  We present a methodology based on the N\'{e}el model to build a classical
spin-lattice Hamiltonian for cubic crystals capable of describing magnetic
properties induced by the spin-orbit coupling like magnetocrystalline
anisotropy and anisotropic magnetostriction, as well as exchange
magnetostriction. Taking advantage of the analytical solutions of the N\'{e}el
model, we derive theoretical expressions for the parameterization of the
exchange integrals and N\'{e}el dipole and quadrupole terms that link them to
the magnetic properties of the material. This approach allows to build accurate
spin-lattice models with the desire magnetoelastic properties. We also explore
a possible way to model the volume dependence of magnetic moment based on the
Landau energy. This new feature can allow to consider the effects of
hydrostatic pressure on the saturation magnetization. We apply this method to
develop a spin-lattice model for BCC Fe and FCC Ni, and we show that it
accurately reproduces the experimental elastic tensor, magnetocrystalline
anisotropy under pressure, anisotropic magnetostrictive coefficients, volume
magnetostriction and saturation magnetization under pressure at
zero-temperature. This work could constitute a step towards large-scale
modeling of magnetoelastic phenomena.
