Nic Shannon : Research

"Seeing the light : experimental signatures of emergent electromagnetism in a quantum spin ice"
Owen Benton, Olga Sikora and Nic Shannon
arXiv:1204.1325

"Quantum Ice : a quantum Monte Carlo study"
Nic Shannon, Olga Sikora, Frank Pollman, Karlo Penc and Peter Fulde
Phys. Rev. Lett. 108, 067204 (2012)

"Extended quantum U(1)-liquid phase in a three-dimensional quantum dimer model"
Olga Sikora, Nic Shannon, Frank Pollman, Karlo Penc and Peter Fulde
Phys. Rev. B 84, 115129 (2011)

"A quantum liquid with deconfined fractional excitations in three dimensions"
Olga Sikora, Frank Pollman, Nic Shannon, Karlo Penc and Peter Fulde
Phys. Rev. Lett. 103, 247001 (2009)

"Angle-resolved NMR: quantitative theory of 75As T1 relaxation rate in BaFe2As2"
Andrew Smerald and Nic Shannon
Phys. Rev. B 84, 184437 (2011)

Chosen as a PRB Editor's Suggestion.

"The double life of electrons in magnetic Fe pnictides, as revealed by NMR"
Andrew Smerald and Nic Shannon
Europhys. Lett. 92, 47005 (2010)

"Spin dynamics of frustrated easy-axis triangular antiferromagnet 2H-AgNiO2 explored by inelastic neutron scattering"
E. M. Wheeler, R. Coldea, E. Wawrzynska, T. Sorgel, M. Jansen, M. M. Koza, J. Taylor, P. Adroguer and N. Shannon
Phys. Rev. B 79, 104421 (2009)..

Chosen as a PRB Editor's Suggestion.

Pierre is now working with David Carpentier and Pascal Degiovanni in ENS Lyon.

"Phase diagram of the classical Heisenberg antiferromagnet on a
triangular lattice in applied magnetic field"
Luis Seabra, Tsutomu Momoi, Philippe Sindzingre and Nic Shannon
Phys. Rev. B 84, 214418 (2011)

"Competition between supersolid phases and magnetization plateaux
in the frustrated easy-axis antiferromagnet on a triangular lattice"
Luis Seabra and Nic Shannon
Phys. Rev. B 83, 134412 (2011)

"Supersolid phases in a realistic three-dimensional spin model"
Luis Seabra and Nic Shannon
Phys. Rev. Lett. 104, 237205 (2010)

Luis is now working with Frank Pollmann at MPI-PKS Dresden.

For more information about what he did in Bristol, please see his homepage.

Supersolid phases in a realistic three-dimensional spin model

Luis Seabra and Nic Shannon, Phys Rev Lett 104, 237205 (2010)

Supersolid phases, in which a superfluid component coexists with conventional crystalline long range order, have recently attracted a great deal of attention in the context of both solid helium and quantum spin systems. Motivated by recent experiments on 2H-AgNiO2, we study the magnetic phase diagram of a realistic three-dimensional spin model with single-ion anisotropy and competing interactions on a layered triangular lattice, using classical Monte Carlo simulation techniques, complemented by spin-wave calculations. For parameters relevant to experiment, we find a cascade of different phases as a function of magnetic field, including three phases which are supersolids in the sense of Liu and Fisher. One of these phases is continuously connected with the collinear ground state of AgNiO2, and is accessible at relatively low values of magnetic field. The nature of this low-field transition, and the possibility of observing this new supersolid phase in AgNiO2, are discussed.

Nematic, vector-multipole, and plateau-liquid states in the classical O(3) pyrochlore antiferromagnet with biquadratic interactions in applied magnetic field

Nic Shannon, Karlo Penc,and Yukitoshi Motome, Phys. Rev. B 81, 184409 (2010)

The classical bilinear-biquadratic nearest-neighbor Heisenberg antiferromagnet on the pyrochlore lattice does not exhibit conventional Neel-type magnetic order at any temperature or magnetic field. Instead spin correlations decay algebraically over length scales r
~T^{-1/2}, behavior characteristic of a Coulomb phase arising from a strong local constraint. Despite this, its thermodynamic properties remain largely unchanged if Neel order is restored by the addition of a degeneracy-lifting perturbation, e.g., further neighbor interactions. Here we show how these apparent contradictions can be resolved by a proper understanding of way in which long-range Neel order emerges out of well-formed local correlations and identify nematic and vector-multipole orders hidden in the different Coulomb phases of the model. So far as experiment is concerned, our results suggest that where long-range interactions are unimportant, the magnetic properties of Cr spinels which exhibit half-magnetization plateaux may be largely independent of the type of magnetic order present.

