Theory of elementary excitations in ferromagnetic semiconductors

Abstract

A field-theoretical perturbation formalism is developed to study the excitations of wide-band ferromagnetic semiconductors described by the s-f (or s-d) interaction model. In lowest (zeroth) order the results are shown to be equivalent to a generalised mean-field theory. A first-order theory for the magnetic Green functions is presented, leading to results for the spectrum of magnetic excitations, which consist of acoustic spin waves, optical spin waves, and a Stoner-like continuum of electron-hole excitations. Analytical arguments are given to establish various general features of the acoustic and optical modes, particularly at T=0, and it is shown that the acoustic magnons are well defined excitations over a wide range of wavevectors. On the other hand the authors conclude that the optical magnons are well defined only in a narrow band of wavevectors close to the Brillouin zone centre. The processes giving rise to the lifetimes of the magnetic excitations in the first order of the perturbation classification correspond to the decay of a magnon into an electron-hole pair with a spin-flip. Some numerical estimates of various effect are given, taking parameters appropriate to EuO.