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The magnetization field or M-field can be defined according to the following equation: = Where d m {\displaystyle \mathrm {d} \mathbf {m} } is the elementary magnetic moment and d V {\displaystyle \mathrm {d} V} is the volume element ; in other words, the M -field is the distribution of magnetic moments in the region or manifold concerned.
In physics, the Landau–Lifshitz–Gilbert equation (usually abbreviated as LLG equation), named for Lev Landau, Evgeny Lifshitz, and T. L. Gilbert, is a name used for a differential equation describing the dynamics (typically the precessional motion) of magnetization M in a solid.
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal n̂, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
In physics and chemistry, specifically in nuclear magnetic resonance (NMR), magnetic resonance imaging (MRI), and electron spin resonance (ESR), the Bloch equations are a set of macroscopic equations that are used to calculate the nuclear magnetization M = (M x, M y, M z) as a function of time when relaxation times T 1 and T 2 are present.
The Brillouin function [4] [5] [2] [6] arises when studying magnetization of an ideal paramagnet.In particular, it describes the dependency of the magnetization on the applied magnetic field, defined by the following equation:
This equation is often represented using derivative notation such that =, where dm is the elementary magnetic moment and dV is the volume element. The net magnetic moment of the magnet m therefore is m = ∭ M d V , {\displaystyle \mathbf {m} =\iiint \mathbf {M} \,\mathrm {d} V,} where the triple integral denotes integration over the volume of ...
Atomic-level dynamics involves interactions between magnetization, electrons, and phonons. [3] These interactions are transfers of energy generally termed relaxation. Magnetization damping can occur through energy transfer (relaxation) from an electron's spin to: Itinerant electrons (electron-spin relaxation) Lattice vibrations (spin-phonon ...
In physics, Gauss's law for magnetism is one of the four Maxwell's equations that underlie classical electrodynamics.It states that the magnetic field B has divergence equal to zero, [1] in other words, that it is a solenoidal vector field.