Effective Nuclear Spin Hamiltonian for Electronic Singlet Ground State System

Abstract

Along the same line as in the previous paper, an effective nuclear spin Hamiltonian is derived for the system where magnetic ions have the electronic singlet ground state and are interacting each other by the exchange interaction. All crystal-field levels of electrons are taken into account so that the Hamiltonian can be used for any realistic case in the nuclear regime. The exchange enhancement appears in the form of (1−η)⁻¹ for the electronic Zeeman energy, the I–I coupling, the pseudo nuclear quadrupole interaction, and the pseudo nuclear Zeeman effect, η being proportional to the exchange constant. Examples are shown for rare earth ions and the resulting I–I coupling has the form of the Heisenberg model in the cubic case but of the X–Y model in the uniaxial case.