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Publication# Quantum dynamics and entanglement of spins on a square lattice

Résumé

Bulk magnetism in solids is fundamentally quantum mechanical in nature. Yet in many situations, including our everyday encounters with magnetic materials, quantum effects are masked, and it often suffices to think of magnetism in terms of the interaction between classical dipole moments. Whereas this intuition generally holds for ferromagnets, even as the size of the magnetic moment is reduced to that of a single electron spin (the quantum limit), it breaks down spectacularly for antiferromagnets, particularly in low dimensions. Considerable theoretical and experimental progress has been made in understanding quantum effects in one-dimensional quantum antiferromagnets, but a complete experimental description of even simple two-dimensional antiferromagnets is lacking. Here we describe a comprehensive set of neutron scattering measurements that reveal a non-spin-wave continuum and strong quantum effects, suggesting entanglement of spins at short distances in the simplest of all two-dimensional quantum antiferromagnets, the square lattice Heisenberg system.

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Magnétisme

Le magnétisme représente un ensemble de phénomènes physiques dans lesquels les objets exercent des forces attractives ou répulsives sur d'autres matériaux. Les courants électriques et les moments mag

Antiferromagnétisme

L'antiferromagnétisme est une propriété de certains milieux magnétiques prédite par Louis Néelen 1936. Contrairement aux matériaux ferromagnétiques, dans les matériaux antiferromagnétiques,

Mécanique quantique

La mécanique quantique est la branche de la physique théorique qui a succédé à la théorie des quanta et à la mécanique ondulatoire pour étudier et décrire les phénomènes fondamentaux à l'œuvre dans

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Quantum magnetism remains a hot topic in condensed matter physics due to its complexity and possible powerful and significant applications in data storage and memory. To understand how the materials can achieve these goals, one should have a clear idea about the fundamentals behind it. In this thesis, we focus on three examples that can help us deepen the knowledge in many-body effects, which stand to be crucial for quantum magnetism.(1) The well-known \textbf{CuSO$_4\cdot$5D$_2$O} material has already demonstrated the model behaviour as one-dimensional Heisenberg antiferromagnet in zero and high ($H>H_{sat}$) fields. The fully-polarized magnetic ground state is described by linear spin-wave theory with magnons, whereas at zero field, the excitations are pairs of topological excitations called spinons. In an intermediate field, the dynamic properties are even more complicated. The inelastic spectrum cannot be reproduced without considering exotic elementary excitations and bound states such as psinons and Bethe strings. Although Bethe in 1931 provided an exact solution for 1D Heisenberg systems, there is still no quantitative comparison between theory and experiment.(2) The magnetic ground state and hence the dynamic properties of the gemstone mineral green dioptase, \textbf{Cu$_6[$Si$_6$O$_{18}]\cdot6$H$_2$O} are under debate: starting from controversial theories and continuing with non-explained experimental observations. Dioptase is a quasi-one-dimensional spin chain with dominant antiferromagnetic interactions. Recent studies claim the classical spin chain behaviour and absence of any quantum fluctuations in the system. In contrast, our experimental findings indicate the presence of continuous excitations above and below T$_N$.(3) Newly synthesized material \textbf{CuSb$_2$O$_6$} of rosiaite-type structure tends to become a quantum spin-liquid (QSL) candidate since the magnetic cations Cu$^{2+}$ are arranged in trigonal layers, and no long-range order is observed down to 2~K. The idea of QSL on the triangular lattice was proposed by P. Anderson in 1973. Since his work, a lot of efforts have been made to explore deeper, both theoretically and experimentally, this state. As for now, there are several requirements needed to be met -- small spin number, absence of long-range order or spin freezing, long-range entanglement, and the associated fractional spin excitations. We aim to establish whether or not CuSb$_2$O$_6$ can be considered as a potential quantum spin-liquid candidate employing different techniques suitable for a powder sample.

Antiferromagnetic insulators at low temperatures offer a clean arena to study non-semiclassical phenomena because the character of interactions is usually known. Macroscopic properties of the system can then be calculated by more or less sophisticated approximations and compared to experimental results. Generally, quantum effects are expected to increase by lowering the couplings or connectivity between the magnetic moments. Magnetic excitations, which can be easily measured by the neutron spectroscopy technique, are particularly sensitive to quantum effects. Answers to questions related to the ground state and the excitation spectra of quantum magnets are of primary importance to understand magnetism. We here study the coupled tetrahedra system Cu2Te2O5X2 (X=Cl, Br) and weakly connected Cu3TeO6 system. Both systems are complex magnetic insulators, with relatively low antiferromagnetic transition temperatures. In the Cu2Te2O5X2 system we observed an unusual situation where an anomalously weak low-energy Goldstone-like mode is accompanied by a strong higher energy gapped mode. When compared to a random phase approximation theory, there is a striking difference in the intensities, but also in the gap size. We propose that the origin of the discrepancy lies in the quantum fluctuations originating between the tetrahedra, which were not taken into account by the theory. In the "spin-web" lattice system Cu3TeO6, no reasonable fit of the semiclassical theory based on the Heisenberg Hamiltonian to the dispersion of excitations has been possible. Here, however, no quantum effects have been explicitly demonstrated. By doing additional polarized neutron spectroscopy experiment, we proved that a strong magnon-phonon coupling in this system significantly changes the properties of the spectrum.

Many physical properties of high-temperature superconductors are two-dimensional phenomena derived from their square-planar CuO2 building blocks. This is especially true of the magnetism from the copper ions. As mobile charge carriers enter the CuO2 layers, the antiferromagnetism of the parent insulators, where each copper spin is antiparallel to its nearest neighbours(1), evolves into a fluctuating state where the spins show tendencies towards magnetic order of a longer periodicity. For certain charge-carrier densities, quantum fluctuations are sufficiently suppressed to yield static long-period order(2-6), and external magnetic fields also induce such order(7-12). Here we show that, in contrast to the chemically controlled order in superconducting samples, the field-induced order in these same samples is actually three-dimensional, implying significant magnetic linkage between the CuO2 planes. The results are important because they show that there are three-dimensional magnetic couplings that survive into the superconducting state, and coexist with the crucial inter-layer couplings responsible for three-dimensional superconductivity. Both types of coupling will straighten the vortex lines, implying that we have finally established a direct link between technical superconductivity, which requires zero electrical resistance in an applied magnetic field and depends on vortex dynamics and the underlying antiferromagnetism of the cuprates.

2005