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Novel phases in a square–lattice frustrated ferromagnet : 1/3–magnetisation plateau, helicoidal spin–liquid and vortex crystal
Novel phases in a square–lattice frustrated ferromagnet : 1/3–magnetisation plateau, helicoidal spin–liquid and vortex crystal
L. Seabra, P. Sindzingre, T. Momoi, N. Shannon
A large part of the interest in magnets with frustrated antiferromagnetic interactions comes from the many new phases found in applied magnetic field. In this Article, we explore some of the new phases which arise in a model with frustrated ferromagnetic interactions, the J1−J2−J3 Heisenberg model on a square lattice. Using a combination of classical Monte-Carlo simulation and spin-wave theory, we uncover behaviour reminiscent of some widely-studied frustrated antiferromagnets, but with a number of new twists. We first demonstrate that, for a suitable choice of parameters, the phase diagram as a function of magnetic field and temperature is nearly identical to that of the Heisenberg antiferromagnet on a triangular lattice, including the celebrated 1/3-magnetisation plateau. We then examine how this phase diagram changes when the model is tuned to a point where the classical ground--state is highly degenerate. In this case, two new phases emerge; a classical, finite-temperature spin-liquid, characterised by a "ring" in the spin structure--factor (q); and a vortex crystal, a multiple-Q state with finite magnetisation, which can be viewed as an ordered lattice of magnetic vortices. All of these new phases persist for a wide range of magnetic field. We discuss the relationship between these results and published studies of frustrated antiferromagnets, together with some of the materials where these new phases might be observed in experiment.
Statistical translation invariance protects a topological insulator from interactions
Statistical translation invariance protects a topological insulator from interactions
A. Milsted, L. Seabra, I. C. Fulga, C. W. J. Beenakker, E. Cobanera
We investigate the effect of interactions on the stability of a disordered, two-dimensional topological insulator realized as an array of nanowires or chains of magnetic atoms on a superconducting substrate. The Majorana zero-energy modes present at the ends of the wires overlap, forming a dispersive edge mode with thermal conductance determined by the central charge c of the low-energy effective field theory of the edge. We show numerically that, in the presence of disorder, the c=1/2 Majorana edge mode remains delocalized up to extremely strong attractive interactions, while repulsive interactions drive a transition to a c=3/2 edge phase localized by disorder. The absence of localization for strong attractive interactions is explained by a self-duality symmetry of the statistical ensemble of disorder configurations and of the edge interactions, originating from translation invariance on the length scale of the underlying mesoscopic array.
Real-time dynamics in the one-dimensional Hubbard model
Real-time dynamics in the one-dimensional Hubbard model
L. Seabra, F. H. L. Essler, F. Pollmann, I. Schneider, and T. Veness
We consider single-particle properties in the one-dimensional repulsive Hubbard model at commensurate fillings in the metallic phase. We determine the real-time evolution of the retarded Green’s function by matrix- product state methods. We find that at sufficiently late times the numerical results are in good agreement with predictions of nonlinear Luttinger liquid theory. We argue that combining the two methods provides a way of determining the single-particle spectral function with very high frequency resolution.
Cascade of field-induced magnetic transitions in a frustrated antiferromagnetic metal
A. I. Coldea, L. Seabra, A. McCollam, A. Carrington, L. Malone, A. F. Bangura, D. Vignolles, P.G. vanRhee, R. D. McDonald, T. Sorgel, M. Jansen, N. Shannon, and R. Coldea
A. I. Coldea, L. Seabra, A. McCollam, A. Carrington, L. Malone, A. F. Bangura, D. Vignolles, P.G. vanRhee, R. D. McDonald, T. Sorgel, M. Jansen, N. Shannon, and R. Coldea
Phys. Rev. B 90, 020401(R) (2014); arXiv
Frustrated magnets can exhibit many novel forms of order when exposed to high magnetic fields, however, much less is known about materials where frustration occurs in the presence of itinerant electrons. Here we re- port thermodynamic and transport measurements on micron-size single crystals of the triangular-lattice metallic antiferromagnet 2H-AgNiO2, in magnetic fields of up to 90 T and temperatures down to 0.35 K. We observe a cascade of magnetic phase transitions at 13.5, 20, 28 and 39 T in fields applied along the easy axis, and we combine magnetic torque, specific heat and transport data to construct the field-temperature phase diagram. The low-field experimental data are compared with theoretical calculations for a frustrated easy-axis Heisenberg model based on realistic parameters for the localized moments of AgNiO2 in an applied magnetic field. The deviations in the measured phase diagram from this model predictions are attributed to the role played by the itinerant electrons.
