Magnetization dynamics: Difference between revisions

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However, the effect of a torque applied to an electron's magnetic moment must be considered in light of [[spin-orbit interaction]]. Because the magnetic moment of an electron is a consequence of its spin and orbit and the associated angular momenta, the magnetic moment of an electron is directly proportional to its angular momentum through the [[gyromagnetic ratio]] <math>\gamma</math>, such that

:<math>\mathbf{m}=-\gamma \mathbf{L}</math>.

The gyromagnetic ratio for a free electron has been experimentally determined as γ<mathsub>\gamma_e e</sub>&nbsp;= &nbsp;{{val|1.760 859 770760859644e11|(4411) \times 10^{11} \mathrm{|u=s^{-1} T^{-1}}<sup>−1</mathsup>⋅T⁻¹}}.<ref>"[http://physics.nist.gov/cgi-bin/cuu/Value?gammae CODATA Value: electron gyromagnetic ratio]," ''The NIST Reference on Constants, Units, and Uncertainty'', <[http://physics.nist.gov/cgi-bin/cuu/Value?eqgammae|search_for=gyromagnetic+ratio+electron http://physics.nist.gov/cgi-bin/cuu/Value?eqgammae|search_for=gyromagnetic+ratio+electron]></ref> This value is very close to that used for Fe-based magnetic materials.

Taking the derivative of the gyromagnetic ratio with respect to time yields the relationship,