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This behavior is described by the Landau–Lifshitz–Gilbert equation: [21] [22] = where γ is the gyromagnetic ratio, m is the magnetic moment, λ is the damping coefficient and H eff is the effective magnetic field (the external field plus any self-induced field). The first term describes precession of the moment about the effective field ...
When an isolated atom is placed in a magnetic field there is an interaction because each electron in the atom behaves like a magnet, that is, the electron has a magnetic moment. There are two types of interaction. Diamagnetism. When placed in a magnetic field the atom becomes magnetically polarized, that is, it develops an induced magnetic moment.
where is the torque, is the magnetic dipole moment, is the angular momentum vector, is the external magnetic field, symbolizes the cross product, and is the gyromagnetic ratio which gives the proportionality constant between the magnetic moment and the angular momentum.
While the transfer of angular momentum on a magnetic moment from an applied magnetic field is shown to cause precession of the moment about the field axis, the rotation of the moment into alignment with the field occurs through damping processes. Atomic-level dynamics involves interactions between magnetization, electrons, and phonons. [3]
This relationship also explains an apparent contradiction between the two equivalent terms, gyromagnetic ratio versus magnetogyric ratio: whereas it is a ratio of a magnetic property (i.e. dipole moment) to a gyric (rotational, from Greek: γύρος, "turn") property (i.e. angular momentum), it is also, at the same time, a ratio between the ...
Equation Angular momentum quantum numbers: ... Magnetic moments. In what follows, B is an applied external magnetic field and the quantum numbers above are used.
The spin magnetic moment of a charged, spin-1/2 particle that does not possess any internal structure (a Dirac particle) is given by [1] =, where μ is the spin magnetic moment of the particle, g is the g-factor of the particle, e is the elementary charge, m is the mass of the particle, and S is the spin angular momentum of the particle (with magnitude ħ/2 for Dirac particles).
The magnetization field or M-field can be defined according to the following equation: =. Where is the elementary magnetic moment and is the volume element; in other words, the M-field is the distribution of magnetic moments in the region or manifold concerned.