Antiferromagnetic order in Pauli-limited unconventional superconductors

We develop a theory of the coexistence of superconductivity (SC) and antiferromagnetism (AFM) in CeCoIn(5). We show that in Pauli-limited nodal superconductors the nesting of the quasiparticle pockets induced by Zeeman pair breaking leads to incommensurate AFM with the magnetic moment normal to the field. We compute the phase diagram and find a first order transition to the normal state at low temperatures, the absence of normal state AFM, and the coexistence of SC and AFM at high fields, in agreement with experiments. We also predict the existence of a new double-Q magnetic phase.     

Coexistence of triplet superconductivity and spin density waves

We discuss the possibility of the coexistence of spin density waves (antiferromagnetism) and triplet superconductivity as a particular example of a broad class of systems where the interplay of magnetism and superconductivity is important. We focus on the case of quasi-one-dimensional metals, where it is known that antiferromagnetism is in close proximity to triplet superconductivity in the pressure versus temperature phase diagram. Over a range of pressures, we propose an intermediate nonuniform phase consisting of antiferromagnetic and triplet superconducting orders. In the coexistence region, we propose a flop transition in the spin density wave order parameter vector, which affects the nature of the superconducting state and leads to the appearance of several new phases.     

SO(4) theory of antiferromagnetism and superconductivity in Bechgaard salts

Motivated by recent experiments with Bechgaard salts, we investigate the competition between antiferromagnetism and triplet superconductivity in quasi-one-dimensional electron systems. We unify the two orders in an SO(4) symmetric framework, demonstrating the existence of such symmetry in one-dimensional Luttinger liquids. SO(4) symmetry strongly constrains the phase diagram, leading to coexistence regions of antiferromagnetic, superconducting, and normal phases, as observed in (TMTSF)(2)PF(6). We predict a sharp neutron scattering resonance in superconducting samples.     

Superconductor order parameter symmetry in UPd Al

The heavy fermion compound UPd₂Al₃ has attracted much interest on account of the coexistence of antiferromagnetism and superconductivity at temperatures below 2 K. The antiferromagnetic fluctuations provide, principally via inelastic neutron scattering, a window on the low frequency dynamics in this material. By an analysis of neutron scattering data, and taking into consideration results from other experimental probes, it is suggested which sheet(s) of the f-electron Fermi surface may play an active role in forming the superconducting state in UPd₂Al₃. The proposed scheme sheds new light on previously reported anomalies in this material. Received 16 July 1999     

Interplay of superconductivity and antiferromagnetism in SmRh4B4

A microscopic theory of interplay of superconductivity and antiferromagnetism in rare earth ternary systems is developed from first principles for less than half filledf atomic shells. Self consistent equations for the superconducting order parameter Δ and magnetic order parameter Γ, are derived using a Green’s function technique and equation of motion method. The theory is applied to explain the experimental results in the antiferromagnetic superconductor SmRh₄B₄. The present model explains true coexistence of superconductivity and antiferromagnetism and the suppression of superconductivity by antiferromagnetism. The behaviour of superconducting order parameter (Δ), magnetic order parameter (Γ), the specific heat, the density of states, free energy and critical field (H _c) is also studied for the system SmRh₄B₄.     

Charge-density-wave transitions in the local-moment magnet Er5Ir4Si10

We report the observation of a new type of charge-density wave (CDW) in the large magnetic-moment rare-earth intermetallic compound, Er5Ir4Si10, which then orders magnetically at low temperatures. Single crystal x-ray diffraction shows the development of a 1D incommensurate CDW at 155 K, which then locks into a purely commensurate state below 55 K. The well-localized Er3+ moments are antiferromagnetically ordered below 2.8 K. We observe very sharp anomalies in the specific heat at 145 and 2.8 K, signifying the bulk nature of these transitions. Our data suggest the coexistence of strongly coupled CDW with local-moment antiferromagnetism in Er5Ir4Si10.     

A neutron diffraction study of the coexistence of antiferromagnetism and superconductivity in GdMo6S8

The present neutron diffraction study confirms that GdMo₆S₈ orders antiferromagnetically in the superconducting state at a Néel temperature T_N = 0.84 K. Previous neutron scattering studies have demonstrated the coexistence of antiferromagnetism and superconductivity in two other rare earth ternary compounds, DyMo₆S₈ and TbMo₆S₆.     

Neutron diffraction study of the magnetic order in the ternary superconductor GdMo6S8

The coexistence of antiferromagnetism and superconductivity has been demonstrated in GdMo₆S₈ by neutron diffraction experiments. Although the magnetic unit cell (2a,a,a) is determined by the RKKY interactions, the direction of magnetic moments is determined by the anisotropic dipolar interactions i.e. in the (100) cubic plane.     

