Spin dynamics of itinerant electrons: local magnetic moment formation and Berry phase

Abstract

The state-of-the-art theoretical description of magnetic materials relies on solving effective Heisenberg spin problems or their generalizations to relativistic or multi-spin-interaction cases that explicitly assume the presence of local magnetic moments in the system. We start with a general interacting fermionic model that is often obtained in ab initio electronic structure calculations and show that the corresponding spin problem can be introduced even in the paramagnetic regime, which is characterized by a zero average value of the magnetization. Further, we derive a physical criterion for the formation of the local magnetic moment and confirm that the latter exists already at high temperatures well above the transition to the ordered magnetic state. The use of path-integral techniques allows us to disentangle spin and electronic degrees of freedom and to carefully separate rotational dynamics of the local magnetic moment from Higgs fluctuations of its absolute value. It also allows us to accurately derive the topological Berry phase and relate it to a physical bosonic variable that describes dynamics of the spin degrees of freedom. As the result, we demonstrate that the equation of motion in the case of a large magnetic moment takes a conventional Landau-Lifshitz form that explicitly accounts for the Gilbert damping due to itinerant nature of the original electronic model.

References in corpus (19)

• Continuous-time Monte Carlo methods for quantum impurity models
• Quantum magnetism and criticality
• Amplitude / Higgs Modes in Condensed Matter Physics
• The `Higgs' Amplitude Mode at the Two-Dimensional Superfluid-Mott Insulator Transition
• Quantum Magnets under Pressure: Controlling Elementary Excitations in TlCuCl3
• Dual fermion approach to the two-dimensional Hubbard model: Antiferromagnetic fluctuations and Fermi arcs
• Quantum and classical criticality in a dimerized quantum antiferromagnet
• Dichotomy between large local and small ordered magnetic moment in Iron-based superconductors
• Beyond extended dynamical mean-field theory: Dual boson approach to the two-dimensional extended Hubbard model
• The Higgs mode in a two-dimensional superfluid
• Topological Thermal Hall Effect in Frustrated Kagomé Antiferromagnets
• Diagrammatic Monte Carlo for Dual Fermions
• Impact of partially bosonized collective fluctuations on electronic degrees of freedom
• Direct observation of the Higgs amplitude mode in a two-dimensional quantum antiferromagnet near the quantum critical point
• Non-equilibrium magnetic interactions in strongly correlated systems
• Universal Properties of the Higgs Resonance in (2+1)-Dimensional U(1) Critical Systems
• Magnetic exchange in $\alpha$-iron from the ab initio calculations in the paramagnetic phase
• Fermionic spinon theory of square lattice spin liquids near the Néel state
• The Higgs Mode of Planar Coupled Spin-Ladders and its Observation in C${}_9$H${}_{18}$N${}_2$CuBr${}_4$

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• Extended regime of coexisting metallic and insulating phases in a two-orbital electronic system
• Exchange interactions in iron and nickel: DFT+DMFT study in paramagnetic phase
• Doping-dependent charge- and spin-density wave orderings in a monolayer of Pb adatoms on Si(111)
• The effect of local magnetic moments on spectral properties and resistivity near the interaction- and doping induced Mott transitions
• Can Orbital-Selective Néel Transitions Survive Strong Nonlocal Electronic Correlations?
• Fluctuating local field approach to free energy of 1D molecules with strong collective electronic correlations
• Reciprocal space study of Heisenberg exchange interactions in ferromagnetic metals
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• Exchange interactions in itinerant magnets: the effects of local particle-hole irreducible vertex corrections and SU(2) symmetry of Hund interaction
• Superconductivity of Bad Fermions: Origin of Two Gaps in HTSC Cuprates
• Multi-band D-TRILEX approach to materials with strong electronic correlations
• Local-moment magnetism in Mn-based pnictides
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