Frustrated magnets can exhibit many novel forms of order when exposed to high magnetic fields, however, much less is known about materials where frustration occurs in the presence of itinerant electrons. Here we re- port thermodynamic and transport measurements on micron-size single crystals of the triangular-lattice metallic antiferromagnet 2H-AgNiO2, in magnetic fields of up to 90 T and temperatures down to 0.35 K. We observe a cascade of magnetic phase transitions at 13.5, 20, 28 and 39 T in fields applied along the easy axis, and we combine magnetic torque, specific heat and transport data to construct the field-temperature phase diagram. The low-field experimental data are compared with theoretical calculations for a frustrated easy-axis Heisenberg model based on realistic parameters for the localized moments of AgNiO2 in an applied magnetic field. The deviations in the measured phase diagram from this model predictions are attributed to the role played by the itinerant electrons.
From fractionally charged solitons to Majorana bound states in a one-dimensional interacting model
From fractionally charged solitons to Majorana bound states in a one-dimensional interacting model
D. Sticlet, L. Seabra, F. Pollmann and J. Cayssol
D. Sticlet, L. Seabra, F. Pollmann and J. Cayssol
We consider one-dimensional topological insulators hosting fractionally charged midgap states in the presence and absence of induced superconductivity pairing. Under the protection of a discrete symmetry, relating positive and negative energy states, the solitonic midgap states remain pinned at zero energy when superconducting correlations are induced by proximity effect. When the supercon- ducting pairing dominates the initial insulating gap, Majorana fermion phases develop for a class of insulators. As a concrete example, we study the Creutz model with induced s-wave superconductivity and repulsive Hubbard type interactions. For a finite wire, without interactions, the solitonic modes originating from the non-superconducting model survive at zero energy, revealing a fourfold degenerate ground state. However, interactions break the aforementioned discrete symmetry and completely remove this degeneracy, thereby producing a unique ground state which is characterized by a topological bulk invariant with respect to the product of fermion parity and bond inversion. In contrast, the Majorana edge modes are robust to interactions. Moreover, the parameter range for which a topological Majorana phase is stabilized expands when increasing the repulsive Hubbard interaction. The topological phase diagram of the interacting model is obtained using a combination of mean-field theory and density matrix renormalization group techniques.
Exotic Ising dynamics in a Bose-Hubbard model
L. Seabra and F. Pollmann
Phys. Rev. B 88, 125103 (2013); arXivWe explore the dynamical properties of a one-dimensional Bose-Hubbard model, where two bosonic species interact via Feshbach resonance. We focus on the region in the phase diagram which is described by an effective, low-energy ferromagnetic Ising model in both transverse and longitudinal fields. In this regime, we numerically calculate the dynamical structure factor of the Bose-Hubbard model using the time-evolving block decimation method. In the ferromagnetic phase, we observe both the continuum of excitations and the bound states in the presence of a longitudinal field. Near the Ising critical point, we observe the celebrated E8 mass spectrum in the excited states. We also point out possible measurements which could be used to detect these excitations in an optical lattice experiment.
