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INTERACTIONS IN PARAMAGNETIC SYSTEMS
MECHANISMS OF EXCHANGE COUPLING
13 other sections not shown
absorption anisotropy annihilation operators antibonding orbitals antiferromagnetic approximation atoms branches Brillouin zone calculated canonical transformation Chapter coefficient conduction electrons configuration consider contribution correlation coupling crystal field denote dependence diagonal diamagnetic dipolar discussed dispersion relation effective exchange electric dipole exchange Hamiltonian exchange integral exchange interaction excited exciton experimental external magnetic field FeF2 Fermi surface ferromagnetic function gives Hartree-Fock hyperfine interaction Hamiltonian interaction processes interaction terms involving ionic ions lattice ligand ions ligand orbitals magnetic field magnetic ions magnetic ordering magnetic systems magnon magnon energies magnon modes magnon-magnon magnon-phonon interaction matrix element mean field theory mechanism metal ion MnF2 momentum neutron scattering noted obtain occupation number one-electron one-magnon one-phonon optical paramagnetic paramagnetic ions perturbation phonon polarization relaxation frequency renormalization representation resonance respectively singlet singly occupied orbitals Sinha spin operators spin waves spin-orbit spin-up spin-wave splitting sublattice symmetry temperature term of eqn theory thermal transition two-magnon unpaired electron values wave vector