Ground states and excitations of frustrated magnetic systems, from the classical limit to the quantum case

The first part of this thesis is devoted to classical magnetic systems. A method for an exhaustive search of states that do not break any spatial symmetry on a given lattice is presented. New Néel states on the kagome lattice are described. Their static structure factors give a way to analyze experimental results. Some non-coplanar spin orders are the only ground states of Heisenberg Hamiltonians. The chirality is a discrete order parameter and give rise to a finite temperature phase transition, studied on a toy model. We show that Z2 topological defects proliferate near chirality domain walls. The order of the transition (first order or Ising like) depends on the spin interactions. The Schwinger boson mean-field theory (SBMFT) allows us to link classical and quantum spin physics: long-range ordered and disordered phases as topological spin liquids can be described in this frame. Symmetry and the way to impose them are analyzed. Different phases are distinguished by their fluxes. These are gauge invariant quantities having a signification as well in a quantum system as in the classical limit. Visons are quantum excitations that change fluxes. Thus, the Z2 vorticies are their classical limit. By relaxing some symmetry constraints, chiral phases are obtained, whose classical limit sends back to the first chapter of this thesis, and whose disordered phase gives chiral spin liquids. The example of the Dzyaloshinskii-Moriya interaction on the kagome lattice is studied.

Lattice symmetries and regular magnetic orders in classical frustrated antiferromagnets

We consider some classical and frustrated lattice spin models with global O(3) spin symmetry. No general analytical method to find a ground state exists when the spin dependence of the Hamiltonian is more than quadratic (i.e., beyond the Heisenberg model) and/or when the lattice has more than one site per unit cell. To deal with these cases, we introduce a family of variational spin configurations, dubbed “regular magnetic orders” (RMO’s), which respect all the lattice symmetries modulo global O(3) spin transformations (rotations and/or spin flips). The construction of these states is made explicit through a group-theoretical approach, and all the RMO’s on the square, triangular, honeycomb, and kagome lattices are listed. Their equal-time structure factors and powder averages are shown for comparison with experiments. Well known Néel states with one, two, or three sublattices on various lattices are RMO’s, but the RMO’s also encompass exotic nonplanar states with cubic, tetrahedral, or cuboctahedral geometry of the T=0 order parameter. Regardless of the details of the Hamiltonian (with the same symmetry group), a large fraction of these RMO’s are energetically stationary with respect to small deviations of the spins. In fact, these RMO’s appear as exact ground states in large domains of parameter space of simple models that we have considered. As examples, we display the variational phase diagrams of the J1-J2-J3 Heisenberg model on all the previous lattices as well as that of the J1-J2-K ring-exchange model on square and triangular lattices.

2011

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

Emergence and Detection of Exotic Phases in Spin-1 Systems

Frédéric Alexis Michaud

EPFL2013