Spin Hamiltonian zero-field splittings

As mentioned above, the electron spin system is strongly coupled to the classical degrees of freedom, in the first place the orientation of a molecule-fixed frame with respect to the lab frame, through anisotropic interactions. We concentrate here on the case of S > 1, where the main anisotropic interaction is denoted as the zero-field splitting, ZFS. In the language of spin Hamiltonians (8,80), the ZFS interaction is written ... 

Values of the spin Hamiltonian reported for d4 ions are given in Table XI. The difficulty in detecting the ESR is due most likely to short spin-lattice-relaxation times and large zero-field splittings. In both octahedral and tetrahedral fields the 5 D state of d4 gives degenerate orbital states which,... 

Values for the spin Hamiltonian are given in Table XIV. The 5D state of d6 has three orbital states for the ground state in octahedral symmetry. Since these three states are connected by the spin-orbit coupling, the spin-lattice-relaxation time is quite short and the zero-field splitting very large. In a distorted octahedral field the large zero-field distortion makes detection of ESR difficult. In the case of ZnF2 the forbidden AM = 4 transition was measured and fitted to Eq. (164). 

The EPR spectra have always been interpreted2994 using an effective S = 2 spin Hamiltonian including the Zeeman term, /iBB g-S, and the hyperfine term, ICa-A-S, which describes the interaction of the unpaired electrons with the copper nucleus (7Cu = I). The spectra are very sensitive to the ratio between the isotropic coupling constant J and the local zero field splitting of nickel(II), Z)Ni.2982 In the limit J DNi it can easily be shown that the following relations hold ... 

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... 

Calculations were also performed for electron spin Hamiltonian dominated by zero field splitting [14,15]. 

Abbreviations CF - crystal field SH - spin Hamiltonian ZFS - zero-field splitting MA - magnetic anisotropy TIP - temperature-independent paramagnetism MP - magnetic parameter averaged (gav, /tip), axial (gz> g > D /up) CSC - complete space calculation. 

Only spatially degenerate states exhibit a first-order zero-field splitting. This condition restricts the phenomenon to atoms, diatomics, and highly symmetric polyatomic molecules. For a comparison with experiment, computed matrix elements of one or the other microscopic spin-orbit Hamiltonian have to be equated with those of a phenomenological operator. One has to be aware of the fact, however, that experimentally determined parameters are effective ones and may contain second-order contributions. Second-order SOC may be large, particularly in heavy element compounds. As discussed in the next section, it is not always distinguishable from first-order effects. 

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

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