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Magnetic materials

As particles of a ferromagnet are made smaller, from a few µm down to nm sizes, which statement correctly describes how their coercivity changes?

  1. ACoercivity is a material property set only by magnetocrystalline anisotropy, so it barely depends on size
  2. BSmaller particles have fewer domain walls and reverse less easily, so it keeps increasing monotonically down to the nm scale
  3. CIt peaks near the critical single-domain size, then falls toward zero as the particles become superparamagnetic
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Answer: C. It peaks near the critical single-domain size, then falls toward zero as the particles become superparamagnetic

Large particles contain many domains, and their magnetization reverses by the motion of domain walls, which move even in weak fields, so the coercivity is small. Making the particles smaller reduces the number of walls, and below a critical size they become single-domain particles with no walls. Reversing the magnetization of a single-domain particle requires rotating the whole magnetization against the magnetic anisotropy, so the coercivity peaks around this size. Making them smaller still makes the energy barrier to reversal, KV, small compared with the thermal energy, so the magnetization reverses spontaneously by thermal activation (superparamagnetism) and the coercivity approaches zero. Coercivity depends strongly on particle size and microstructure, not only on the anisotropy, so it is not constant, and below the critical size it does not keep increasing. Particles for magnetic recording media are designed between these upper and lower limits.

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  1. Take the energy barrier for thermal reversal of the magnetization of a single-domain particle of volume V as KV (K is the magnetic anisotropy constant); for a measurement time of about 100 s, KV = 25kT is a guide to the boundary for superparamagnetism. With K = 1.1×10⁴ J/m³, a temperature of 300 K and the Boltzmann constant k = 1.38×10⁻²³ J/K, which value is closest to the upper limit of the diameter of a spherical particle that becomes superparamagnetic?
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