Theoretical studies on the magnetic quantum tunneling rates in Mn clusters by the path integral method

Magnetic quantum tunneling rates in Mn clusters are investigated theoretically by the path integral method in relation to the topological structures and integer or half-integer spins. A general expression of the imaginary-time transition amplitude is presented by the path integral formulation of the non-linear σ model, and effective Lagrangians for the manganese clusters are also derived to obtain a general expression of the imaginary-time amplitude.