Effective-Spin Hamiltonian for "Non-Kramers" Doublets

The use of a spin-½ formalism to analyze paramagnetic and paraelectric resonance experiments of "non-Kramers" doublets leads to a break with the accepted meaning of effective-spin Hamiltonians. The operators appearing in the Hamiltonian do not have the transformation properties of spin angular momentum in real space. It is shown that in a spin-1 formalism an invariant effective Hamiltonian exists in which the operators do have these properties. In this formalism, operators for linear and quadratic electric-field effects are given and discussed. The $S_4$ and $D_{2d}$ symmetries are the only ones in which an electric field parallel to the main axis splits the "non-Kramers" doublet linearly.