Table of Contents
Coercivity
Stan Zurek, Coercivity, Encyclopedia Magnetica, https://e-magnetica.pl/doku.php/coercivity |
* This page is being edited and may be incomplete or incorrect.
Coercivity, magnetic coercivity, coercive field, or coercive force, typically denoted by HC - such a value of the externally applied unidirectional magnetic field strength H that reduces the instantaneous state of magnetisation of a material to zero, typically from the initial point of remanence BR.1)2)3)4)5)6) Because of its position on the hysteresis loop (second quadrant) the value of coercivity is typically stated as a negative number in A/m units.
S. Zurek, E-Magnetica.pl, CC-BY-4.0
The value of coercivity is an important parameter and it is used for classification of magnetic materials into three broad groups:8)
- soft magnetic materials (HC < 1 kA/m),
- hard magnetic materials (HC > 100 kA/m)
- semi-hard magnetic materials (1 kA/m < HC < 100 kA/m)
But this is not a strict classification as the function, application, or application of the given material can dictate the actual “type”.9)
Reaching coercivity (i.e. where B, J, or M = 0) does not mean that the material was fully or even partially demagnetised, and much more elaborate procedures are needed to ensure that demagnetisation is achieved.10)11)
The “state of magnetisation” can be expressed in different ways and hence there can be several types of coercivity, which can be used interchangeably depending on the context:
- for magnetic flux density B (also known as “magnetic induction B”), so for the B-H loop it is the induction coercivity BHC
- for magnetic polarisation J (so J-H loop) it is the polarisation coercivity JHC
- for magnetisation M (so M-H loop) it is the magnetisation coercivity, which could be marked as MHC or HCM 12)13)
- in CGS units the polarisation can be referred to as “intrinsic induction” and hence there is intrinsic coercivity HCi - this is synonymous with JHC but typically expressed in different units14)15)16)17) (SI system uses the name “magnetic polarisation” J in tesla, but CGS uses “intrinsic induction” Bi in gauss, or magnetisation M which can be expressed either in gauss or in oersted)
- the name intrinsic coercivity iHc can be also applied to data expressed by magnetisation 18)
- in soft magnetic materials the difference between B and J is negligibly small away from magnetic saturation (hence BHC ≈ JHC) and thus typically no distinction is made between the two values and just HC is used
- if clear from the context then only HC is used as a symbol for any type of coercivity19)
- in some cases the value of HC is quoted as μ0·HC so that the unit of T can be used instead of kA/m 23)
- remanence coercivity HC,r is such such a value of H that after its application and reduction to zero the remnant flux density becomes zero (see explanation and illustration below in the text)
- another name for coercive field used in the past was starting field Hs because it was “the field necessary to start the change in magnetization along the steep part of the loop”24)
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Typical values of coercivity
S. Zurek, E-Magnetica.pl, CC-BY-4.0
The value of coercivity is not directly important for soft ferromagnets as such, because for them permeability is a typically a better figure of merit. However, there is an inverse relationship between the two quantities, because higher coercivity increases the width of the hysteresis loop and therefore reduces permeability and increases power loss.26)
Therefore, a low coercivity is a pre-requisite to obtaining high permeability, and vice versa. The materials which have the highest permeability μr also have very low coercivity HC, as listed in the table below.27)28)29)
The value of coercivity is also closely and directly linked with hysteresis loss especially under alternating excitation. It is therefore critical that for a low loss material its coercivity has to be a low value. The relation to power loss is described in more detail below.
Yet, for power transformation it is the power loss that is typically specified, not coercivity. Only in some special signal application (such as fluxgate sensors or impulse transformers) coercivity might be a directly relevant quantity. This parameter is also important for semi-hard magnetic materials used in magnetic data storage, because it dictates the immunity to external magnetic fields so that the data can be safely retained once recorded in the magnetic structure.30)
Typical coercivity of materials | ||
---|---|---|
Material31)32) | Coercivity BHC (A/m) | Permeability μr (-) |
magnetically soft | ||
Co-based amorphous ribbon | 0.24 | 1 000 000 |
Ni-Fe alloy (80-20) | 0.4 | 500 000 |
Fe-based nanocrystalline ribbon | 0.8 | 200 000 |
grain-oriented electrical steel | 20 | 40 000 |
non-oriented electrical steel | 100 | 2 000 |
magnetically semi-hard | ||
Vicalloy33) | 20 000 | 30 |
magnetically hard | ||
Alnico2 | 43 800 | 6.4 |
Alnico8 | 119 000 | 2.1 |
Sm2Co17 | 480 000 | 1.05 |
N5234) | 820 000 | 1.05 |
S. Zurek, E-Magnetica.pl, CC-BY-4.0
S. Zurek, E-Magnetica.pl, CC-BY-4.0
Physical units of coercivity
Coercivity Hc is expressed in the same units as magnetic field strength H. In engineering applications, in the SI system this is typically in A/m (ampere per metre), and in the CGS system it is in Oe (oersted).37)38)39)
However, in some physics experiments the magnetic field is sometimes expressed in the same units as magnetic flux density, namely T (tesla), by scaling the values by the permeability of vacuum.40)
The CGS units is are still widely used especially in the physics experiments and thus they are still frequently used in scientific papers.
