Oscillatory tunnel splittings in spin systems: A discrete Wentzel-Kramers-Brillouin approach

Certain spin Hamiltonians that give rise to tunnel splittings that are view ed in terms of interfering instanton trajectories are restudied using a dis crete WKB method, that is more elementary, and also yields wave functions a nd preexponential factors for the splittings. A novel turning point inside the classically forbidden region is analyzed, and a general formula is obta ined for the splittings. The result is applied to the Fes system. A previou s result for the oscillation of the ground state splitting with external ma gnetic field is extended to higher levels.