# Coercivity
**Coercivity** is the intensity of the external magnetic field required to reduce the magnetization of a ferromagnetic material to zero after the material has been magnetized to saturation. It is denoted Hc, called the coercive field or (in older literature) the coercive force, and is measured in amperes per meter (A/m) or oersteds (Oe).[1](https://archive.nptel.ac.in/content/storage2/courses/115103038/pdf/mod5.pdf) • [2](https://technav.ieee.org/topic/coercive-force/) Coercivity measures a material's resistance to demagnetization and is one of the central parameters of the magnetic hysteresis loop, the curve traced as magnetization responds to a field cycled between positive and negative values.[1](https://archive.nptel.ac.in/content/storage2/courses/115103038/pdf/mod5.pdf) • [3](https://openstax.org/books/university-physics-volume-2/pages/12-7-magnetism-in-matter)
| Key fact | Detail |
|---|---|
| Definition | Reverse field that brings magnetization (or induction) to zero after saturation; symbol Hc, units A/m or Oe[1](https://archive.nptel.ac.in/content/storage2/courses/115103038/pdf/mod5.pdf) |
| Soft vs hard | Soft magnetic materials: Hc below about 103 A/m; hard (permanent magnet) materials: above 104 A/m[4](https://www.sciencedirect.com/topics/chemistry/magnetic-material) |
| Extrinsic property | Coercivity depends on microstructure (grain size, defects, grain boundaries) as well as intrinsic anisotropy[5](https://www.sciencedirect.com/topics/engineering/coercivity) |
| Working formula | Hc(T) = αHA(T) − NeffMs(T), combining defect/misalignment effects and the demagnetizing field[6](https://pmc.ncbi.nlm.nih.gov/articles/PMC8183520/) |
| Grain-size effect | In Nd-Fe-B magnets coercivity rises as grain size falls, originally fitted as Hc = a − b lnD[6](https://pmc.ncbi.nlm.nih.gov/articles/PMC8183520/) |
| Measurement standards | IEC 60404-7 covers open-circuit measurement from 0.2 A/m to 160 kA/m; ASTM A977 covers hysteresigraph testing of high-coercivity magnets[7](https://www.evs.ee/en/evs-en-iec-60404-7-2020) • [8](https://store.astm.org/a0977_a0977m-07.html) |
| Typical spread | Supermalloy Hc ≈ 0.004 gauss versus Alnico V ≈ 550 gauss[9](https://www.feynmanlectures.caltech.edu/II_37.html) |
## Position on the hysteresis loop
When a ferromagnet is driven to saturation and the applied field is then reversed, magnetization does not return to zero when the field does; the material retains remanence. The reverse field at which the magnetization first reaches zero is the coercivity. On the induction (B-H) loop, the corresponding intercept is the coercive field in the induction sense, and the two definitions are often used interchangeably, though they are distinct quantities.[1](https://archive.nptel.ac.in/content/storage2/courses/115103038/pdf/mod5.pdf) • [10](https://www2.fisica.unlp.edu.ar/magnet/Cullity_Graham.pdf)
**Two coercivities for magnets.** Permanent-magnet practice distinguishes bHc, the reverse field at which the magnetic induction B becomes zero, from jHc (also written Hci), the intrinsic coercivity at which the vector sum of the micro magnetic dipole moments is zero.
