  Classical ground state of the isotropic Heisenberg spin Hamiltonian on a
primitive Bravais lattice is known to be a single-Q planar spin spiral. A
uniaxial anisotropy and external magnetic field distort this structure by
generating the higher-order Fourier harmonics at wave-vectors nQ in the spatial
spin configuration. These features are not captured in the formalism based on
the Luttinger-Tisza theorem, where the classical ground state energy is
minimized under the ``weak'' condition on the length of the spins. We discuss
why the correct solution is lost in that approach and present an alternative
microscopic treatment of the problem. It allows to find the classical ground
state for general Q for both easy-axis and easy-plane uniaxial second-order
anisotropy, and for any orientation of the magnetic field, by treating the
effect of anisotropy (but not the field) as a perturbation to the exchange
structure. As a result, the classical ground state energy, the uniform
magnetization, and the magnetic Bragg peak intensities that are measured in
experiment, are calculated.
