The collective behavior of spins in a dilute magnetic semiconductor is
determined by their mutual interactions and influenced by the underlying
crystal structure. Hence, we begin with the atomic quantum-mechanical
description of this system using the proposed variational-perturbation
calculus, and then turn to the emerging macroscopic picture employing
phenomenological constants. Within this framework we study spin waves and
exchange stiffness in the p-d Zener model of (Ga,Mn)As, its thin layers and
bulk crystals described by the spds* tight-binding approximation. Analyzing the
anisotropic part of exchange, we find that the Dzyaloshinskii-Moriya
interaction may lead to the cycloidal spin arrangement and uniaxial in-plane
anisotropy in thin layers, resulting in a surface-like anisotropy in thicker
films. We also derive and discuss the spin-wave contribution to magnetization
and Curie temperature. Our theory reconstructs the values of stiffness
determined from the temperature dependence of magnetization, but reproduces
only partly those obtained from analyzing precession modes in (Ga,Mn)As thin
films.Comment: 17 pages, 12 figures (added Eq. 36, replaced Fig. 10