## Soft and hard magnetic materials
The coercivity value sorts ferromagnetic materials into two engineering classes. Soft magnetic materials, with Hc below about 103 A/m (often well below 100 A/m), follow an applied field closely and lose little energy per cycle; they serve as cores in transformers, inductors, motors, and sensors. Hard magnetic materials, with Hc above 104 A/m, retain strong remanence and are used as permanent magnets.[4](https://www.sciencedirect.com/topics/chemistry/magnetic-material) • [11](https://technav.ieee.org/topic/soft-magnetic-materials/) Because coercivity directly controls hysteresis loss per cycle, minimizing it is a design goal for soft materials, while a high remanence combined with high coercivity is essential for permanent magnets.[11](https://technav.ieee.org/topic/soft-magnetic-materials/) • [12](https://files.core.ac.uk/download/pdf/62733797.pdf)
The spread is wide. In Richard Feynman's tabulation, supermalloy has a coercive force of about 0.004 gauss while transformer silicon steel is about 0.05 gauss, armco iron about 0.6 gauss, and Alnico V about 550 gauss.[9](https://www.feynmanlectures.caltech.edu/II_37.html)
## Physical origin
Coercivity is an extrinsic property: it depends not only on intrinsic magnetic parameters such as the anisotropy field HA and saturation magnetization Ms, but on the microstructure.[5](https://www.sciencedirect.com/topics/engineering/coercivity) In a polycrystalline material, domain walls moving under an applied field become pinned at strains, dislocations, impurities, and grain boundaries; the wall sticks until the field rises enough for it to snap past, and this jerky motion (the [Barkhausen effect](https://www.edgepedia.org/barkhausen-effect)) is the microscopic basis of hysteresis and its energy loss.[9](https://www.feynmanlectures.caltech.edu/II_37.html) Local variations in magnetic properties produce local variations in domain-wall energy and thereby forces that resist wall motion.[5](https://www.sciencedirect.com/topics/engineering/coercivity)
A common working expression for permanent magnets is
\[ H_{c}(T) = \alpha H_{A}(T) - N_{\mathrm{eff}} M_{s}(T) \]
where the first term captures the reduction of the anisotropy field by defects and grain misalignment (parameter α) and the second term the reduction due to the [demagnetizing field](https://www.edgepedia.org/demagnetizing-field), with Neff an effective demagnetizing factor.[6](https://pmc.ncbi.nlm.nih.gov/articles/PMC8183520/) The relevant length scale is the domain-wall thickness, around 4 nm in rare-earth magnets.[13](https://doi.org/10.1088/2043-6254/aa597c)
## Coercivity in Nd-Fe-B magnets
Sintered Nd-Fe-B magnets, the dominant high-performance permanent magnets, illustrate how microstructure engineering controls coercivity. Their average grain size is above 3 μm, and the accepted reversal mechanism is nucleation of demagnetized domains at edge defects and sharp corners of Nd2Fe14B grains with low anisotropy constant K; as a result the achieved coercivity is far below the anisotropy field HA of the 2:14:1 phase, roughly 0.2 HA, because of intergranular exchange coupling through a ferromagnetic intergranular phase.[5](https://www.sciencedirect.com/topics/engineering/coercivity) • [6](https://pmc.ncbi.nlm.nih.gov/articles/PMC8183520/)
**Grain size.** Coercivity of anisotropic Nd-Fe-B increases as grain size decreases, originally described by the linear-in-log relation Hc = a − b lnD of Ramesh et al. Micromagnetic simulations attribute the gain to a lower effective demagnetizing constant Neff and reduced stray field from neighboring grains as grains shrink; the effective demagnetizing field NeffMs falls with grain size, raising coercivity.[6](https://pmc.ncbi.nlm.nih.gov/articles/PMC8183520/) Below about 3 μm, conventional powder processing can instead reduce coercivity, because oxidation of metallic Nd during sintering leaves the grains without the Nd-rich intergranular phase needed for magnetic isolation.[6](https://pmc.ncbi.nlm.nih.gov/articles/PMC8183520/)
**Grain boundary diffusion.