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Date: 16-2-2021
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Anisotropy
The natural direction of magnetization in a microscopic ferromagnetic domain is usually constrained to lie along one or more easy axes. Since magnetism is associated with circulating electron currents, time reversal symmetry requires that a state with a certain magnetization distribution M(r) should have the same energy as the state with reversed magnetization along the same axis, −M(r). This tendency is represented by the anistropy energy Ea, of which the leading term is
........(1)
where θ is the angle between the direction of M and the easy axis. Here Ea and Ku, the anistropy constant, are measured in J m−3. Typical values range from less than 1 kJ m−3 to more than 10 MJ m−3. Anisotropy limits the coercivity available in hard magnets.
.........(2)
where the magnetic constant μ0 is 4π × 10−7 J A−2 m−1. Anisotropy also leads to unwanted coercivity in soft magnets. It may be noted from the units that μ0 always multiplies H2 or MH in expressions for magnetic energy per unit volume.
Atomic densities in solids are around n = 1029 m−3, so if anisotropy energy per atom is expressed in terms of an equivalent temperature using Ea/n= kBT , it is in the range 1 mK–10 K. The energy is usually small in relation to the Curie temperature, but it is nevertheless decisive in determining the hysteresis.
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