Basics of the spin Hamiltonian formalism

Abstract

Based on the relation between quantum mechanical concepts such as effective Hamiltonians (EHs), perturbation theory (PT), and unitary transformations, and phenomenological aspects of spin Hamiltonians (SHs), the present tutorial tries to address the basics of the SH formalism. Using simple physical models and historical important examples, we have reviewed the derivation methods and applications of the SHs for a brief and in-depth description of various sources of anisotropies and interactions such as electronic (EZ), and nuclear Zeeman (NZ), terms, electron-exchange interaction (EE), zero-field splitting (ZFS), spin-spin (SS), spin-orbit (SO), nuclear quadrupole (NQ), and hyperfine couplings (HFCs), in a step-wise manner. In this way, this tutorial is tailored for the graduate students and young researchers who intend to begin their studies in the field of magnetism, electron magnetic resonance (EMR), spectroscopy, and related areas.

Pentacoordinate cobalt(ii) single ion magnets with pendant alkyl chains: shall we go for chloride or bromide?

“…The SH was defined in the formwhere D and E are axial and rhombic parameters of zero-field splitting, respectively; is the vector of magnetic field induction; is the gyromagnetic tensor; and and Ŝ x , y , z are the vector operators of spin and its components, respectively. 44 The Griffith–Figgis Hamiltonian was postulated in the following formwhere and L̂ x , y , z are vector operators of angular momentum and its components, respectively; λ is the constant of the spin–orbit interaction; and Δ ax and Δ rh are parameters of a crystal field with axial and rhombic symmetry, respectively. 42 To improve the agreement between the models and experimental results, the effect of the molecular field was included in both cases (quantified by parameter zj ), which accounts for weak magnetic exchange interactions with neighboring magnetic centers.…”

Magneto-structural correlations in oxalate-bridged Sr(ii)Cr(iii) coordination polymers: structure, magnetization, X-band, and high-field ESR studies

“…The height of magnetic anisotropy barrier in systems with easy axis of magnetization can be expressed as |D|S 2 (for integer spins) 6 , where D is axial zerofield splitting (ZFS) parameter D defined in spin-Hamiltonian approach. 7,8 The barrier height could be changed by modifications of local environments such as using different ligand field, coordination ions and symmetry. 9,10 In order to characterize complexes with desired magnetic properties, it is necessary to be able to precisely determine magnetic anisotropy.…”

Dirac imprints on the g -factor anisotropy in graphene

“…with g 0 representing the pure g-factor, µ B the Bohr magneton and B an external magnetic field. On the other hand, the effective spin model, commonly employed experimentally to describe the Zeeman energy, includes an effective g tensor and fictitious spin operators [15][16][17],…”