Physics of coercivity
Coercivity depends not only the type of material, but also on the state of that material. For example, very pure monocrystal of iron can have coercivity around 1 A/m, in the polycrystalline state it could be 100 A/m, and for single-domain iron particles of an appropriate size it could be even beyond 10 kA/m.41)
Changes in magnetisation state of a material can occur as a result of domain wall motion (including domain nucleation) or domain rotation. Therefore, any factors which can impact on these processes can also affect the coercivity. Domain wall movement can require less energy than rotation, and therefore as a general rule for high-coercivity materials the state of a single domain is preferable, whereas for low coercivity (high permeability) free domain wall motion is required.42)
S. Zurek, E-Magnetica.pl, CC-BY-4.0
Domain wall pinning
Domain wall pinning is one of the mechanisms that impacts domain wall movement.44) Any non-uniformities in the magnetic materials such non-magnetic voids, crystal defects, grain boundaries, inclusions, or precipitates can give rise to a local energy increase which must be overcome before the domain wall can move through such entity.
It is said that under a static condition the a domain wall is “pinned” to such location, or that such defects are “pinning sites”.45)46) There is actually a physical evidence of such pinning, because the domain wall movements happen in jerky motion (rather than smooth continuous) and this can be detected for example through the Barkhausen noise phenomenon.
In the absence of other factors a domain wall will rest in some position of local energy minimum, such as being “stuck” at one of the pinning sites. And for example when some external magnetic field is applied there will be magnetic pressure exerted on the wall, which when increased sufficiently high will make the wall overcome the pinning force and the domain can rapidly accelerate towards the next pinning position (Barkhausen jump event). The process is then repeated, with the next local jump, and so on. If there is a lower local energy minimum just after a larger one then the wall may jump over it.
However, when the direction of the applied magnetic field is reversed, then different pinning sites might be involved in the process, so that effectively a different path is generated, as shown in the image below. Each such Barkhausen jump represents rapid change in magnetisation which generates local micro eddy currents, which dissipate energy, so the process is lossy in its nature.
These individual energy losses add up, and if the magnetisation process is cyclic in one direction then a loop is formed, called hysteresis loop. As illustrated below, the position of the coercivity and remanence points on such a loop can be easily identified.47)
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In most soft magnetic materials the domain structure is extremely complex, for example due to angular misalignment of local grains in the polycrystalline structure.
herzereusm49)
S. Zurek, E-Magnetica.pl, CC-BY-4.0
Asymmetric coercivity
S. Zurek, E-Magnetica.pl, CC-BY-4.0
S. Zurek, E-Magnetica.pl, CC-BY-4.0
Measurement of coercivity
Coercivity of magnetic materials is measured by using a measurement system appropriate for the type of material (soft, hard, semi-hard). However, from the magnetic viewpoint the procedure is similar in all cases, and can be broadly described as follows:
- Before the procedure the material can be in any state of magnetisation (demagnetised, or magnetised, to any level, or in its remanence state).
- The first step (1) is to apply magnetic field which is high enough so that the state of magnetic saturation is obtained. The level of excitation is dictated by the type of material under test, and its expected value of coercivity. In any case, the applied saturating H must be much much greater than the HC to be measured, so Hsat » HC.
- After saturation, the excitation is reduced (2) to H = 0 (thus returning the material to the remanence point BR = JR, or MR).
- Then a negative field is applied (3) progressively, so that the state of magnetisation begins to approach zero. The quantity of magnetisation (flux density B, polarisation J, or magnetisation M) is measured continuously during this phase. The value of H at which B, J, or M becomes zero represents the coercive field HC for that value.
- Measurement of remanence coercivity HC,R is more complicated, because it can only be quantified after switching the applied field back to zero (4) and checking if the remnant flux density, polarisation, or magnetisation is zero. If the curve does not return to (0,0) then the saturating procedure must be repeated and a different level of negative field needs to be applied, etc.
- Coercivity can be measured in both directions, for positive or negative applied field. The procedure is identical in both cases, but simply performed with the opposing magnetic polarity, or reversed position of the sample in the measurement system (and the value of HC,R may be then averaged from both directions).54)
In soft (and semi-hard) ferromagnets
S. Zurek, E-Magnetica.pl, CC-BY-4.0
The permeability of typical soft magnetic materials is high and for lower fields the difference between the flux density B and the polarisation J is negligible in practice. Therefore, there is no need define or measure two separate values, because around the coercivity values it is also true that B ≈ J, and consequently HC ≈ BHC ≈ JHC.