A quantum liquid with deconfined fractional excitations in three dimensions

Olga Sikora, Frank Pollman, Nic Shannon, Karlo Penc and Peter Fulde, Phys. Rev. Lett. 103, 247001 (2009)

Excitations which carry ``fractional'' quantum numbers are known to exist in one dimension in polyacetylene, and in two dimensions, in the fractional quantum Hall effect. Fractional excitations have also been invoked to explain the breakdown of the conventional theory of metals in a wide range of three-dimensional materials. However the existence of fractional excitations in three dimensions remains highly controversial. In this Letter we report direct numerical evidence for the existence of a quantum liquid phase supporting fractional excitations in a concrete, three-dimensional microscopic model - the quantum dimer model on a diamond lattice. We demonstrate explicitly that the energy cost of separating fractional monomer excitations vanishes in this liquid phase, and that its energy spectrum matches that of the Coulomb phase in (3+1) dimensional quantum electrodynamics.

Magnetocaloric effect in the frustrated square lattice J1-J2 model

B. Schmidt, P. Thalmeier and Nic Shannon, Phys. Rev. B 76, 125113 (2007)

We investigate the magnetocaloric properties of the two-dimensional frustrated J1-J2 model on a square lattice. This model describes well the magnetic behavior of two classes of quasi-two-dimensional S=1/2 vanadates, namely, the Li2VOXO4 X=Si,Ge and AAVOPO42 A,A=Pb,Zn,Sr,Ba compounds. The magnetocaloric effect MCE consists of the adiabatic temperature change upon changing the external magnetic field. In frustrated systems, the MCE can be enhanced close to the saturation field because of massive degeneracies among low-lying excitations. We discuss results for the MCE in the two distinct antiferromagnetic regimes of the phase diagram. The numerical finite temperature Lanczos method as well as analytical methods based on the spin-wave expansion are employed and results are compared. We give explicit values for the saturation fields of the vanadium compounds. We predict that at subcritical fields there is first a
positive maximum followed by a sign change of the MCE, characteristic of all magnetically ordered phases.

Doped singlet-pair crystal in the Hubbard model on the checkerboard lattice

Didier Poilblanc, Karlo Penc and Nic Shannon, Phys. Rev. B 75, 220503(R) (2007)

In the limit of large nearest-neighbor and on-site Coulomb repulsions, the Hubbard model on the planar pyrochlore lattice maps, near quarter filling, onto a doped, quantum, fully packed loop model. The phase diagram exhibits at quarter filling a quantum state of matter, the resonating singlet-pair crystal, an insulating phase breaking lattice symmetry. Properties of a few doped holes or electrons are investigated. In contrast to the doped quantum antiferromagnet, phase separation is restricted to very small hopping, leaving an extended "window" for superconducting pairing. However, the latter is more fragile for large hopping than in the case of the antiferromagnet. The existence of a fermionic supersolid is discussed.

Octupolar order in the multiple spin exchange model on a triangular lattice

Tsutomu Momoi, Philippe Sindzingre and Nic Shannon, Phys. Rev. Lett. 97, 257204 (2006)

We show how a gapless spin liquid with hidden octupolar order arises in applied magnetic field, in a model applicable to thin films of He III with competing ferromagnetic and antiferromagnetic (cyclic) exchange interactions. Evidence is also presented for nematic --- i.e. quadrupolar --- correlations bordering on ferromagnetism in the absence of magnetic field.

