Path Integral Method for Tunneling of Spin Systems and the Macroscopic Quantum Effect of Magnetization

The quantum tunneling effect in a ferromagnetic particle which can be evaluated only for the ground state previously is extended to excited states within the framework of instanton method. The tunneling between n-th degenerate states of neighboring wells is dominated by a periodic pseudoparticle configuration with which a formula of level-splitting valid for entire energy region is derived. In low energy region periodic instanton results coincide exactly with those derived through the LSZ reduction procedure. The tunneling effect increases at excited states. These results should be useful in further investigation of phase transition problem in ferromagnetic particles.