What is Coercivity?

The strength of the reverse magnetic field needed to bring the magnetization (or flux density) of a magnetized material back to zero. Materials with small coercivity are soft magnetic, and those with large coercivity hard magnetic.

Japanese name: 保磁力

Coercivity appears in 6 practice questions across 2 topics, including Magnetic materials, Electronic, magnetic and optical materials.

Field: Electronic, magnetic and optical materials

A quantity that differs by more than six orders of magnitude

Coercivity expresses how strong a reverse field is needed to reverse the magnetization of a magnetized material, and its unit is A/m (1 Oe ≈ 79.6 A/m). In soft magnetic materials it ranges from below 1 A/m for high-permeability alloys such as Supermalloy to a few to a few tens of A/m for electrical steel sheet. In permanent magnets, ferrite magnets reach a few hundred kA/m and the intrinsic coercivity of neodymium magnets about 1000–3000 kA/m. Such large differences among ferromagnets arise because coercivity depends strongly on microstructure, not just on composition.

Coercivity determined by microstructure

The anisotropy field calculated from magnetocrystalline anisotropy is the theoretical upper limit of coercivity, but actual coercivities are much smaller. This is because magnetization reverses when reverse domains nucleate at defects and domain walls move to spread them. The more inclusions, precipitates, grain boundaries and internal stresses catch (pin) domain walls, the larger the coercivity. The goal is a microstructure in which reverse domains hardly nucleate for permanent magnets, and a clean microstructure in which domain walls move easily for soft magnetic materials.

Relation to grain size

In ordinary soft magnetic materials, grain boundaries hinder domain wall motion, so larger grains lower the coercivity. When the grain size falls below a few tens of nanometers, smaller than the magnetic exchange length, however, the anisotropies of neighboring grains are averaged out and cancel, and coercivity drops sharply in proportion to the sixth power of grain size (Herzer's random anisotropy model). Nanocrystalline soft magnetic alloys exploit this effect. It is a design approach opposite to that for permanent magnets, whose coercivity peaks at the single-domain particle size.

Measurement and selection for the application

Coercivity is found by applying a field to a specimen, measuring its magnetization curve (hysteresis loop), and reading the field at which magnetization or flux density becomes zero. For permanent magnets, a closed-circuit BH tracer is used to eliminate the effect of the demagnetizing field, and a vibrating sample magnetometer (VSM) is used for powders and thin films. Magnetic recording media need a coercivity that meets two conditions at once: small enough to be written, yet large enough that thermal fluctuations do not erase the data. Coercivity changes greatly with temperature, so it is evaluated at the service temperature.

Try it: questions about Coercivity

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
Show answer and explanation

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.

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?

  1. AHcJ ≥ HcB
  2. BHcJ ≤ HcB
  3. CAlways HcJ = HcB, regardless of the material
Show answer and explanation

Answer: A. HcJ ≥ HcB

When B reaches zero at a reverse field H = −HcB, B = µ₀(H + M) gives M = HcB > 0, so the magnetization is still positive. Bringing M to zero requires an even stronger reverse field, so HcJ ≥ HcB. The options HcJ ≤ HcB and always equal are therefore wrong. Also, in a reverse field M does not exceed the remanent magnetization, so HcB cannot exceed Br/µ₀. In materials with a very large HcJ, such as neodymium magnets, HcB levels off near this upper limit of Br/µ₀. Whether a magnet resists demagnetization at high temperature or in a strong reverse field is judged by HcJ, which shows whether the magnetization itself reverses. In soft magnetic materials with small coercivities, the difference between the two is negligibly small.

FAQ

What is the unit of coercivity?

In SI units it is A/m, and kA/m is also common. In the older CGS unit oersted (Oe), 1 Oe = 1000/(4π) A/m ≈ 79.6 A/m. It is sometimes given as µ₀Hc in tesla (T), converted to flux density units.

What is the difference between coercivity HcB and intrinsic coercivity HcJ?

HcB is the reverse field that brings the flux density B to zero, and HcJ the reverse field that brings the magnetization M to zero; HcJ ≥ HcB always. Whether a magnet resists demagnetization is judged by HcJ, which expresses reversal of the magnetization itself.

How can the coercivity of soft magnetic materials be lowered?

Reduce impurities and inclusions, remove internal stress and strain by annealing, and enlarge the grains. Other methods are choosing compositions with small magnetocrystalline anisotropy and magnetostriction, or nanocrystallizing to average out the anisotropy.

Coercivity in the explanations

Questions that mention Coercivity (6)

  1. As particles of a ferromagnet are made smaller, from a few µm down to nm sizes, which statement correctly describes how their coercivity changes?
  2. 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?
  3. What is the main material reason that neodymium magnets, with Nd₂Fe₁₄B as the main phase, can have a large coercivity?
  4. Which correctly describes a soft magnetic material suitable for a transformer core?
  5. When an external magnetic field is applied to a demagnetized ferromagnet and gradually increased, which correctly describes how magnetization proceeds?
  6. What is the main purpose of adding Dy or Tb to neodymium magnets used at high temperatures, such as in electric-vehicle motors?

Related terms

Magnetic domain Saturation magnetization Domain wall Magnetocrystalline anisotropy Superparamagnetism Soft magnetic material Eddy-current loss Curie temperature Maximum energy product Indirect-bandgap semiconductor

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