General Technical Information

- How are the magnetic properties of permanent magnets specified?
- What are the key features of a demagnetization curve?
- Why are there often two different curves presented?
- What do the specific parameters physically mean, and what are their units?
- What are some typical values of these for commercially grades of magnet?
- What is a "load line"?
- How to calculate the "load line", using the capacity of a magnet to hold an item?
- What is the temperature dependence of permanent magnets?
- What is thermal aging? (Define recoverable and non-recoverable flux loss and relate to B
_{r}vs. Temp and T_{g})

Magnet block and powder are measured using specialized test instrumentation which, in general terms, determine how a magnet responds to a changing magnetic field, because that is what happens in most "magnetic circuits" or applications. The vast majority of applications require knowledge of the "demagnetization curve" of a magnetic material – this is a fraction of the full "hysteresis loop" and is a measure of how much magnetism is left in the material as an increasing reverse magnetic field is applied to it. There are other names for this measurement, such as the "second quadrant of the hysteresis loop". If an engineer understands the demagnetizing conditions that are imposed on the magnet by the application, then the demagnetization curve can be used to predict the performance of the magnetic circuit. The temperature of the magnet in the circuit must be known and the demagnetization curve at that temperature must be used if accurate results are to be obtained – the properties of all magnet materials depend on temperature.

The demagnetization curve is measured by first saturating the material (exposing it to enough magnetic field so that it is magnetically aligned) and then gradually decrease the magnetic field while constantly measuring the magnetic flux within the magnet. Once the field becomes negative (the reverse direction compared to the original saturating field) it begins to demagnetize the magnet and the available magnetic flux from it reduces. Eventually, no more flux is available and the magnet starts to remagnetize in the opposite direction. Schematically this looks like

The horizontal axis is the strength of the magnetic field applied by the instrument, and the vertical axis is a measure of the magnetic flux in the magnet. The key magnetic parameters that are always extracted from this curve are

**B**– the remanent induction, the measure of the magnetic flux density when there is no external magnetic field present_{r}**H**– the coercivity, the magnetic field at which the induction switches direction_{c}**H**– the intrinsic coercivity, the magnetic field at which the magnetization switches direction_{ci}**BH**– the maximum energy product, a measure of the amount of energy stored within the magnet (not a point on the curve, but derived from the curve)_{max}

The general shape of the curve shows that the magnetization decreases slowly initially, then it drops off abruptly when the "knee" is passed. It is generally unwise to use a magnet in a demagnetizing field, which is greater than the field at the knee.

The "**normal curve**" (the one resembling a straight line, from B_{r} to H_{c}) plots the magnetic field (H) against the induction (B), while the "**intrinsic curve**" plots H against the magnetization (M – but actually it is 4π times M, or 4πM). The two are related by the equation

B = H + 4πM

So we can see that if we deliberately apply H and know either **B** or **M** then we can calculate the other. Both of them are measures of the number of lines of magnetic flux which pass through the magnet. Generally, magnetic circuit designers need to use B values and some others find it easier to use M values.

H_{c} and H_{ci} specifically relate to how difficult it is to demagnetize the material. If an application has strong fields which apply a large reverse field, and then a higher value for H_{ci}(and similarly, H_{c}) is necessary if the magnet is to do its job. There are two sets of units in use today; the CGS system and the SI system. The CGS unit for B (and M) is the Gauss (G) and the SI unit is the Tesla (T). BH_{max} is calculated by multiplying all of the discrete B and H pairs (BxH) and finding what H value produces the largest product of B times H – this is sometimes phrased "the area of the largest rectangle, which can fit underneath the normal demagnetization curve". This "maximum energy product" is a crude figure of merit for magnetic materials and it represents the __maximum__ energy, which can be stored inside the magnet. BH_{max} has the CGS unit of GaussOersted (GOe), but a million of these (MGOe) is more traditional, and the SI unit is joule per cubic meter (J/m^{3}), but a thousand of these is more common (kJ/m^{3}).

Permanent magnets can be either "**bonded**" or "**fully dense**" depending on the manufacturing process. **Bonded magnets** are made from magnetic powders mixed with a binder and **fully dense** magnets are undiluted by any binding materials, and hence tend to be much stronger. It is important that we first consider the intrinsic properties of the magnet families (since bonded magnets are just diluted fully dense magnets). For fully dense magnets:

Formally, a specific load line is a line of constant B/H represented on the demagnetization curve by a line extending from the origin outward, but physically is related to the shape of the magnet (and the air gap in the magnetic circuit). The shorter the magnet (or the larger the air gap), the lower the value of the load line. The load line represents the effect of self demagnetizing fields – stray magnetic fields from the magnet interfere with the flux lines inside the magnet, decreasing the available amount of flux.

