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 (64)

• Continuous-time Monte Carlo methods for quantum impurity models
• A continuous-time solver for quantum impurity models
• Continuous Time Quantum Monte Carlo method for fermions
• 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
• Chiral spin liquid and emergent anyons in a Kagome lattice Mott insulator
• First- principle calculations of magnetic interactions in correlated systems
• Three-spin interactions in optical lattices and criticality in cluster Hamiltonians
• Higgs mode and its decay in a two dimensional antiferromagnet
• Anisotropic Spin Hamiltonians due to Spin-Orbit and Coulomb Exchange Interactions
• Topological-chiral magnetic interactions driven by emergent orbital magnetism
• Dual fermion approach to the two-dimensional Hubbard model: Antiferromagnetic fluctuations and Fermi arcs
• Quantum and classical criticality in a dimerized quantum antiferromagnet
• Dual boson approach to collective excitations in correlated fermionic systems
• Dichotomy between large local and small ordered magnetic moment in Iron-based superconductors
• Efficient perturbation theory for quantum lattice models
• About the strength of correlation effects in the electronic structure of iron
• Beyond extended dynamical mean-field theory: Dual boson approach to the two-dimensional extended Hubbard model
• Dynamical Screening in Correlated Electron Materials
• LDA++ approach to electronic structure of magnets: correlation effects in iron
• The Higgs mode in a two-dimensional superfluid
• Topological order in the pseudogap metal
• Pseudogap and Fermi surface topology in the two-dimensional Hubbard model
• Role of higher-order exchange interactions for skyrmion stability
• Topological Thermal Hall Effect in Frustrated Kagomé Antiferromagnets
• Strong-Coupling Expansion for the Hubbard Model
• Impact of nonlocal correlations over different energy scales: A Dynamical Vertex Approximation study
• Quantum dynamical screening of the local magnetic moment in Fe-based superconductors
• Raman scattering from Higgs mode oscillations in the two-dimensional antiferromagnet Ca${}_2$RuO${}_4$
• Consistent partial bosonization of the extended Hubbard model
• Fingerprints of the local moment formation and its Kondo screening in the generalized susceptibilities of many-electron problems
• Mechanisms of finite temperature magnetism in the three-dimensional Hubbard model
• Self-consistent Dual Boson approach to single-particle and collective excitations in correlated systems
• Diagrammatic Monte Carlo approach for diagrammatic extensions of dynamical mean-field theory -- convergence analysis of the dual fermion technique
• Diagrammatic Monte Carlo for Dual Fermions
• Direct observation of the Higgs amplitude mode in a two-dimensional quantum antiferromagnet near the quantum critical point
• Impact of partially bosonized collective fluctuations on electronic degrees of freedom
• Effective Heisenberg model and exchange interaction for strongly correlated systems
• From local to non-local correlations: the Dual Boson perspective
• Probing the topology of the quantum analog of a classical skyrmion
• Dual Boson Diagrammatic Monte Carlo Approach Applied to the Extended Hubbard Model
• Non-equilibrium magnetic interactions in strongly correlated systems
• Universal Properties of the Higgs Resonance in (2+1)-Dimensional U(1) Critical Systems
• Spin dynamics and relaxation in the classical-spin Kondo-impurity model beyond the Landau-Lifschitz-Gilbert equation
• Characteristic Timescales of the Local Moment Dynamics in Hund's-metals
• Two-site fluctuations and multipolar superexchange interactions in strongly correlated systems
• Dual Boson approach with instantaneous interaction
• 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
• Momentum-dependent susceptibilities and magnetic exchange in bcc iron from supercell DMFT calculations
• Effective Ising model for correlated systems with charge ordering
• Imprinting and driving electronic orbital magnetism using magnons
• Fermi-surface reconstruction without symmetry breaking
• Relaxation of a classical spin coupled to a strongly correlated electron system
• Dual fermion method as a prototype of generic reference-system approach for correlated fermions
• Collective magnetic fluctuations in Hubbard plaquettes captured by fluctuating local field method
• Four-spin-exchange- and magnetic-field-induced chiral order in two-leg spin ladders
• The Higgs Mode of Planar Coupled Spin-Ladders and its Observation in C${}_9$H${}_{18}$N${}_2$CuBr${}_4$
• A new approach to strongly correlated fermion systems: the spin-particle-hole coherent-state path integral
• A strong-coupling expansion for the Hubbard model
• Dzyaloshinskii-Moriya interaction in absence of spin-orbit coupling
• Orbital isotropy of magnetic fluctuations in correlated electron materials induced by Hund's exchange coupling

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• Non-perturbative intertwining between spin and charge correlations: A "smoking gun" single-boson-exchange result
• Local and nonlocal electronic correlations at the metal-insulator transition in the Hubbard model in two dimensions
• 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
• Protection of Correlation-Induced Phase Instabilities by Exceptional Susceptibilities
• 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
• Local magnetic moment formation and Kondo screening in the presence of Hund exchange: the two-band Hubbard model analysis
• Long-term memory magnetic correlations in the Hubbard model: A dynamical mean-field theory analysis