In a ferromagnet, the magnitude of the magnetization  at each spacetime point is approximated by the saturation magnetization  (although it can be smaller when averaged over a chunk of volume). The Landau-Lifshitz equation, a precursor of the LLG equation, phenomenologically describes the rotation of the magnetization in response to the effective field  which accounts for not only a real magnetic field but also internal magnetic interactions such as exchange and anisotropy. An earlier, but equivalent, equation (the Landau–Lifshitz equation) was introduced by :
where  is the electron gyromagnetic ratio and  is a phenomenological damping parameter, often replaced by
where  is a dimensionless constant called the damping factor. The effective field  is a combination of the external magnetic field, the demagnetizing field, and various internal magnetic interactions involving quantum mechanical effects, which is typically defined as the functional derivative of the magnetic free energy with respect to the local magnetization . To solve this equation, additional conditions for the demagnetizing field must be included to accommodate the geometry of the material.