Nematic order in square lattice frustrated ferromagnets

Nic Shannon, Tsutomu Momoi and Philippe Sindzingre, Phys. Rev. Lett. 96, 027213 (2006)

We present a new scenario for the breakdown of ferromagnetic order in a two-dimensional quantum magnet with competing ferromagnetic and antiferromagnetic interactions. In this, dynamical effects lead to the formation of two-magnon bound states, which undergo Bose-Einstein condensation, giving rise to bond-centered nematic order. This scenario is explored in some detail for an extended Heisenberg model on a square lattice. In particular, we present numerical evidence confirming the existence of a state with d-wave nematic correlations but no long range magnetic order, lying between the saturated ferromagnetic and collinear antiferromagnetic phases of the ferromagnetic J1-J2 model. We argue by continuity of spectra that this phase is also present in a model with 4-spin cyclic exchange.

Half-Magnetization Plateau Stabilized by Structural Distortion in the Antiferromagnetic Heisenberg Model on a Pyrochlore Lattice

Karlo Penc, Nic Shannon and Hirouki Shiba, Phys. Rev. Lett. 93, 197203 (2004)

Magnetization plateaux, visible as anomalies in magnetic susceptibility at low temperatures, are one of the hallmarks of frustrated magnetism. We show how an extremely robust half-magnetization plateau can arise from coupling between spin and lattice degrees of freedom in a pyrochlore antiferromagnet, and develop a detailed symmetry of analysis of the simplest possible scenario for such a plateau state. The application of this theory to the spinel oxides CdCr2O4 and HgCr2O4, where a robust half-magnetization plateau has been observed, is discussed.

Cyclic exchange, isolated states and spinon deconfinement in an XXZ Heisenberg model on the checkerboard lattice

Nic Shannon, Gregoire Misguich and Karlo Penc Phys. Rev. B 69, 220403(R) (2004)

The antiferromagnetic Ising model on a checkerboard lattice has an ice-like ground state manifold with extensive degeneracy. and, to leading order in Jxy, deconfined spinon excitations. We explore the role of cyclic exchange arising at order Jxy^2/Jz on the ice states and their associated spinon excitations. By mapping the original problem onto an equivalent quantum six-vertex model, we identify three different phases as a function of the chemical potential for flippable plaquettes --- a phase with long range Neel order and confined spinon excitations, a non-magnetic state of resonating square plaquettes, and a quasi-collinear phase with gapped but deconfined spinon excitations. The relevance of the results to the square-lattice quantum dimer model is also discussed.

Spin-wave expansion, finite temperature corrections, and order from disorder effects in the double exchange model

Nic Shannon and A. V. Chubukov, Phys. Rev. B 65, 104418 (2002)

The magnetic excitations of a double-exchange (DE) model are usually discussed in terms of an equivalent ferromagnetic Heisenberg model. We argue that this equivalence is valid only at a quasiclassical level - both quantum and thermal corrections to the magnetic poperties of a DE model differ from any effective Heisenberg model because its spin excitations interact only indirectly, through the exchange of charge fluctuations. To demonstrate this, we perform a large-S expansion for the coupled spin and charge degrees of freedom of the DE model, aimed at projecting out all electrons not locally aligned with core spins. We generalized the Holstein-Primakoff transformation to the case when the length of the spin is an operator by itself, and explicitly construct fermionic and bosonic operators to fourth order in 1/S. This procedure removes all spin variables from the Hund coupling term, and yields an effective Hamiltonian with an overall scale of electron hopping, for which we evaluate corrections to the magnetic and electronic properties in a 1/S expansion to order O(1/S^2). We also consider the effect of a direct superexchange antiferromagnetic interaction between core spins. We find that the competition between ferromagnetic double exchange and an antiferromagnetic superexchange provides on example of an ``order from disorder'' phenomenon - when the two interactions are of comparable strength, an intermediate spin configuration either a canted or a spiral state is selected by quantum and/or thermal fluctuations.

Fractional charges in pyrochlore lattices

Peter Fulde, Karlo Penc and Nic Shannon, Annalen der Physik 11, 892 (2002)

A pyrochlore lattice is considered where the average electron number of electrons per site is half--integer, concentrating on the case of exactly half an electron per site. Strong on-site repulsions are assumed, so that all sites are either empty or singly occupied. Where there are in addition strong nearest--neighbour repulsions, a tetrahedron rule comes into effect, as previously suggested for magnetite. We show that in this case, there exist excitations with fractional charge (+/-) e/2. These are intimately connected with the high degeneracy of the ground state in the absence of kinetic energy terms. When an additional electron is inserted into the system, it decays into two point like excitations with charge -e/2, connected by a Heisenberg spin chain which carries the electron's spin.

