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Magnetic materials

Check the differences between diamagnetism, paramagnetism, ferromagnetism and ferrimagnetism, saturation magnetization calculations, domains and domain walls, single-domain particles and superparamagnetism, losses in soft magnetic materials, and the coercivity and maximum energy product of permanent magnets with multiple-choice questions.

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Magnetic materials: key points

The magnetism of a material is classified by how its atomic magnetic moments are arranged. Ferromagnets, in which the exchange interaction aligns the moments parallel, have a spontaneous magnetization even without an external field, but they split into many domains to lower the magnetostatic energy created by surface poles. During magnetization, domain walls move in weak fields and the magnetization inside the domains rotates in strong fields. Ferrimagnets (ferrites), in which the antiparallel moments of two sublattices do not cancel, are oxides with a high electrical resistance.

In applications, soft magnetic materials with small coercivity and low loss are used for transformer and motor cores, and hard magnetic materials (permanent magnets) with large coercivity and a large maximum energy product are used for the field magnets of motors and generators. In soft magnetic materials, magnetocrystalline anisotropy and magnetostriction are kept small, and eddy-current loss is suppressed by thin sheets and higher resistivity. In permanent magnets, a strong uniaxial magnetocrystalline anisotropy raises the coercivity. Small particles become single-domain, and even smaller ones become superparamagnetic.

All Magnetic materials questions (15)
  1. Which type of magnetism does a material show if its magnetic susceptibility χ is negative and very small, on the order of 10⁻⁵?
  2. Which statement correctly describes the ferrimagnetism shown by ferrites such as magnetite (Fe₃O₄)?
  3. Take the magnetic moment per atom of iron (BCC, lattice parameter 0.2866 nm) as 2.22 µB. Which value is closest to the saturation magnetization Ms at 0 K, when all the moments are aligned? Take the Bohr magneton as µB = 9.27×10⁻²⁴ A·m².
  4. Magnetite Fe₃O₄ has the inverse spinel structure: the A sites (tetrahedral) hold one Fe³⁺, the B sites (octahedral) hold one Fe³⁺ and one Fe²⁺, and the moments on the A and B sites are antiparallel. Taking Fe³⁺ as 5 µB and Fe²⁺ as 4 µB, with only spin contributing, what is the magnetic moment per Fe₃O₄ formula unit?
  5. What is the main reason a ferromagnet splits into many magnetic domains even without an external field?
  6. As particles of a ferromagnet are made smaller, from a few µm down to nm sizes, which statement correctly describes how their coercivity changes?
  7. 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?
  8. What is the main reason permalloy, Fe with about 78% Ni, shows an extremely high permeability?
  9. Grain-oriented electrical steel (Fe with about 3% Si) used for transformer cores has especially low loss and high permeability when magnetized along the rolling direction. Which reason is correct?
  10. Assume the eddy-current loss of electrical steel sheet is proportional to t²f²Bm², where t is the sheet thickness, f the frequency and Bm the peak flux density (with the same resistivity). At the same frequency and flux density, by roughly what factor does the eddy-current loss change if the thickness is reduced from 0.50 mm to 0.35 mm?
  11. An alternating field at 50 Hz is applied to electrical steel sheet with an electrical resistivity of 4.8×10⁻⁷ Ω·m and a relative permeability of 5000. Which value is closest to the skin depth δ = √(2ρ/(ωµ))? Take ω = 2πf, µ = µᵣµ₀ and µ₀ = 4π×10⁻⁷ H/m.
  12. On the demagnetization curve of a permanent magnet, let the magnitude of the reverse field that brings the flux density B to zero be the coercivity HcB, and the magnitude of the reverse field that brings the magnetization M to zero be the intrinsic coercivity HcJ. From the relation B = µ₀(H + M), which relationship between them is correct?
  13. For an ideal permanent magnet whose demagnetization curve is the straight line B = Br + µ₀H (with a sufficiently large HcJ) and whose remanent flux density is Br = 1.40 T, which value is closest to the maximum energy product (BH)max? Take µ₀ = 4π×10⁻⁷ H/m.
  14. What is the main material reason that neodymium magnets, with Nd₂Fe₁₄B as the main phase, can have a large coercivity?
  15. What is the main purpose of adding Dy or Tb to neodymium magnets used at high temperatures, such as in electric-vehicle motors?

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