Landau–Lifshitz–Gilbert equation with symmetric coefficients of the dissipative function

• An advancement in the understanding of the Landau–Lifshitz–Gilbert equation is presented.
• A method to turn symmetric the kinetic coefficients in the equation is presented.
• The correct expression for the dissipative function in the presence of a magnetic field is obtained.
• An extra term proportional to H2H2 is obtained in Gilbert’s equation that permits to explain considerable damping in the magnetization.

A method to introduce the damping terms in the equations of motion of magnetization in a material consists in defining a positive dissipative function that has a quadratic form in the velocities. The coefficients that appear in this dissipative function must be symmetric. The theory developed by Onsager (1931) states that under the presence of an external magnetic field these coefficients are not symmetric, and therefore, it is not possible to introduce a dissipative function. In this article we present a method to make symmetric the kinetic coefficients and define this dissipative function in a way that allows the introduction of the damping terms in the equations of motion.