Kondo atoms, double exchange molecules, and a novel large S expansion for the ordered Kondo lattice

Nic Shannon, J. Phys. Condens. Matt. 13, 6371 (2001)

Kondo lattice models are widely used to describe systems where local magnetic moments couple to itinerant electrons. We construct a novel large S expansion scheme for an ordered Kondo lattice, starting from the eigenstates of the Kondo coupling on a single site, and paying particular attention to the special case of two sites sharing a single electron, which we solve exactly. The expansion scheme which we introduce is shown to reproduce all features of this exact solution, to O(1/S^2), and to offer a better physical starting point than previous approaches for calculating the properties of systems on a lattice in the "double exchange" limit of strong Hund's rule coupling.

The double life of electrons in magnetic iron pnictides, as revealed by NMR

A. Smerald and N. Shannon, Europhys. Lett 92, 47005 (2010).

We present a phenomenological, two-fluid approach to understanding the magnetic excitations in Fe pnictides, in which a paramagnetic fluid with gapless, incoherent particle-hole excitations coexists with an antiferromagnetic fluid with gapped, coherent spin wave excitations. We show that this two-fluid phenomenology provides an excellent quantitative description of NMR data for magnetic "122" pnictides, and argue that it finds a natural justification in LSDA and spin density wave calculations. We further use this phenomenology to estimate the maximum renormalisation of the ordered moment that can follow from low-energy spin fluctuations in Fe pnictides. We find that this is too small to account for the discrepancy between ab initio calculations and neutron scattering measurements.

Field-induced insulator-to-metal crossover in quasi-one-dimensional Li0:9Mo6O17

X. Xu, A.F. Bangura, J.G. Analytis, J.D. Fletcher, M.M.J. French, N. Shannon, N E Hussey, A. He, S. Zhang, D. Mandrus, and R. Jin
Phys. Rev. Lett 102, 206602 (2009).

We report a detailed magnetotransport study of the highly anisotropic quasi-one-dimensional oxide Li0:9Mo6O17 whose in-chain electrical resistivity diverges below a temperature Tmin > 25 K. For T < Tmin, a magnetic field applied parallel to the conducting chain induces a large negative magnetoresistance and ultimately, the recovery of a metallic state. At the highest fields studied, there is evidence for the emergence of superconductivity with an elevated onset temperature Tc > 10 K. We show evidence that this insulator/superconductor transition is a consequence of field-induced suppression of a density-wave gap in a highly one-dimensional conductor.

Spin dynamics of frustrated easy-axis triangular antiferromagnet 2H-AgNiO2 explored by inelastic neutron scattering

E. M. Wheeler, R. Coldea, E. Wawrzynska, T. Sorgel, M. Jansen, M. M. Koza, J. Taylor, P. Adroguer, and N. Shannon
Phys. Rev. B 79, 104421 (2009)

We report inelastic neutron-scattering measurements of the spin dynamics in the layered hexagonal magnet 2H-AgNiO2, which has stacked triangular layers of antiferromagnetically coupled Ni2+ spins (S=1) ordered in a collinear alternating stripe pattern. We observe a broad band of magnetic excitations above a small gap of 1.8 meV and extending up to 7.5 meV, indicating strongly dispersive excitations. The measured dispersions of the boundaries of the powder-averaged spectrum can be quantitatively explained by a linear spin-wave dispersion for triangular layers with antiferromagnetic nearest- and weak next-nearest-neighbor couplings, a strong easy-axis anisotropy, and additional weak interlayer couplings. The resulting dispersion relation has global minima not at magnetic Bragg wave vectors but at symmetry-related soft points and we attribute this anomalous feature to the strong competition between the easy-axis anisotropy and the frustrated antiferromagnetic couplings. We have also calculated the quantum corrections to the dispersion relation to order 1/S in spin-wave theory by extending the work of Chubukov and Jolicoeur [Phys. Rev. B 46, 11137 (1992)] and find that the presence of easy-axis anisotropy significantly reduces the quantum renormalizations predicted for the isotropic model.

