Spin-Hamiltonian formalisms in electron magnetic resonance (EMR) and related spectroscopies

The historical development leading to, and the current status of, the spin-Hamiltonian (SH) formalisms. characterizing electron magnetic resonance (EMR), also referred to as electron paramagnetic (or spin) resonance (EPR or ESR), is reviewed. The spin-Hamiltonian concept is briefly outlined to set a framework for definitions of relevant terms. Meanings of the terms which are often confused with each other, e.g. physical versus effective Hamiltonian, real versus effective versus fictitious spin, microscopic SH (MSH), zero-field-splitting (ZFS) Hamiltonian, generalized SH (GSH), and phenomenological SH (PSH), are elucidated. Various general approaches to 'derive' MSH as well as to 'construct' GSH for transition ions are discussed, This enables clarification of relationship between the ZFS Hamiltonian and (a) the crystal-field (CF), (b) electronic spin-spin, and (c) nuclear-quadrupole Hamiltonians. The inadmissibility of the odd-order ZFS terms (1 = 3, 5) is also discussed, A brief general classification of the major operator and parameter notations used in the literature to describe ZFS Hamiltonian is provided. Other important areas relevant to EMR, where the SH concept plays a central role, are outlined.