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:<math>\frac{\mathrm{d}\mathbf{m}}{\mathrm{d}t}=-\gamma \left( \boldsymbol{\tau} + \boldsymbol{\tau_{d}} \right)</math>,
where the damping torque is given by
:<math>\boldsymbol{\tau_{d}}=-\frac{\alpha}{\gamma m} \left( \mathbf{m} \times \frac{\mathrm{d}\mathbf{m}}{\mathrm{d}t}\right)</math>.
By way of the [[Micromagnetism|micromagnetic theory]]<ref>R. M. White, ''Quantum Theory of Magnetism: Magnetic Properties of Materials'' (3rd Ed.), Berlin: Springer-Verlag, 2007.</ref>, the Landau-Lifshitz-Gilbert equation also applies to the [[Mesoscopic scale|mesoscopic]]- and macroscopic-scale [[magnetization]] <math>M</math> of a sample by simple substitution,
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