Chosen as a PRB Editor's Suggestion.

Local Tunneling Spectroscopy across a Metamagnetic Critical Point in the Bilayer Ruthenate Sr3Ru2O7

K. Iwaya, S. Satow, T. Hanaguri, N. Shannon, Y. Yoshida, S. I. Ikeda, J. P. He, Y. Kaneko, Y. Tokura, T. Yamada, and H. Takagi
Phys. Rev. Lett. 99, 057208 (2007)

The local spectroscopic signatures of metamagnetic criticality in Sr3Ru2O7 were explored using scanning tunneling microscopy (STM). Singular features in the tunneling spectrum were found close to the Fermi level, as would be expected in a Stoner picture of itinerant electron metamagnetism. These features showed a pronounced magnetic field dependence across the metamagnetic critical point, which cannot be understood in terms of a naive Stoner theory. In addition, a pseudogap structure was observed over several tens of meV, accompanied by a c(2x2) superstructure in STM images. This result represents a new electronic ordering at the surface in the absence of any measurable surface reconstruction.

Patterning of Sodium Ions and the Control of Electrons in Sodium Cobaltate

M.Roger, D.J.P. Morris, D.A. Tennant, M.J.Gutmann, J.P. Goff, J.-U. Hoffmann, R. Feyerherm, E. Dudzik, D. Prabhakaran,
N. Shannon, B. Lake and P.P. Deen, Nature 445, 631 - 634 (2007)

NaxCoO2 has emerged as a material of exceptional scientific interest due to the potential for thermoelectric applications, and because the strong interplay between the magnetic and superconducting properties has led to close comparisons with the physics of the high-Tc cuprates. The density, x, of the sodium in the intercalation layers can be altered electrochemically, directly changing the number of conduction electrons on triangular Co layers. Recent electron diffraction measurements reveal a kaleidoscope of Na+ ion patterns as a function of concentration5. Here we use single-crystal neutron diffraction to determine the long-range three-dimensional superstructures. We show that the sodium ordering and its associated distortion field are governed by pure electrostatics, and the organizational principle is the stabilization of charge droplets that order long range at some simple fractional fillings. Our results provide a good starting point to understand the electronic properties in terms of a Hubbard Hamiltonian taking into account the electrostatic potential from the Na superstructures. The resulting depth of potential wells in the Co layer is greater than the single-particle hopping kinetic energy. As a consequence, holes occupy preferentially the lowest potential regions and, therefore, the Na+ ion patterning plays a decisive role in the transport and magnetic properties.

Spin Correlations in the Paramagnetic Phase and Ring Exchange in La2CuO4

A. M. Toader, J. P. Goff, M. Roger, N. Shannon,J. R. Stewart, and M. Enderle, Phys. Rev. Lett. 94, 197202 (2005)

Spin correlations in the paramagnetic phase of La2CuO4 have been studied using polarized neutron scattering, with two important results. First, the temperature dependence of the characteristic energy scale of the fluctuations and the amplitude of the neutron structure factor are shown to be in quantitative agreement with the predictions of the quantum nonlinear sigma model. Second, a comparison of a high-temperature series expansion of the equal-time spin correlations with the diffuse neutron intensity provides definitive experimental evidence for ring exchange.

Intrinsic Inhomogeneities in Manganite Thin Films Investigated with Scanning Tunneling Spectroscopy

T. Becker, C. Streng, Y. Luo, V. Moshnyaga, B. Damaschke, Nic Shannon, and K. Samwer, Phys. Rev. Lett. 89, 237203 (2002)

Thin films of La0.7Sr0.3MnO3 on MgO show a metal insulator transition and colossal magnetoresistance. The shape of this transition can be explained by intrinsic spatial inhomogeneities, which give rise to a domain structure of conducting and insulating domains at the submicrometer scale. These domains then undergo a percolation transition. The tunneling conductance and tunneling gap measured by scanning tunneling spectroscopy were used to distinguish and visualize these domains.