Phase diagram of the classical Heisenberg antiferromagnet on a triangular lattice in an applied magnetic field
Phase diagram of the classical Heisenberg antiferromagnet on a triangular lattice in an applied magnetic field
L. Seabra, T. Momoi, P. Sindzingre, and N. Shannon
The Heisenberg antiferromagnet on a two-dimensional triangular lattice is a paradigmatic problem in frustrated magnetism. Even in the classical limit S → ∞, its properties are far from simple. The “120-degree” ground state favored by the frustrated antiferromagnetic interactions contains a hidden chiral symmetry and supports two distinct types of excitation. And, famously, in an applied magnetic field, three distinct phases, including a collinear one-third magnetisation plateau, are stabilized by thermal fluctuations. The questions of symmetry breaking raised by this model are deep and subtle, and after more than thirty years of study many of the details of its phase diagram remain surprisingly obscure. In this paper we use modern Monte Carlo simulation techniques to determine the finite-temperature phase diagram of the classical Heisenberg antiferromagnet on a triangular lattice in an applied magnetic field. At low to intermediate values of the magnetic field, we find evidence for a continuous phase transition from the paramagnet into the collinear one-third magnetization plateau, belonging to the three-state Potts universality class. We also find evidence for conventional Berezinskii-Kosterlitz-Thouless transitions from the one-third magnetization plateau into the canted “Y state” and into the 2:1 canted phase found at high fields. However, the phase transition from the paramagnet into the 2:1 canted phase, while continuous, does not appear to fall into any conventional universality class. We argue that this, like the chiral phase transition discussed in the zero field case, deserves further study as an interesting example of a finite-temperature phase transition with compound order-parameter symmetry. We comment on the relevance of these results for experiments on magnetic materials with a triangular lattice.
Competition between supersolid phases and magnetization plateaus in the frustrated easy-axis antiferromagnet on a triangular lattice
Competition between supersolid phases and magnetization plateaus in the frustrated easy-axis antiferromagnet on a triangular lattice
L. Seabra and N. ShannonPhys. Rev. B 83, 134412 (2011); arXiv
The majority of magnetic materials possess some degree of magnetic anisotropy, either at the level of a single ion, or in the exchange interactions between different magnetic ions. Where these exchange interactions are also frustrated, the competition between them and anisotropy can stabilize a wide variety of new phases in applied magnetic field. Motivated by the hexagonal delafossite 2H-AgNiO2, we study the Heisenberg antiferromagnet on a layered triangular lattice with competing first- and second-neighbor interactions and single-ion easy-axis anisotropy. Using a combination of classical Monte Carlo simulation, mean-field analysis, and Landau theory, we establish the magnetic phase diagram of this model as a function of temperature and magnetic field for a fixed ratio of exchange interactions, but with values of easy-axis anisotropy D extending from the Heisenberg (D = 0) to the Ising (D = ∞) limits. We uncover a rich variety of different magnetic phases. These include several phases which are magnetic supersolids (in the sense of Matsuda and Tsuneto or Liu and Fisher), one of which may already have been observed in AgNiO2. We explore how this particular supersolid arises through the closing of a gap in the spin-wave spectrum, and how it competes with rival collinear phases as the easy-axis anisotropy is increased. The finite temperature properties of this phase are found to be different from those of any previously studied magnetic supersolid.
Supersolid phases in a realistic three-dimensional spin model
Supersolid phases in a realistic three-dimensional spin model
L. Seabra and N. ShannonPhys. Rev. Lett. 104, 237205 (2010); arXivSupersolid 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 transition, and its possible observation, are discussed.
Two dimensional frustrated magnets in high magnetic field
L. Seabra, N. Shannon, P. Sindzingre, T. Momoi, B. Schmidt, and P. Thalmeier
Frustrated magnets in high magnetic field have a long history of offering beautiful surprises to the patient investigator. Here we present theresults of extensive classical Monte Carlo simulations of a variety of models of two dimensional magnets in magnetic field, together with complementary spin wave analysis. Striking results include (i) a massively enhanced magnetocaloric effect in antiferromagnets bordering on ferromagnetic order, (ii) a route to an m = 1/3 magnetization plateau on a square lattice, and (iii) a cascade of phase transitions in a simple model of AgNiO2.
Phase diagram of the spin-1/2 J1-J2-J3 Heisenberg model on the square lattice with ferromagnetic J1
Phase diagram of the spin-1/2 J1-J2-J3 Heisenberg model on the square lattice with ferromagnetic J1
P. Sindzingre, L. Seabra, N. Shannon, and T. Momoi
J. Phys. Conf. 145, 012048 (2009)
Phase diagram of the S = 1/2, J1-J2-J3 Heisenberg model on the square lattice with ferromagnetic 1st neighbor and antiferromagnetic 2nd and 3rd neighbor interactions is studied by means of exact diagonalization and spin wave calculations. Quantum fluctuations are shown to induce phases that are not present classically and a shift in the wave vector of the spiral phases. Results are compared with recent experimental data.
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