Spin Hamiltonian formalism

For the evaluation of magnetically split Mossbauer spectra within the spin-Hamiltonian formalism, the purely -dependent Hamiltonian must be extended by an appropriate... 

The spin-Hamiltonian formalism is a crutch in the sense that it is a parameterized theory, but it provides a common theoretical frame for the various experimental techniques with a minimum number of adjustable parameters that describe the essential physics of the system under investigation. Even more important is the fact that the same parameters can be derived relatively easily from quantum chemical calculations. Therefore, theoreticians appreciate the concept as a convenient place to rest in the analysis of experimental data by theoretical means [123, 124]. 

Blinc R (2007) Order and Disorder in Perovskites and Relaxor Ferroelectrics. 124 51-67 Boca R (2005) Magnetic Parameters and Magnetic Functions in Mononuclear Complexes Beyond the Spin-Hamiltonian Formalism 117 1-268 Bohrer D, see Schetinger MRC (2003) 104 99-138 Bonnet S, see Baranoff E (2007) 123 41-78... 

Ignoring the other perturbations which determine the energy level structure of the ground state, and hence details of the ESR experiment, the results of the experiment for the present purposes are conventionally summarized by the spin Hamiltonian formalism. In simplest form we have... 

This new formalism, known as spin-Hamiltonian formalism, does not contain the L operator, which would require more laborious calculations. Its effects are parametrically included in the g tensor, which would pass from ellipsoidal to spherical in the absence of orbital angular momentum. 

Such splitting is called zero field splitting and indicated as ZFS. It adds up to the Zeeman energy. In the spin-Hamiltonian formalism, i.e. when the effects of the orbital angular momentum are parameterized, it is indicated as... 

The most common approach to the interpretation of EPR and Mossbauer spectra of siderophores is the spin Hamiltonian formalism. The wavefimctions are parameterized in terms of a few coupling constants that arise in the spin Hamiltonian description of the electronic states. In this approach, the crystal field potential is generally described by a series of spherical harmonics. The corresponding operators are tabulated. ... 

The Spin Hamiltonian Formalism Determination of Zero-Field Splitting D and Rhombicity E/D of Paramagnetic Iron Centers by Mossbauer Spectroscopy... 

The spin Hamiltonian formalism, which is also needed to interpret, for example, electron paramagnetic resonance or magnetic circular dichroism spectra see Magnetic Circular Dichroism (MCD) Spectroscopy), was first applied to the interpretation of magnetic Mossbauer spectra by Wickmann, Klein and Shirley and was implemented into a computer program by Miinck et al. in the early 1970s. For most studies of mononuclear iron centers with electron spin quantum number S, the following electronic Hamiltonian is used ... 

The low-lying states arising from the coupling between nickel(II) (Si = 1) and copper(II) (Sz = i) can be described, in a spin Hamiltonian formalism, using the total spin S = Si + Sz-Two states can arise with S = and respectively. In all the pure nickel(II)-copper(II) complexes reported to the exchange interaction is antiferromagnetic making... 

Paramagnetic species trapped in solid materials usually possess anisotropic g- and hyperfine couplings. Zero-field splittings occur when 5 > V2. The spin Hamiltonian formalism described in Appendix A3.1 is a convenient means to summarise the different interactions. The following spin-Hamiltonian is adequate to illustrate most aspects of the analysis. 

The first three terms are usually the ones of relevance for the ESR analysis, where D and A are the zero-field (or fine structure) and hyperfine coupling tensors. They are represented by 3-3 symmetric matrices and specified by three principal values and three principal directions as for the -tensor. The remaining nuclear Zeeman and quadrupole (/ > Vi) terms do not affect the ESR spectra, unless they are of comparable magnitude to the hyperfine coupling, but must be taken into account in the analysis of ENDOR and ESEEM spectra. The spin Hamiltonian formalism introduced by M.H.L. Pryce and A. Abragam [79] is used explicitly or implicitly in the ESR literature as a convenient way to summarise resonance parameters. 

A nucleus with / > i has, like an electron, a magnetic moment. The interaction of this moment with that of the electron is called the hyperfine interaction and may be treated using the effective spin Hamiltonian formalism in Eq. (4). If we assume that is diagonal in the xyz coordinate system, we may write... 

To stay within a spin Hamiltonian formalism, the permutation operator has to be replaced by spin operators, which can be done in the following way [19] ... 

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