Coexistence of f-wave superconductivity, charge order, and spin antiferromagnetism around nonmagnetic impurities in Na0.33CoO2.1.3H2O

To check whether charge dynamics is responsible for the superconductivity in NaxCoO2.yH2O, we investigate local electronic and magnetic structure around nonmagnetic impurities embedded in this material at x=0.33 in the vicinity of charge instability, by using a phenomenological model within the slave-boson framework including competitions among a square root of 3 x square root of 3 charge order, antiferromagnetism, and f-wave superconductivity. Around the repulsive impurities, it is found that both local charge and spin orders are induced. Furthermore, the f-wave pairing order parameter is decreased on one sublattice but increased on another honeycomb sublattice. If the charge dynamics is responsible for the superconductivity, the predicted local electronic and magnetic structure could be observed by the STM and spatial resolved NMR experiments.     

Coexistence of superconductivity and density wave orders in a one-dimensional correlated system

By the field theory approach, we investigate a one-dimensional correlated electronic system modelled by the extended Hubbard Hamiltonian including a nearest-neighbor and a next-nearest-neighbor spin-exchange interactions with easy-axis anisotropy. At half filling, we obtain weak-coupling phase diagram. In addition to two insulating phases with transverse and longitudinal spin-density-wave orders, two metallic phases, characterized by the coexistence of singlet superconductivity and charge-density-wave orders and by the coexistence of triplet superconductivity and spin-density-wave orders, are realized in the ground state. Away from half filling, the degeneracy is split and the superconducting orders are favored.     

重费米子超导与竞争序

与其他非常规超导系列相比, 重费米子超导体往往具有丰富多样的竞争序, 超导与各种竞争序相伴而生, 电子配对与反铁磁涨落、铁磁涨落、价态涨落、电四极矩涨落等量子临界涨落密切相关, 扩充了非常规超导的研究内容. 重费米子材料中的f电子往往同时参与超导与各种竞争序的形成, 表现出局域与巡游的二重性. 重费米子二流体理论为理解重费米子超导与竞争序的关系提供了新的思路.     

The competition and coexistence of antiferromagnetism and <Emphasis Type="Italic">d</Emphasis>-wave superconductivity: probing coupled thermal fluctuations in a two dimensional minimal model

We consider the coexistence of antiferromagnetism and d-wave superconductivity, motivated by what one observes in the quasi-two dimensional organic salts. We study an electronic model that approximates some features of the Hubbard model, e.g., a repulsion that promotes local moments and Neel order, and an attractive intersite density–density coupling that promotes d-wave superconductivity. Staying at half-filling and a fixed attractive interaction we probe the effect of varying repulsion, using mean field theory for the ground state but retaining the full O(3) × U(1) spectrum of classical fluctuations at finite temperature. The ground state is superconducting at weak repulsion, a Neel ordered insulator at large repulsion, and a coexistence of the two orders in the intermediate regime. We observe four distinct kinds of thermal behaviour depending on the strength of repulsion. Starting with weak repulsion these are, first, a d-wave superconductor renormalised by magnetic fluctuations, second, a d-wave state transiting to an antiferromagnetic insulator and then to the normal state, third, a coexistent state transiting to the antiferromagnetic insulator and then the normal state, and, fourth, a Neel ordered insulator with weak pairing fluctuations. The low temperature state is either “nodal” or gapped, due to long range order, and the low energy spectral weight generally increases monotonically with temperature. At intermediate repulsion, however, the transition from the d-wave state to Neel antiferromagnet causes a loss of low energy weight which is gradually regained only at high temperature.     

Competitive coexistence of superconductivity with antiferromagnetism in CeRhIn5

We carried out ac magnetic susceptibility measurements under pressures P on the heavy fermion antiferromagnet CeRhIn5. We report bulk superconductivity (SC) at ambient pressure with a transition temperature Tc approximately or equal to 90 mK. The degraded SC in a powdered or polished sample was restored by annealing, showing that the SC state is sensitive to inhomogeneity. In a coexistence region of the SC with antiferromagnetism (AF), we find that Tc(P)(n)TN(P)(1-n) = const where TN indicates a Néel temperature and n denotes a ratio of electronic specific heat coefficients below and above TN, indicating the competition of the SC and the AF for states at the Fermi surface.     

On the implementation of the coexistence phase of antiferromagnetism and superconductivity in heavy-fermion intermetallides

The region of the state diagram in which the pressure-induced quantum phase transition occurs with the destruction of the antiferromagnetic ordering and the appearance of the superconductivity has been described within the periodic Anderson model. It has been shown that a microscopically homogeneous coexistence phase of antiferromagnetism and superconductivity is implemented in the vicinity of the critical point, which was experimentally found in the heavy-fermion compound CeRhIn₅. In this region, the pressure increase is accompanied by the experimentally observed strong growth of the effective fermion mass.     

