In physics, magnetization dynamics is the branch of solid-state physics that describes the evolution of the magnetization of a material.
Rotation Physics A magnetic moment m {\displaystyle m} in the presence of a magnetic field H {\displaystyle H} experiences a torque τ {\displaystyle \tau } that attempts to bring the moment and field vectors into alignment. The classical expression for this alignment torque is given by
τ = μ 0 m × H {\displaystyle {\boldsymbol {\tau }}=\mu _{0}\mathbf {m} \times \mathbf {H} } , and shows that the torque is proportional to the strengths of the moment and field and to the angle of misalignment between them. From classical mechanics, torque is defined as the time rate of change of angular momentum L {\displaystyle L} or, stated mathematically,
τ = d L d t {\displaystyle {\boldsymbol {\tau }}={\frac {\mathrm {d} \mathbf {L} }{\mathrm {d} t}}} . Absent any other effects, this change in angular momentum would be realized through the dipole moment coming into rotation to align with the field.
Precession 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 γ {\displaystyle \gamma } , such that
m = − γ L {\displaystyle \mathbf {m} =-\gamma \mathbf {L} } . The gyromagnetic ratio for a free electron has been experimentally determined as γe = 1.760859644(11)×1011 s−1⋅T−1. 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,
d m d t = − γ d L d t = − γ τ {\displaystyle {\frac {\mathrm {d} \mathbf {m} }{\mathrm {d} t}}=-\gamma {\frac {\mathrm {d} \mathbf {L} }{\mathrm {d} t}}=-\gamma {\boldsymbol {\tau }}} . Thus, due to the relationship between an electron's magnetic moment and its angular momentum, any torque applied to the magnetic moment will give rise to a change in magnetic moment parallel to the torque. Substituting the classical expression for torque on a magnetic dipole moment yields the differential equation,
d m d t = − γ μ 0 ( m × H ) {\displaystyle {\frac {\mathrm {d} \mathbf {m} }{\mathrm {d} t}}=-\gamma \mu _{0}\left(\mathbf {m} \times \mathbf {H} \right)} . Specifying that the applied magnetic field is in the z {\displaystyle z} direction and separating the differential equation into its Cartesian components,
d m x d t = − γ μ 0 m y H z d m y d t = γ μ 0 m x H z d m z d t = 0 {\displaystyle {\frac {\mathrm {d} m_{x}}{\mathrm {d} t}}=-\gamma \mu _{0}m_{y}H_{z}\qquad {\frac {\mathrm {d} m_{y}}{\mathrm {d} t}}=\gamma \mu _{0}m_{x}H_{z}\qquad {\frac {\mathrm {d} m_{z}}{\mathrm {d} t}}=0} , it can be explicitly seen that the instantaneous change in magnetic moment occurs perpendicular to both the applied field and the direction of the moment, with no change in moment in the direction of the field.
… excerpt ends here. Continue reading the full article.