Furthermore, the presence of air gap in a magnetic circuit of the sample leads to significantly lower effective permeability so that the B-H loop becomes “sheared” (slanted). However, the sheared loop (B-H, J-H, or M-H) crosses the horizontal axis at the point which is in practice negligibly close to the loop for the closed magnetic circuit (i.e. without the air gap present). This allows measurement of coercivity of soft magnetic materials on open samples, as described for instance by the international standard IEC 60404-7 Method of measurement of the coercivity (up to 160 kA/m) of magnetic materials in an open magnetic circuit.55)
S. Zurek, E-Magnetica.pl, CC-BY-4.0
The excitation is applied in a typical way, by first saturating the sample of material to some suitable value (e.g. 200 kA/m for highly permeable materials)56), then reducing the field to zero, and then applying negative field until the measured B reduces to zero.
IEC 60404-7 57) specifies the relationship between the induction coercivity BHC and the polarisation coercivity JHC by the equation below, which for high-permeability materials reduces to negligible difference between the two values.
$$ {_B}{H_C} = {_J}{H_C} · \left( 1 - μ_0 · \frac{ΔH}{ΔB} \right) $$ | (A/m) |
where: μ0 - permeability of vacuum (H/m), ΔH/ΔB - slope of the B-H curve around the coercivity point (B = 0). |
Sample under test should be ideally of elongated shape (ratio of length to width 5:1 or more) and it should be placed in the axis of the demagnetising solenoid.58)
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It should be noted that the absolute accuracy of the B measurement is not important, because the important information is the location of the zero crossing. Therefore, the B measurement can be optimised as a zero-detector. The zero crossing can be detected by several means as illustrated for sample (1) in a solenoid (2):60)
- Hall-effect sensor (3) can be placed near one end of the sample, but in such a way that it is off the sample axis and configured to detect the radial component.
- Pair of fluxgate sensors (4) can be placed outside of the solenoid. The sensors should be configured to measure the radial field, making them a differential pair which will suppress effects of some external field. For best results the sensor should be placed near the centre of the solenoid, and the sample end should coincide with the location of the sensors.61)
- Vibrating coil can be placed near or around one end of the sample.
Saturation
Practically sufficient level of magnetic saturation is obtained if increasing the saturating field by 50% does not increase the measured coercivity by more than 1%. The saturating field can be applied by an electromagnet (solenoid) or a permanent magnet.62)
In commercial systems saturating soft magnetic materials is achieved typically with a field 140-450 kA/m,w hich can be obtained by DC current from a variable DC power source, or by pulse methods from a LC circuit.63)64) The saturating solenoid can be enclosed in a shielding box.65)66)
For physically large and electrically conductive samples there can be significant eddy currents and the saturating field should be applied for sufficient long time for these currents to die away and for the field to penetrate and to saturate also the inside of the sample. The standard IEC 60404-7 suggests that in some cases the saturation dwell time might be up to 20 seconds.67) The standard allows using permanent magnets as the source of magnetic field for saturation.
In hard ferromagnets
For high-energy permanent magnets the required field might be even higher than H > 1 MA/m, so it is technically more difficult to apply such fields, but otherwise the procedure is similar to soft ferromagnets because sufficiently large current has to be passed through the magnetising/demagnetising coil.
In soft magnetic materials, the value of Hc is relatively low, the lower the better. For that reason the component $μ_0 · \vec{H}$ in the equation $\vec{B} = \vec{J} + μ_0 · \vec{H}$ is negligibly smaller than $J$ and therefore $J \approx B$ = 0 at the coercivity point of $H_c$.
In hard magnetic materials the value of HC is relatively high, the higher the better. The contribution of $μ_0 · \vec{H}$ is no longer negligible and thus two HC points have to be distinguished:68)
- at B = 0 the coercivity value is BHc
- at J = 0 the coercivity value is JHc
- and such that: | BHc | < | JHc |
Pulsed measurements
It is possible but difficult to obtain full saturation of magnets with solenoids driven by a DC current, because of the resistive losses in the conductor of the solenoid. If the slowly varying current is used then the measurement is similar to as described above for the soft ferromagnets.70)
Less expensive methods used in production and testing employ pulsed currents. A capacitor is charged to a controlled level of voltage and discharged through a coil, via diode. This produces a uni-directional pulse of very high current which is capable of magnetising, saturating, or demagnetising a magnet.
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a
b 72)
Pulses can be applied by successive demagnetisation, or by always returning to the same saturation point, synonymous with first-order reversal curves (FORC).73)
Furlani - overcome demagnetising field
Coercivity and magnetic energy
Power loss
a
Stored energy
b
Other uses of coercivity
S. Zurek, E-Magnetica.pl, CC-BY-4.0
As with remanence, coercivity can be defined as measured after saturation so that it has always the same value, related to material properties (rather than the sample properties).
But in other types of analyses it can be useful to use the “coercivity” as measured after other amplitudes or modes of excitation (e.g. varying frequency), for any B-H loop crossing the B=0 level.75) In such cases the value of “coercivity” is a function of the amplitude of excitation as well as the frequency, or even waveshape of the applied signals.
a 76)
bb77)
Magnetic properties
a
Non-destructive testing
Coercivity is related to microstructure and therefore it can be used for non-destructive testing.
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