Quadrupolar Ordering in Two-Dimensional Spin-One Systems

The principal aim of this thesis is to gain a better understanding of the competition between magnetic and quadrupolar degrees of freedom on two-dimensional lattices. Recent experimental investigations of the material NiGa2S4 revealed several anomalous properties that might be accounted for within the framework of quadrupolar ordering. Exhibiting both a ferroquadrupolar and an antiferroquadrupolar phase, the S = 1 bilinear-biquadratic Heisenberg model on the triangular lattice is a possible candidate for describing the low-temperature behaviour of the system. In this work, we put forward a more realistic model that includes single-ion anisotropy. We perform a thorough investigation of the variational phase diagram of this model and we show that it exhibits a variety of unconventional phases. We derive the excitation spectrum of the quadrupolar phases in the phase diagram and we point out that ferroquadrupolar order is particularly sensitive to the nature of anisotropy. Finally, we study quantum effects in the perturbative limit of large anisotropy and we argue that the non-trivial degeneracy of the mean-field solution is lifted by an emergent supersolid phase. We also discuss our results in the context of NiGa2S4. In the second part of the thesis, we aim at gaining an insight into the interplay between geometrical frustration and quadrupolar degrees of freedom by mapping out the phase diagram of the spin-one bilinear-biquadratic model on the square lattice. Our variational approach reveals a remarkable 1/2-magnetization plateau of mixed quadrupolar and magnetic character above the classically degenerate "semi-ordered" phase, and this finding is corroborated by exact diagonalization of finite clusters. "Order-by-disorder" phenomenon gives rise to a state featuring three-sublattice antiferroquadrupolar order below the plateau, which is truly surprising given the bipartite nature of the square lattice. We place particular emphasis on investigating the properties of the SU(3) Heisenberg model, which is shown to feature a subtle competition between quantum and thermal fluctuations. Our results suggest a suppression of two-sublattice Néel order in a finite window below the SU(3) point. Experimental implications for the Mott-insulating states of three-flavour fermionic atoms in optical lattices are discussed.

Emergence and Detection of Exotic Phases in Spin-1 Systems

Frédéric Alexis Michaud

This work is devoted to the study of spin S = 1 systems, and more precisely to the emergence of exotic quantum phases in such systems, and to the establishment of tools to observe such phases. It is split in four main chapters. In the first chapter, we show how spin S = 1 systems can emerge from microscopic models, and which kinds of interaction might appear in the effective spin model. We start from a two-orbital Hubbard model, and by a strong coupling development to fourth order, we derive an effective model. We will see that three types of interaction appear beyond the Heisenberg interaction : a plaquette interaction, a biquadratic interaction and a three-spin interaction. In the second chapter, we study Raman scattering on systems with quadrupolar order to show that it can be used to probe such order. We first start by deriving an effective light scattering operator following Shastry and Shraiman calculation on spin S = 1/2 systems. Using this effective operator, we compute the Raman spectra with exact diagonalization and linear flavor-wave theory. We show that two different regimes appear depending on the incoming photon energy, and that combining this to different polarizations accessible with Raman scattering, the presence of quadrupolar order can be established with this probe. The third chapter is devoted to the study of the three-spin interaction that appeared in the first chapter on a chain. We start by establishing the classical and the mean field phase diagram of this system. We then turn to the quantum case. We show that, whatever the value of the spin is, the ground state is perfectly dimerized for a particular value of the three-spin interaction. The presence of such a point in the phase diagram implies the existence of a quantum phase transition when increasing the three-spin interaction. By an intensive numerical study, we show that this transition is continuous, and that its critical behavior is the one of a SU(2)k=2S Wess-Zumino-Witten model, at least for spins S = 1/2,1,3/2,2. In the last section of this chapter, we study the phase diagram of the chain for spin S = 1 under a magnetic field. We conclude this work with a study of the three-spin interaction on a square lattice. The classical and mean field phase diagram are established. It is shown that for a large three-spin interaction, the classical ground state is highly degenerate. This degeneracy is lifted in the quantum case by a process of order by disorder. We compute the quantum fluctuations with linear spin-wave theory, and show that some phases are selected over others. We confirm these results by an exact diagonalization study of the system.

