Dear all,
I am learning the Landau-Lifshitz-Gilbert equation for spin dynamics, which could be expressed as,
dm/dt = -(gamma/(1+alpha^2))m×B - (gamma/Ms)(alpha/(1+alpha^2))m×(m×B)
where m, B, gamma, and alpha represent the magnetic moment, magnetic field, gyromagnetic ratio, and damping coefficient.
However, when I consider the dynamics of a single spin, I feel confused that the magnetic field antiparallel to the magnetic moment could not drive the switching of the single spin! Correspondingly, if I solve the equation as an ODE (regardless of the spatial degree), the critical magnetic field to switch the magnetic moment could be infinity.
What's the problem here? Is there any mistake I made here?
Looking forward to your guidance and advice. Thanks a lot in advance!
Yours,
Ken
When the magnetic field is completely parallel or antiparallel to the magnetic moment, the torque on the magnetic moment is zero because m×B=0. In this case, the magnetic field cannot manipulate the magnetic moment. However, in real systems, thermal disturbances can slightly deflect the magnetic moment from the magnetic field, making the torque non-zero. As a result, an antiparallel magnetic field can reverse the magnetic moment.
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