Unconventional mechanisms of magnetic ordering in frustrated models of quantum magnetism

In this thesis we investigate in the semiclassical approximation how unconventional magnetic ordering, that is magnetic ordering which is not predicted at the classical level, emerges in a variety of frustrated models of quantum magnetism. The first part of this thesis presents our semiclassical investigation of the magnetization processes of the anisotropic triangular lattice Heisenberg antiferromanget and of the J1 − J2 square lattice Heisenberg antiferromanget. Existing analytical, numerical and experimen- tal evidences report that these systems exhibit a magnetization plateau respectively at 1/3 and 1/2 of the saturation value and whose structure can be understood in simple terms as a collinear spin structure. We develop a strategy to estimate the semiclassical energy of collinear spin structures away from their classical stability point. In this framework we are able to predict the stabilization of a collinear up-up-down structure with a magnetization equal to one third of the saturation value in a wide anisotropy range for the triangular lattice Heisen- berg antiferromanget. Similarly we find that the four sublattice up-up-up-down structure with magnetization equal to 1/2 of the saturation value is stabilized deep into the classically striped ordered region of the J1 − J2 square lattice Heisenberg antiferromanget. In the case of the anisotropic triangular lattice Heisenberg antiferromagnet a brief digression is made to the zero field case. The semiclassical approach confirms that quantum fluctuations favor collinear structures over the classical spiral states in either the weakly and strongly coupled chain regimes. The second part of the thesis is devoted to the study of fully frustrated transverse field Ising models. These models have emerged as an alternative tool to access the physics of the quan- tum dimer models (QDM) of Rokhsar and Kivelson at the purely kinetic point. We studied the classical phase diagram of this model for the square and honeycomb lattice geometries. In either case the effect of quantum fluctuations and the relevance to the physics of the QDM is discussed. In the case of the honeycomb lattice geometry we find that the classical phase diagram is rather involved with columnar and plaquette states separated by an infinite series of states of mixed nature. From the study of quantum fluctuations we conjecture that the sqrt(12) × sqrt(12) plaquette phase dominates over the columnar structure down to zero transverse field in the limit S = 1/2. In the case of the square lattice geometry we find that at the classical level the plaquette state is stabilized below the polarized state down to zero transverse field. In agreement with the most recent quantum Monte Carlo results, we show that for S = 1/2 quantum fluctuations favor columnar oder in the whole field range below saturation even though this structure is never classically stable in this parameter range.

Magnetic anisotropy of Fe and Co ultrathin films deposited on Rh(111) and Pt(111) substrates: An experimental and first-principles investigation

Harald Brune, Markus Etzkorn, Pietro Gambardella, Anne Lehnert, Géraud Moulas, Stefano Rusponi

We report on a combined experimental and theoretical investigation of the magnetic anisotropy of Fe and Co ultrathin layers on strongly polarizable metal substrates. Monolayer (ML) films of Co and Fe on Rh(111) have been investigated in situ by x-ray magnetic circular dichroism (XMCD), magneto-optic Kerr effect, and scanning tunneling microscopy. The experiments show that both magnetic adlayers exhibit ferromagnetic order and enhanced spin and orbital moments compared to the bulk metals. The easy magnetization axis of 1 ML Co was found to be in plane, in contrast to Co/Pt(111), and that of 1 ML Fe out of plane. The magnetic anisotropy energy (MAE) derived from the magnetization curves of the Fe and Co films is one order of magnitude larger than the respective bulk values. XMCD spectra measured at the Rh M2,3 edges evidence significant magnetic polarization of the Rh(111) surface with the induced magnetization closely following that of the overlayer during the reversal process. The easy axis of 1–3 ML Co/Rh(111) shows an oscillatory in-plane/out-of-plane behavior due to the competition between dipolar and crystalline MAE. We present a comprehensive theoretical treatment of the magnetic anisotropy of Fe and Co layers on Rh(111) and Pt(111) substrates. For free-standing hexagonally close-packed monolayers the MAE is in plane for Co and out of plane for Fe. The interaction with the substrate inverts the sign of the electronic contribution to the MAE, except for Fe/Rh(111), where the MAE is only strongly reduced. For Co/Rh(111), the dipolar contribution outweighs the band contribution, resulting in an in-plane MAE in agreement with experiment while for Co/Pt(111) the larger band contribution dominates, resulting in an out-of-plane MAE. For Fe films however, the calculations predict for both substrates an in-plane anisotropy in contradiction to the experiment. At least for Fe/Pt(111) comparison of theory and experiment suggests that the magnetic structure of the adlayer is more complex than the homogenous ferromagnetic order assumed in the calculations. The angular momentum and layer-resolved contributions of the overlayer and substrate to the MAE and orbital moment anisotropy are discussed with respect to the anisotropic hybridization of the 3d, 4d, and 5d electron states and vertical relaxation. The role of technically relevant parameters such as the thickness of the surface slab, density of k points in the Brillouin zone, and electron-density functionals is carefully analyzed.

2010

Quadrupolar Ordering in Two-Dimensional Spin-One Systems

Tamás András Tóth

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.

EPFL2011

Exotic phases of quantum frustrated magnets

Julien Dorier

In this work, we study two examples of frustrated magnetic systems whose degrees of freedom are spins (or pseudo-spins) on two-dimensional lattices. The first part presents the results obtained for the quantum compass model on a square lattice. This model is a minimal model for the orbital degrees of freedom of transition metal compounds. We use exact diagonalizations, quantum Monte Carlo simulations as well as a perturbative approach in order to study the ground state degeneracy in the thermodynamic limit and the type of order in the ground state. The second part of this work is devoted to the study of the magnetic properties of SrCu2(BO3)2, which is one of the few quasi two-dimensional quantum magnets whose magnetization curve as a function of the magnetic field shows plateaus. The magnetic degrees of freedom are described by a spin 1/2 Heisenberg model on the Shastry-Sutherland lattice in the presence of an external magnetic field. In order to study the magnetic properties at zero-temperature, we use perturbative continuous unitary transformations to derive an effective Hamiltonian in which the triplets Sz = 1 are particles moving on a background of singlets. This Hamiltonian is characterized by a kinetic energy dominated by correlated hopping, which let a particle hop only if there is another particle nearby. In order to better understand the effect of the correlated hopping, we start by studying a minimal model. By using exact diagonalizations, quantum Monte Carlo and a semi-classical approximation we show that the correlated hopping can stabilize a phase characterized by a condensation of pairs of particles and strongly favor supersolid phases. Next, we determine the zero-temperature phase diagram of the effective model by using a classical approximation. A comparison to previous theoretical works and experimental measurements shows that the Shastry-Sutherland model cannot reproduce the series of magnetization plateaus measured experimentally. This suggest that the residual interactions, which were neglected, could be crucial for SrCu2(BO3)2.

EPFL2008