EPFL2013

The Interplay Between Structural and Electronic Degrees of Freedom in Superconductors

Mathieu Julien Gino Cottet

More than one hundred years after the discovery of superconductivity in Leiden, the intriguing physics of several unconventional classes of superconductors continue to fascinate and challenge scientists from all over the world. The majority of these compounds belongs to a major class of materials known as strongly correlated systems that exhibit interesting and diverse physical properties, like the high-temperature superconductivity, the Mott-insulator transition, the colossal magnetoresistance or the structurally-driven electronic phase transitions. Rigorous and deep investigations of the electronic properties, as well as their tunability, should lead to new attractive commercial applications. With the use of time-resolved experiments or bulk sensitive techniques, which represent the main subject of this thesis, the electronic and magnetic properties of strongly correlated type-II superconductors and high-temperature copper-oxide superconductors are accessible. These techniques take advantages of the photon tunability in the case of optical pump-probe by allowing one to record the transient response of the material over the whole visible spectrum, or in the case of X-ray diffraction, the tunability of the synchrotron radiation thanks to the slicing operating at the SLS (Swiss Light Source) in Villigen, Switzerland. Cryo-LTEM allows one to work across the (H ,T ) phase diagram of type-II superconductors, thus enabling the study of the coexistence between normal and superconducting state by careful regulation of the applied magnetic field near the specimen. The Chapter 1 (1) is a general introduction dedicated to the historical evolution of our understanding of superconductivity, according to the theories and general concepts used and developed is this thesis. Chapter 2 (3) is dedicated to the experimental techniques. A careful description of the different setups, as well as a theoretical development needed for the calculations is presented. In Chapter 3 (4), the investigation of magnesium diboride superconductor by means of cryo-LTEM is presented. By observing the field-dependent vortex lattices in this system and performing calculations using the theoretical frameworks developed by Ginzburg-Landau and Abrikosov, I found that this compound belongs to the type-II family [1], and not to the novel type 1.5 class of superconductor. In Chapter 4 (5), I present the investigation related the charge density waves compound Lu5Ir4Si10. The use of ultrafast time-resolved optical pump-probe experiments, coupled with ab-anitio theoretical calculations of the electron-phonon coupling and the electronic structure, permits to shine new light on the nature of this transition which we identified as a structurally-driven Peierls transition [2]. The Chapter 5 (6) is dedicated to the investigation of the high-temperature copper-oxide superconductor, La2−x Srx CuO4, for different doping levels; the experiment was carrying out at the SLS on the Micro-XAS beamline, By using a transient temperature model and comparing our experimental results with temperature-dependent density of states calculations, we report on the electronic temperature dependence of the electron-phonon coupling constant (submitted to Phys. Rev. B).

EPFL2013

Stabilization of the chiral phase of theSU(6m)Heisenberg model on the honeycomb lattice withmparticles per site formlarger than 1

Jérôme Dufour, Frédéric Mila

Low-dimensional quantum magnets at finite temperatures present a complex interplay of quantum and thermal fluctuation effects in a restricted phase space. While some information about dynamical response functions is available from theoretical studies of the one-triplet dispersion in unfrustrated chains and ladders, little is known about the finite-temperature dynamics of frustrated systems. Experimentally, inelastic neutron scattering studies of the highly frustrated two-dimensional material SrCu2(BO3)2 show an almost complete destruction of the one-triplet excitation band at a temperature only 1/3 of its gap energy, accompanied by strong scattering intensities for apparent multi-triplet excitations. We investigate these questions in the frustrated spin ladder and present numerical results from exact diagonalization for the dynamical structure factor as a function of temperature. We find anomalously rapid transfer of spectral weight out of the one-triplet band and into both broad and sharp spectral features at a wide range of energies, including below the zero-temperature gap of this excitation. These features are multi-triplet bound states, which develop particularly strongly near the quantum phase transition, fall to particularly low energies there, and persist all the way to infinite temperature. Our results offer valuable insight into the physics of finite-temperature spectral functions in SrCu2(BO3)2 and many other highly frustrated spin systems.

2016

Emergence and Detection of Exotic Phases in Spin-1 Systems

Frédéric Alexis Michaud

EPFL2013

The Interplay Between Structural and Electronic Degrees of Freedom in Superconductors

Mathieu Julien Gino Cottet

EPFL2013