down electrons.…”

Optical study of hybridization and hidden order in URu2Si2

“…The gapping of incommensurate magnetic excitations at the hidden order transition has been shown by neutron scattering [44,45], and these account for much of the entropy lost. Band structure calculations [46,47] have yielded a picture of the Fermi surface with strong nesting in the pressure-induced anti-ferromagnetic state, and quantum oscillation measurements [37] demonstrate that there is no significant Fermi surface restructuring between HO and LM-AFM, which implies that the Fermi surface calculated for the latter state applies equally well to the former. Incommensurate nesting will lead to the formation of a spin-density wave gap at F and will be accompanied by a sharp absorption feature in the optical data [6,48], while a commensurate antiferromagnetic order of the localized moments would not be visible in optical measurements because it would not lead to a gap in the excitation spectrum at F .…”