Rebecca Flint

Hastatic order in the heavy-fermion compound URu2Si2.

The development of collective long-range order by means of phase transitions occurs by the spontaneous breaking of fundamental symmetries. Magnetism is a consequence of broken time-reversal symmetry, whereas superfluidity results from broken gauge invariance. The broken symmetry that develops below 17.5 kelvin in the heavy-fermion compound URu2Si2 has long eluded such identification. Here we show that the recent observation of Ising quasiparticles in URu2Si2 results from a spinor order parameter that breaks double time-reversal symmetry, mixing states of integer and half-integer spin. Such ‘hastatic’ order hybridizes uranium-atom conduction electrons with Ising 5f2 states to produce Ising quasiparticles; it accounts for the large entropy of condensation and the magnetic anomaly observed in torque magnetometry. Hastatic order predicts a tiny transverse moment in the conduction-electron ‘sea’, a colossal Ising anisotropy in the nonlinear susceptibility anomaly and a resonant, energy-dependent nematicity in the tunnelling density of states.The development of collective long-range order via phase transitions occurs by the spontaneous breaking of fundamental symmetries. Magnetism is a consequence of broken time-reversal symmetry while superfluidity results from broken gauge invariance. The broken symmetry that develops below 17.5K in the heavy fermion compound URu2Si2 has long eluded such identification. Here we show that the recent observation of Ising quasiparticles in URu2Si2 results from a spinor order parameter that breaks double time-reversal symmetry, mixing states of integer and half-integer spin. Such “hastatic order” hybridizes conduction electrons with Ising 5f2 states of the uranium atoms to produce Ising quasiparticles; it accounts for the large entropy of condensation and the magnetic anomaly observed in torque magnetometry. Hastatic order predicts a tiny transverse moment in the conduction sea, a collosal Ising anisotropy in the nonlinear susceptibility anomaly and a resonant energy-dependent nematicity in the tunneling density of states. 1 ar X iv :1 20 7. 48 28 v1 [ co nd -m at .s tr -e l] 1 9 Ju l 2 01 2 The hidden order (HO) that develops below 17.5K in the heavy fermion compound URu2Si2 is particularly notable, having eluded identification for twenty five years[1–13]. Recent spectroscopic[14–18], magnetometric[19] and high-field measurements[20, 21] suggest that the HO is connected with the formation of an itinerant heavy electron fluid, a consequence of quasiparticle hybridization between localized, spin-orbit coupled f-moments and mobile conduction electrons. Though the development of hybridization at low temperatures is usually associated with a crossover, in URu2Si2 both optical [22] and tunnelling [15–17] probes suggest that it develops abruptly at the HO transition, leading to proposals[10, 11] that the hybridization is an order parameter. High temperature bulk susceptibility measurements on URu2Si2 show that the local 5f moments embedded in the conduction sea are Ising in nature[1, 26], while quantum oscillation (QO) experiments deep within the HO phase reveal that the quasiparticles exhibit a giant Ising anisotropy[21, 23, 24]. The Zeeman splitting depends solely on the c-axis component of the magnetic field, ∆E = g(θ)μBB[24], with a g-factor g(θ) = g cos θ, where θ is the angle relative to the c-axis. The g-factor anisotropy exceeds 30, corresponding to an anisotropy of the Pauli susceptibility in excess of 900; this anisotropy is also observed in the angle-dependence of the Pauli-limited upper critical field of the superconducting state[23, 24], showing that the Ising quasiparticles pair to form a heavy fermion superconductor. This giant anisotropy suggests that the f-moment is transferred to the mobile quasiparticles through hybridization[28]. In the tetragonal crystalline environment of URu2Si2 such Ising anisotropy is only natural in integer spin configurations[4, 27], thus the most likely valence of the U ions with an integer spin is a 5f 2 configuration. Moreover, the observation of paired Ising quasiparticles in a superconductor with Tc ∼ 1.5K indicates that this 5f 2 configuration is degenerate to within an energy resolution of gμBHc ∼ 5K. In URu2Si2, tetragonal symmetry protects a magnetic non-Kramers Γ5 doublet, the candidate origin of the Ising quasiparticles[4, 29]. The quasiparticle hybridization of half-integer spin conduction electrons with an integer spin doublet in URu2Si2 has profound implications for hidden order; such mixing can not occur without broken double time-reversal symmetry. Time-reversal, Θ̂, is an anti-unitary quantum operator with no associated quantum number[30]. However double-reversal Θ̂, equivalent to a 2π rotation, forms a unitary operator with an associated quantum number, the “Kramers index” K[30]. The Kramers index, K = (−1)2J of a quantum state of to-

Evidence of an odd-parity hidden order in a spin-orbit coupled correlated iridate

A rare combination of strong spin–orbit coupling and electron–electron correlations makes the iridate Mott insulator Sr_2IrO_4 a promising host for novel electronic phases of matter. The resemblance of its crystallographic, magnetic and electronic structures to La_2CuO_4, as well as the emergence on doping of a pseudogap region and a low-temperature d-wave gap, has particularly strengthened analogies to cuprate high-T_c superconductors. However, unlike the cuprate phase diagram, which features a plethora of broken symmetry phases in a pseudogap region that includes charge density wave, stripe, nematic and possibly intra-unit-cell loop-current orders, no broken symmetry phases proximate to the parent antiferromagnetic Mott insulating phase in Sr_2IrO_4 have been observed so far, making the comparison of iridate to cuprate phenomenology incomplete. Using optical second-harmonic generation, we report evidence of a hidden non-dipolar magnetic order in Sr_2IrO_4 that breaks both the spatial inversion and rotational symmetries of the underlying tetragonal lattice. Four distinct domain types corresponding to discrete 90°-rotated orientations of a pseudovector order parameter are identified using nonlinear optical microscopy, which is expected from an electronic phase that possesses the symmetries of a magneto-electric loop-current order. The onset temperature of this phase is monotonically suppressed with bulk hole doping, albeit much more weakly than the Neel temperature, revealing an extended region of the phase diagram with purely hidden order. Driving this hidden phase to its quantum critical point may be a path to realizing superconductivity in Sr_2IrO_4.

