Decay rates and decoherence of an interstitial two-level spin impurity in a ferromagnetic lattice

Abstract

The decay rates of a two-level interstitial impurity, weakly coupled to a anisotropic ferromagnetic spin lattice are derived. Using the spin-wave theory and Bogoliubov transformations, the lattice Hamiltonian is diagonalized leading to the identification of the critical point. The elimination of the lattice spin degrees of freedom in the derivation of the master equation is restricted by the periodicity of the lattice which fixes the form of the spectral density in the continuum limit. This fact has a great impact on the form and the values of the decay rate and the Lamb shift. It is found that the time dependent decay rates exhibit strong non-Markovian features as they assume negative values. The exact analytical form of the decay rate and the Lamb shift are derived for particular situations. The analytical and the numerical calculations reveal that in addition to the lattice criticality, there exist other critical resonance-like points about which the bahavior of the decay rate, and hence the reduced density matrix, changes drastically.