** Coating sintered magnets with Dy or Tb (as oxides, fluorides, or pure metals) and heat treating at 800–1000 °C for 3–10 h diffuses the heavy rare earth into the magnet and forms an HRE-enriched shell around each Nd2Fe14B grain with a high anisotropy field. Because only a small amount of the heavy rare earth is used locally, the remanence loss from antiferromagnetic Dy-Fe coupling is minimized. This process is now widely used to make high-coercivity magnets for traction motors and wind turbines.[6](https://pmc.ncbi.nlm.nih.gov/articles/PMC8183520/)
**Temperature.** Coercivity of Nd-Fe-B falls severely at elevated temperature. Its thermal stability is quantified by the temperature coefficient βHc = ΔHc / (Hc(RT)·ΔT); a typical value for a Dy-free sintered magnet is about −0.6% K−1 at 160 °C.[6](https://pmc.ncbi.nlm.nih.gov/articles/PMC8183520/)
## Measurement
Coercivity is measured by tracing the hysteresis loop. For soft materials, ring samples or frames made entirely of the test material close the flux path; such methods do not apply to permanent magnets, which are instead incorporated in a magnetic circuit with a closed flux path on a hysteresigraph. ASTM A977/A977M covers determination of initial magnetization, demagnetization, and recoil curves of hard materials, yielding residual induction, coercive field strength, knee field, energy product, and recoil permeability; it is applicable to materials with Hci between about 100 Oe and 35 kOe (8 kA/m to 2.8 MA/m) and Br from 500 G to 20 kG (50 mT to 2 T). High-coercivity rare-earth specimens may need magnetizing fields beyond what iron-core electromagnets produce, so they are premagnetized externally before transfer into the measuring yoke.[8](https://store.astm.org/a0977_a0977m-07.html) For open-circuit measurement, IEC 60404-7 specifies a method applicable to all magnetic materials with coercivities from 0.2 A/m to 160 kA/m, with special precautions below 40 A/m, in highly conductive materials, and for non-ellipsoidal specimens.[7](https://www.evs.ee/en/evs-en-iec-60404-7-2020)
## References
1. [NPTEL, Physics of Magnetic Recording, Lecture 35: Coercivity](https://archive.nptel.ac.in/content/storage2/courses/115103038/pdf/mod5.pdf)
2. [Coercive force, IEEE Technology Navigator](https://technav.ieee.org/topic/coercive-force/)
3. [Magnetism in Matter, University Physics Volume 2, OpenStax](https://openstax.org/books/university-physics-volume-2/pages/12-7-magnetism-in-matter)
4. [Magnetic Material, ScienceDirect Topics](https://www.sciencedirect.com/topics/chemistry/magnetic-material)
5. [Coercivity, ScienceDirect Topics](https://www.sciencedirect.com/topics/engineering/coercivity)
6. [Most frequently asked questions about the coercivity of Nd-Fe-B permanent magnets, PMC](https://pmc.ncbi.nlm.nih.gov/articles/PMC8183520/)
7. [EVS-EN IEC 60404-7:2020, Method of measurement of the coercivity of magnetic materials in an open magnetic circuit](https://www.evs.ee/en/evs-en-iec-60404-7-2020)
8. [ASTM A977/A977M-07, Standard Test Method for Magnetic Properties of High-Coercivity Permanent Magnet Materials Using Hysteresigraphs](https://store.astm.org/a0977_a0977m-07.html)
9. [The Feynman Lectures on Physics, Vol. II Ch. 37: Magnetic Materials](https://www.feynmanlectures.caltech.edu/II_37.html)
10. [Cullity & Graham, Introduction to Magnetic Materials, Ch. 1: Definitions and Units](https://www2.fisica.unlp.edu.ar/magnet/Cullity_Graham.pdf)
11. [Soft magnetic materials, IEEE Technology Navigator](https://technav.ieee.org/topic/soft-magnetic-materials/)
12. [istanbul technical university graduate school of science](https://files.core.ac.uk/download/pdf/62733797.pdf)
13. [Perspectives for high-performance permanent magnets: applications, coercivity, and new materials, AIP Advances](https://doi.org/10.1088/2043-6254/aa597c)
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*Topic: Encyclopedia › Physical world and mathematics › Physics › Matter and radiation physics › Condensed matter physics › Electronic and magnetic properties › Magnetism in condensed matter › Domains, magnetization reversal, and micromagnetics*
*Initially written Sep 17, 2026 · Reviewed: Oct 15, 2026 · Edited: Oct 15, 2026 · Last review: Oct 15, 2026*
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