On the theory of impurities in a lattice of magnetic ions: Crystalline field effects

We present a formalism for treating the problem of impurities in a lattice of magnetic rare earth ions. Latter are subject to a crystalline field and special attention is paid to non-Kramers ions in a singlet ground state. Our calculations are restricted to the paramagnetic regime. We derive the conditions for magnetic localized modes to occur and discuss the appearance of local magnetic instabilities. It is shown that the impurity effects are especially large if the system is close to a magnetic phase transition. Furthermore we compute the influence of impurities on the magnetic transition temperature. For the case of vacancies or nonmagnetic impurities the dependence of the Curie temperature on impurity concentration is derived. It is demonstrated that small amounts of impurities can often completely suppress magnetic ordering.