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It is known from quantum mechanics that there is a proportionality
relationship between the magnetic spin momentum
and
angular momentum
of electrons. This relationship can be
expressed as
(1.72)
where
m A s is the absolute
value of the gyromagnetic ratio
(1.73)
is the Landé splitting factor,
C is the electron charge,
kg is
the electron mass and
m/s is the speed of light.
By applying the momentum theorem one can relate the rate of change
of the angular momentum to the torque exerted on the particle by
the magnetic field
:
By using Eq. (1.72 ), one ends up with a model
which describes the precession of the spin magnetic moment around
the field:
(1.75)
The frequency of precession is the Larmor frequency
(1.76)
Eq. (1.75 ) can be written for each
spin magnetic moment within the elementary volume
:
(1.77)
where now the magnetic field
is intended to be spatially
uniform. Now, by taking the volume average of both sides of the
latter equation, one has:
(1.78)
and, therefore, recalling the definition
(1.1 ) of magnetization vector field
, we end up with the following continuum gyromagnetic
precession model:
(1.79)
Next: 1.3.2 The Landau-Lifshitz equation
Up: 1.3 The Dynamic Equation
Previous: 1.3 The Dynamic Equation
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Massimiliano d'Aquino
2005-11-26