Consider the classical 2D-model of a Heisenberg easy-plane AFM, with the Hamiltonian

Here **J > 0** is the exchange constant, describes
anisotropy with the xy-plane as the easy-plane.
Spins
are classical vectors on a 2D-square lattice with lattice
constant **a**. denotes lattice sites of one sublattice,
and 's are the set of displacements to the
nearest-neighbors on the other sublattice. We are interested in
the small anisotropy case .

A continuum model of AFM's can be derived from (1) in the usual way, see [2],[4],[6]. We define the magnetization vector and the sublattice magnetization vector on the set of nearest-neighbor pairs, with the constraints , . Then, for low frequencies and small gradients, , the magnetization of an AFM is small, . The magnetization can be considered as a ``slave'' variable, and can be expressed as , where is a susceptibility defined below [Eq. (3)]. After eliminating one obtains equations for only. Using the usual angular variables, () these equations can be written in the form[4],[6]

where **c** is the magnon phase velocity, is
the characteristic length scale. For the Hamiltonian
(1)

Wed Sep 6 18:51:57 CDT 1995