Heavy electrons and the symplectic symmetry of spin

The recent discovery of two heavy-fermion materials PuCoGa5 and NpPd5Al2, which transform directly from Curie paramagnets into superconductors, reveals a new class of superconductors where local moments quench directly into the superconducting condensate. Unlike other heavy-electron superconductors, where Cooper pairing is thought to be driven by spin fluctuations, these higher-transition-temperature materials do not seem to be close to a magnetic instability. Large-N expansions have been invaluable in describing heavy-fermion metals, but so far cannot treat superconductivity. Here, we introduce a new class of large-N expansion that uses symplectic symmetry to protect the odd time-reversal parity of spin and sustain Cooper pairs as well-defined singlets. We show that when a lattice of magnetic ions exchange spin with their metallic environment in two distinct symmetry channels, they can simultaneously satisfy both channels by forming a condensate of composite pairs between local moments and electrons. In the tetragonal crystalline environment relevant to PuCoGa5 and NpPd5Al2, the lattice structure selects a natural pair of spin exchange channels, predicting a unique anisotropic paired state with either d- or g-wave symmetry. This pairing mechanism also predicts a large upturn in the NMR relaxation rate above Tc and strong enhancement of Andreev reflection in tunnelling measurements. The Kondo problem—dealing with localized magnetic impurities embedded in a sea of conduction electrons—can be treated on an equal footing with superconductivity for a large system of interacting electrons.

Nodal to nodeless superconducting energy-gap structure change concomitant with fermi-surface reconstruction in the heavy-fermion compound CeCoIn(5).

The London penetration depth λ(T) was measured in single crystals of Ce_{1-x}R_{x}CoIn_{5}, R=La, Nd, and Yb down to T_{min}≈50  mK (T_{c}/T_{min}∼50) using a tunnel-diode resonator. In the cleanest samples Δλ(T) is best described by the power law Δλ(T)∝T^{n}, with n∼1, consistent with the existence of line nodes in the superconducting gap. Substitutions of Ce with La, Nd, and Yb lead to similar monotonic suppressions of T_{c}; however, the effects on Δλ(T) differ. While La and Nd substitution leads to an increase in the exponent n and saturation at n∼2, as expected for a dirty nodal superconductor, Yb substitution leads to n>3, suggesting a change from nodal to nodeless superconductivity. This superconducting gap structure change happens in the same doping range where changes of the Fermi-surface topology were reported, implying that the nodal structure and Fermi-surface topology are closely linked.

Spin-state crossover in multiferroic Ca3Co2-xMnxO6

Ca3Co2−xMnxO6 (x ∼ 0.96) is a multiferroic with spin-chains of alternating Co 2+ and Mn ions. The spin state of Co remains unresolved, due to a discrepancy between high temperature X-ray absorption (S = 3 2 ) and low temperature neutron (S = 1 2 ) measurements. Using a combination of magnetic modeling and crystal-field analysis, we show that the existing low temperature data cannot be reconciled within a high spin scenario by invoking spin-orbit or Jahn-Teller distortions. To unify the experimental results, we propose a spin-state crossover with specific experimental predictions.

Tandem pairing in heavy-fermion superconductors.

We consider the internal structure of a d-wave heavy-fermion superconducting condensate, showing that it necessarily contains two components condensed in tandem: pairs of quasiparticles on neighboring sites and composite pairs consisting of two electrons bound to a single local moment. These two components draw upon the antiferromagnetic and Kondo interactions to cooperatively enhance the superconducting transition temperature. This tandem condensate is electrostatically active, with an electric quadrupole moment predicted to lead to a superconducting shift in the nuclear quadrupole resonance frequency.

Molecular pairing and fully gapped superconductivity in Yb-doped CeCoIn(5).

The recent observation of fully gapped superconductivity in Yb doped CeCoIn_{5} poses a paradox, for the disappearance of nodes suggests that they are accidental, yet d-wave symmetry with protected nodes is well established by experiment. Here, we show that composite pairing provides a natural resolution: in this scenario, Yb doping drives a Lifshitz transition of the nodal Fermi surface, forming a fully gapped d-wave molecular superfluid of composite pairs. The T^{4} dependence of the penetration depth associated with the sound mode of this condensate is in accordance with observation.

Basal-plane nonlinear susceptibility: A direct probe of the single-ion physics in URu2Si2

The microscopic nature of the hidden order state in URu2Si2 is dependent on the low-energy configurations of the uranium ions, and there is currently no consensus on whether it is predominantly 5f^2 or 5f^3. Here we show that measurement of the basal-plane nonlinear susceptibility can resolve this issue; its sign at low-temperatures is a distinguishing factor. We calculate the linear and nonlinear susceptibilities for specific 5f^2 and 5f^3 crystal-field schemes that are consistent with current experiment. Because of its dual magnetic and orbital character, a \Gamma_5 magnetic non-Kramers doublet ground-state of the U ion can be identified by

Ising quasiparticles and hidden order in URu2Si2

\chi_1^c(T) \propto \chi_3^\perp(T)

Chiral RKKY interaction in Pr2Ir2O7

where we have determined the constant of proportionality for URu2Si2.