Nodeless d-wave superconducting pairing due to residual antiferromagnetism in underdoped Pr2-xCexCuO4-delta

We investigate the doping dependence of the penetration depth versus temperature in electron-doped Pr(2-x)Ce(x)CuO(4-delta) using a model which assumes the uniform coexistence of (mean-field) antiferromagnetism and superconductivity. Despite the presence of a d(x2-y2) pairing gap in the underlying spectrum, we find nodeless behavior of the low-T penetration depth in the underdoped case, in accord with experimental results. As doping increases, a linear-in-T behavior of the penetration depth, characteristic of d-wave pairing, emerges as the lower magnetic band crosses the Fermi level and creates a nodal Fermi surface pocket.     

Two-Fermi-surface superconducting state and a nodal d-wave energy gap of the electron-doped Sm1.85Ce0.15CuO(4-δ) cuprate superconductor

We report on laser-excited angle-resolved photoemission spectroscopy in the electron-doped cuprate Sm1.85Ce0.15CuO(4-δ). The data show the existence of a nodal hole-pocket Fermi surface both in the normal and superconducting states. We prove that its origin is long-range antiferromagnetism by an analysis of the coherence factors in the main and folded bands. This coexistence of long-range antiferrmagnetism and superconductivity implies that electron-doped cuprates are two-Fermi-surface superconductors. The measured superconducting gap in the nodal hole pocket is compatible with a d-wave symmetry.     

Coexistence of ferro- and antiferromagnetism in itinerant electron systems

Condition for the coexistence of ferro- and antiferromagnetism is obtained in the itinerant electron model by taking into account the effect of spin fluctuations. It is found that the canted antiferromagnetism can appear, but the ferrimagnetism does not appear in isotropic itinerant electron systems. Expressions for parallel and perpendicular susceptibilities in the states of antiferro-, ferro- and canted antiferromagnetism are derived. Possible magnetic phase diagrams, i.e. various combinations of the magnetic transition among simple ferromagnetism, simple antiferromagnetism and two types of canted antiferromagnetism, where the uniform and staggered magnetizations are parallel and perpendicular to the easy direction and vice versa, are suggested for an itinerant electron system with the uniaxial anisotropy. It is also shown that the uniaxial anisotropy does not change the unstable situation of ferrimagnetism. The comparison with the observed results is discussed.     

Dispersion of magnetic excitations in optimally doped superconducting YBa2Cu3O6.95

Detailed neutron scattering measurements of YBa2Cu3O6.95 found that the resonance peak and incommensurate magnetic scattering induced by superconductivity represent the same physical phenomenon: two dispersive branches that converge near 41 meV and the in-plane wave vector q(AF)=(pi/a,pi/a) to form the resonance peak. One branch has a circular symmetry around q(AF) and quadratic downward dispersion from approximately 41 meV to the spin gap of 33+/-1 meV. The other, of lower intensity, disperses from approximately 41 meV to at least 55 meV. Our results exclude a quartet of vertical incommensurate rods in q-omega space expected from spin waves produced by dynamical charge stripes as an origin of the observed incommensurate scattering in optimally doped YBCO.     

Magnetism and superconductivity in a quasi-2D anisotropic system doped with charge carriers

The theory of multiband superconducting systems with variable density of charge carriers is analyzed. The possibility of emergence of nonphonon high-temperature superconductivity due to the predominance of electron–electron interband interactions over intraband interactions, as well as due to the fact that the thermodynamic and magnetic properties of multiband systems in the superconducting phase differ qualitatively from those of single-band systems, is indicated. Phase transitions in a quasi-2D anisotropic medium upon a change in the carrier concentration, i.e., a transition from the commensurate to the incommensurate state of the spin density wave, are analyzed. Such a transition is observed when the Umklapp processes in the lattice structure are taken into account. These processes facilitate a deviation of wavevector Q of the spin density wave from 2k_F, as well as a displacement of the bandgap relative to the Fermi surface. This leads to the generation of free charge carriers and the possibility of superconductivity. It is shown that superconductivity accompanies the magnetism. The conditions for the coexistence of these two phenomena are determined.     

Theoretical studies on magnetic superconductors

The discovery of magnetic superconductors has posed the problem of the coexistence of two kinds of orders (magnetic and superconducting) in some temperature intervals in these systems. New microscopic mechanisms developed by us to explain the coexistence and reentrant behaviour are reported. The mechanism for antiferromagnetic superconductors which shows enhancement of superconductivity below the magnetic transition is found relevant for rare-earth systems having less than half-filled f-atomic shells. The theory will be compared with the experimental results of SmRh₄B₄ system. A phenomenological treatment based on a generalized Ginzburg-Landau approach will also be presented to explain the anomalous behaviour of the second critical field in some antiferromagnetic superconductors. These magnetic superconductors provide two kinds of Bose fields, namely, phonons and magnons which interact with each other and also with the conduction electrons. Theoretical studies of the effects of the excitations of these modes on superconducting pairing and magnetic ordering in these systems will be discussed.