Semiclassical theory of the magnetization process of the triangular lattice Heisenberg model

Motivated by the numerous examples of 1/3 magnetization plateaux in the triangular-lattice Heisenberg antiferromagnet with spins ranging from 1/2 to 5/2, we revisit the semiclassical calculation of the magnetization curve of that model, with the aim of coming up with a simple method that allows one to calculate the full magnetization curve and not just the critical fields of the 1/3 plateau. We show that it is actually possible to calculate the magnetization curve including the first quantum corrections and the appearance of the 1/3 plateau entirely within linear spin-wave theory, with predictions for the critical fields that agree to order 1/S with those derived a long time ago on the basis of arguments that required going beyond linear spin-wave theory. This calculation relies on the central observation that there is a kink in the semiclassical energy at the field where the classical ground state is the collinear up-up-down structure and that this kink gives rise to a locally linear behavior of the energy with the field when all semiclassical ground states are compared to each other for all fields. The magnetization curves calculated in this way for spin 1/2, 1, and 5/2 are shown to be in good agreement with available experimental data.

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

Magnetic states and spin-wave modes in single ferromagnetic nanotubes

Daniel Rüffer

In this thesis the electrical properties, magnetic states and spin wave resonances of individual magnetically hollow ferromagnetic nanotubes have been studied. They were prepared from the different materials Nickel (Ni), Permalloy (Py) and Cobalt-Iron-Boron (CoFeB), deposited as shells onto non-magnetic Gallium-Arsenide (GaAs) semiconductor nanowires via Atomic Layer Deposition (ALD), thermal evaporation and magnetron sputtering, respectively. The resulting nanotubes had lengths between 10 to 20 μm, diameters of 150 to 400 nm and tube walls (shells) which were 20 to 40nm thick. Structural analysis of the tubes by Transmission Electron Microscopy revealed a poly(nano)crystalline (Ni, Py) and amorphous (CoFeB) structure. Electrical transport experiments as a function of temperature revealed different transport mechanisms for each of the materials. Electron-phonon scattering dominated the temperature dependence of the resistivity in Ni, while a clear evidence for electron magnon scattering was observed in Py. Electron-electron interaction in granular and amorphous media was identified as the major contribution to the temperature dependence in CoFeB. The Anisotropic Magnetoresistance (AMR) ratios have been determined for all tubes and different temperatures. Ni nanotubes exhibited a large relative AMR effect of 1.4% at room temperature. The AMR measurements provided information about the magnetic configurations as well as the magnetization reversal mechanism. Indications for the formation of vortex segments in Ni tubes were found for the magnetization reversal when the magnetic field was perpendicular to the nanotube axis. In cooperation with the Poggio group in Basel, cantilever magnetometry has been used for the further characterization of the nanotube magnetization. The magnetization curves were compared to the AMR measurements and finite element method (FEM) micromagnetic simulations. The comparison between the experimental results and the simulations suggested that the roughness of Ni tubes gave rise to segmented magnetic switching. An almost perfect axial alignment of the remanent magnetization has been observed in Py and CoFeB nanotubes. The influence of the inhomogeneous internal field in transverse magnetic fields was investigated by simulation. The segment-wise alignment of spins with the field direction is argued to provoke characteristic kinks in the hysteresis curve and measured AMR effect. Magnetothermal spatial mapping experiments using the anomalous Nernst effect (ANE) complemented the magnetotransport experiments in cooperation with the group of Prof. Grundler in Munich. Here, first evidence of end-vortices entering the nanotube before reversal could be found. Electrically detected spin wave resonance experiments have been performed in cooperation with the group of Prof. Grundler on individual nanotubes. The detected voltage, generated by the spin rectification effect, revealed multiple resonances in the GHz frequency. The experimentally observed resonances were compared to calculated ones extracted from dynamic simulations. With this comparison, the signatures could be attributed to azimuthally confined spin-wave modes. The deduced dispersion relation suggested the quantization of exchange dominated spin waves in that resonance frequencies follow roughly a quadratic dependence on the wave vector.

EPFL2014

Semiclassical evidence of columnar order in the fully frustrated transverse-field Ising model on the square lattice

Tommaso Coletta, Frédéric Mila

We investigate the zero-temperature phase diagram of the fully frustrated transverse-field Ising model on the square lattice both in the classical limit and in the presence of quantum fluctuations. At the classical level (the limit of infinite spin S), we find that upon decreasing the transverse field Gamma this model exhibits a phase transition from the fully polarized state into an eightfold degenerate translational symmetry breaking state. This phase can be identified to correspond to plaquette order in the dimer language and remains the lowest-energy state in the entire range of fields below the critical one, Gamma(c). The eightfold degenerate solution that corresponds to columnar order in the dimer language is a saddle point of the classical energy. It is degenerate with the plaquette solution at Gamma = 0 and is only slightly higher in energy in the whole interval 0 < Gamma < Gamma(c). The effect of quantum fluctuations is investigated in the context of a large S expansion both for the plaquette and columnar structures. For this purpose we employ an approximate method allowing to estimate from above the fluctuation-induced correction to the energy of a configuration which at the classical level is a saddle point of the energy, not a local minimum, and find that the harmonic quantum fluctuations show a clear tendency to overcome the energy difference between the two states. For relatively high fields, the transition from the plaquette to the columnar state takes place at values of S large enough to be in the domain of validity of the harmonic approximation.