Anisotropic g-Tensor and Abragam’s Dipole Alphabet: New Words

The impact of g-tensor anisotropy on the dipole–dipole interaction (DDI) of Kramers paramagnetic centers (PCs) with spins of ½ is theoretically considered in the point dipole limit. The magnetic moment may be expressed in terms of the tensor G = g^T.g and the signature of the g-tensor (sign of its determinant). This means that the DDI spin Hamiltonian depends only on the G of the PCs involved and on their respective g-tensor signatures. Abragam’s dipole alphabet for isotropic PCs consists of six letters by Abragam (The principles of nuclear magnetism, Clarendon Press, Oxford, 1961), each letter a product of a spin operator and a spatial coordinate. Pairs of letters correspond to zero-, single-, and double-quantum coherences. In the case of like anisotropic spins, the dipole alphabet has the same structure but with different coordinate factors that depend on the tensor G and its orientation in the laboratory frame. In the general case, anisotropic spins have nine letters in their dipole alphabet. Analytic expressions for all the letters are obtained. The DDI spin Hamiltonian for anisotropic PCs can contain terms having the appearance of isotropic exchange-like and quadrupolar-like interactions resulting entirely from the DDI.