Spin-Wave Impurity States in Ferromagnets

TLDR

The authors develop a theory of spin‑wave impurity states from the Heisenberg exchange Hamiltonian using Green’s function techniques and derive a general expression for the width of virtual states by analyzing impurity‑induced changes in the density of states. Numerical analysis of simple cubic ferromagnetic insulators shows that dilute impurities generate low‑lying s‑like impurity states and virtual states—some lying outside the spin‑wave band and others with long lifetimes—whose energies depend on the impurity‑to‑host spin and exchange ratios, potentially influencing the material’s specific heat and thermal conductivity.

Abstract

The effect of dilute impurities on the spin-wave spectrum of ferromagnetic insulators has been studied. The theory of spin-wave impurity states is developed from the Heisenberg exchange Hamiltonian using Green's function techniques. The low-lying, $s$-like, impurity states for cubic crystals are discussed and shown to depend only upon the unperturbed spin-wave density of states. Numerical results are obtained for simple cubic crystals. It is shown that localized states lying outside of the spin-wave band as well as virtual states which decay into the continuum can exist. The energy of the $s$-, $p$-, and $d$-like states is obtained as a function of the ratios of the impurity spin and effective exchange to those of the host atoms. The nature of the virtual states is discussed and a general expression for the width is obtained by considering the change in the density of states due to the impurities. Low-lying, $s$-like, virtual states with long lifetimes are found to exist, and it is suggested that these states may cause significant effects in the spin-wave specific heat and thermal conductivity of impure ferroinsulators.