Effective magnetic field parameter tensor

The crystal field does, however, have a dramatic effect on the magnetic anisotropy of lanthanide complexes. For complexes of less than cubic symmetry the three principal values of the susceptibility tensor are unequal. For uniaxial symmetry, Xx — Xy Xz and for biaxial symmetry Xx Xy Xz- Very extensive studies632-640 have been carried out on the single crystal susceptibilities of the D3d lanthanide hexakis(antipyrene) triiodides over the temperature range 80-300 K, and crystal field parameters were obtained. This crystal field-induced anisotropy is responsible for the effectiveness of lanthanide complexes as NMR shift reagents, and single crystal anisotropies of lanthanide complexes have been determined in this connection also.563... 

The electronic g-tensor is a fundamental parameter in descriptions of the electronic Zeeman effect and one of the key elements in characterization of EPR spectra. It couples the external magnetic field, B, with the total spin angular momentum, S, of the molecule and is conventionally evaluated as the second derivative of the molecular energy ... 

In an analysis of the diffusion equations in magnetic fields, Dumarque et al. introduced a diffusivity tensor and an effectiveness parameter related to the difference between diffusivity in the presence and in the absence of a magnetic field. In a less general, but somewhat more amenable approach to numerical estimations, Lielmezs and Musbally derived a magnetic correction factor called the arithmetic mean average fractional integral diffusion coefficient... 

In a seminal contribution, Bleaney demonstrated that when the crystal-field splitting of the ground multiplet is smaller or comparable to kT, a situation often met with lanthanide complexes, the anisotropic part of the axial paramagnetic susceptibility tensor originates from second-order effects and can be simply estimated by the product of magnetic constants Cj, characteristics of the electronic configuration of each lanthanide (i.e., Bleaney factor), multiplied by the second-rank crystal-field parameter Bq (Eq. (34), Bleaney, 1972). 

As the ENDOR spectrum is in effect an NMR spectrum obtained by devious means, when considering the response of a nucleus with spin / one must keep track of all interactions that it and its coupled electron spin undergo. The energy levels of an unpaired electronic spin S in an externally applied magnetic field, and the associated EPR spectra, are described in detail elsewhere in this volume. As described therein, the interaction of an electronic spin in an external magnetic field is characterized by the parameter g. In a molecule, the magnitude of the electron spin interaction depends on the orientation of the molecule with respect to the external magnetic field, and thus g is a tensor quantity. 

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