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Concept

Spin-1/2

Résumé

In quantum mechanics, spin is an intrinsic property of all elementary particles. All known fermions, the particles that constitute ordinary matter, have a spin of 1/2. The spin number describes how many symmetrical facets a particle has in one full rotation; a spin of 1/2 means that the particle must be rotated by two full turns (through 720°) before it has the same configuration as when it started. Particles having net spin 1/2 include the proton, neutron, electron, neutrino, and quarks. The dynamics of spin-1/2 objects cannot be accurately described using classical physics; they are among the simplest systems which require quantum mechanics to describe them. As such, the study of the behavior of spin-1/2 systems forms a central part of quantum mechanics. Stern–Gerlach experiment The necessity of introducing half-integer spin goes back experimentally to the results of the Stern–Gerlach experiment. A beam

Source officielle

https://en.wikipedia.org/wiki/Spin-1/2

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Cours associés (42)

Presentation of particle properties, their symmetries and interactions. Introduction to quantum electrodynamics and to the Feynman rules.

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Solid State Physics IV provides a materials and experimental technique oriented introduction to the electronic and magnetic properties of strongly correlated electron systems. Established knowledge is complemented by current research trends, aiming to prepare the students for independent research.

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Séances de cours associées (89)

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Publications associées (30)

Possibility to detect the bound state of the Heisenberg ferromagnetic chain at intermediate temperature

Frédéric Mila, Mithilesh Nayak

Motivated by the lack of direct evidence with inelastic neutron scattering of the well documented bound state of Heisenberg ferromagnets, we use the time-dependent thermal density matrix renormalization group algorithm to study the temperature dependence of the dynamical spin structure factor of Heisenberg ferromagnetic spin chains. For spin 1/2, we show that the bound state appears as a well defined excitation with significant spectral weight in the temperature range J/12 less than or similar to T less than or similar to J/3, pointing to the possibility of detecting it with inelastic neutron scattering near k = pi provided the temperature is neither too low nor too high-at low temperature, the spectral weight only grows as T-3/2 and, at high temperature, the bound state peak merges with the two-magnon continuum. For spin 1, the situation is more subtle because the bound state with two neighboring spin flips competes with an antibound state with two spin flips on the same site. As a consequence, the relative spectral weight of the bound state is smaller than for spin 1/2 and a weak resonance due to the antibound state appears in the continuum. A clearer signature of the bound state (antibound state) can be obtained if a negative (positive) biquadratic interaction is present.

AMER PHYSICAL SOC2022

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Static and dynamic properties of non-collinear quantum antiferromagnets explored by neutron scattering

Luc Testa

This thesis is devoted to the investigation of static and dynamic properties of two different sets of quantum magnets with neutron scattering techniques and the help of linear spin wave theory. Both systems are copper-based with spin-1/2, which makes them ideal to study the interplay between purely quantum and semi-classical effects. I start with the analysis of the antiferromagnet SeCuO3, which has a canted spins structure. Through careful inelastic neutron scattering experiments on thermal and cold triple-axis spectrometers, I demonstrate that this compound exhibits three primary types of excitations that are intrinsically opposite : spin waves (magnons), singlet to triplet excitations (triplons), and fractional spins excitations (spinons). Such a strong coexistence and interdependence of these collective excitations has not been observed yet, thereby the quantification and description of the excitations in SeCuO3 leads the way to further theoretical work on multi-excitation spin systems, as well as the existence of quantum effects in high dimensional systems.\ My second project is on the extraction of the magnetic structure of three members of the A(BO)Cu4(PO4)4 chiral family, namely (A; B) = (Ba; Ti), (Sr; Ti) and (Pb; Ti), from spherical neutron polarimetry measurements. I prove that the first two compounds exhibit a highly non-collinear magnetic structure, with the Cu spins forming clusters of 'two-in--two-out' arrangements on each structural unit. This structure is stabilised by the presence of a strong Dzyaloshinskii-Moriya interaction, and explains the observation of magnetoelectric effects as emerging from quadrupole moments. The analysis of the latter compound did not lead to the confirmation of its magnetic structure due to strong nuclear-magnetic interference. I conclude this thesis by the investigation of the magnetic excitation spectrum of some members of the (A; B) family, probed by inelastic neutron scattering measurements. Indeed, its particular crystallographic structure makes it an ideal playground to study tetramerisation effects on the two dimensional square lattice. Additionally, the aforementioned Dzyaloshinskii-Moriya interaction ensures the presence of a structural gap, which competes with the quantum one emerging from tetramerisation effects. Using linear spin wave theory, I describe (Ba; Ti) as a chequerboard system with almost equal intra- and inter-plaquette couplings, with weak quantum effects. I also provide a qualitative description of (Pb; Ti), which exhibits similar physics, and conclude by presenting the first results on the highly symmetric compound (K; Nb), which shows hints of a strong quantum behaviour.

EPFL2021

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Motivated by the ongoing investigation of SrCu2(BO3)(2) under pressure, we study a variant of the two-dimensional Shastry-Sutherland (SS) spin-1/2 model with two types of dimers. Combined with the frustration of the SS model, this modification induces, in a large parameter range, a dimensional reduction at low energies, with nearly decoupled effective S = 1 Haldane chains forming along one of the diagonals of the lattice. We also present evidence that the intermediate plaquette solid phase of the undistorted SS model remains stable in a finite region of the phase diagram.

2011

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Static and dynamic properties of non-collinear quantum antiferromagnets explored by neutron scattering

Luc Testa

EPFL2021