Holding capacity refers to the ability of a magnet to apply force to either another magnet or a piece of a magnetically permeable material (like an iron based soft magnet). There are equations that relate to the shape of a magnet and its potential ability to __hold__ another piece of ferromagnetic, material. If F is the force between the two objects:

F = AB^{2}/8π (where the units of F are dynes)

Where A is the area of contact and B is the induction in the magnet (in Gauss). The trick is calculating B, since it is some point on the demagnetization curve of the material that the magnets are made of, specifically the place where the geometry dependant load line intersects it. The "normal" load line, B_{d}/H_{d}, can be calculated using

B_{d}/H_{d} = (L_{m}/A_{m})(πS)^{1/2}

where Lm is the thickness of the magnet, Am is the area of the magnet, and S is one half of the exposed surface area of the magnet (the sides and backs, etc.).

For example, if there are 2 rectangular magnets (1 cm x 1 cm x 0.5 cm thick, with the poles on the large faces) with their pole faces in direct contact, then L_{m} = 1 cm (the combined thicknesses), A_{m} = 1 cm^{2}, S = 6/2 = 3 cm^{2}, and the normal load line is 3.1. For rare earth magnets the B vs. H curve is a straight line so that we can use the B_{r} and H_{c} values, plus trigonometry to find where a line originating at the origin and with a slope of 3.1 intersects the line going between H_{c} and B_{r}. This B value is then the one used in the force equation. If there are 978,608 dynes in a kilogram, and a MQP-B compression bonded magnet is used with B_{r} = 6800 Gauss and H_{c} = 5200 Oe (from the product literature) then B would be 4789 Gauss and the force would be 0.93 kg.

If the magnets were of a grade approximately equivalent to 40 MGOe sintered NdFeB magnet with B_{r} = 12.55 kG and H_{c} = 12.1 kOe, then the induction (B) would be 9404 Gauss and the force would be 3.6 kg.

Different permanent magnet groups respond differently to changes in operating temperature, for example ferrite shows an increase in H_{c} as the temperature is increased while the rest of the magnet types show a decrease. All groups show a decrease in B_{r} as temperature increases, and all become non-magnetic eventually at a temperature called the Curie temperature, T_{c}. The most common temperature related parameters for the types of magnets are:

NdFeB tends to be used with a -40^{o}C to 200^{o}C temperature window, depending on the alloy composition and binder characteristics. Here is an example of the temperature dependence of the MQP-14-12 powder demagnetization curves:

Aging behaviour of a magnet can be determined by the flux loss over time for a given temperature. The total flux loss is composed of reversible loss, recoverable irreversible loss and structural loss. Flux loss is incurred by a magnetization reversal mechanism occurring with increased operating temperature, as illustrated below. On cooling, part of this loss is recoverable (known as reversible loss, R), and part is not recovered and is known as irreversible loss (I). Irreversible loss is partly recoverable through remagnetization and partly permanent due to structural losses (corrosion or oxidation). Recoverable losses (R and I) are inversely proportional to the intrinsic coercivity, and tend to increase with lower H_{ci}values.

Recoverable irreversible loss can be predicted by temperature coefficients of B_{r} (commonly known as Î±/%^{o}C^{-1}) and H_{ci}(known as Î²/%^{o}C^{-1}), as defined by the following equations:

Î±= [(B_{r(T1)} – B_{r(RT)})/(B_{r(RT)} x {T-RT})] x 100%

Î²= [(H_{ci(T1)} – H_{ci(RT)})/(H_{ci}(RT) x {T-RT})] x 100%

where, B_{r(T)} and H_{ci(T)} denote the B_{r} and H_{ci}values at temperature T measured in degrees Celsius, and B_{r(RT)} and H_{(RT)} are the B_{r} and H_{ci}values at room temperature, respectively.

An Illustration of Irreversible Loss due to Magnetization Reversal.

Note that magnets with a smaller load line (for these standard measurements, cylinders with a smaller aspect ratio) degrade more than those with a larger load line – self demagnetizing fields are more important for short magnets. The same is true for losses at the same temperature for longer times – there are larger losses for magnets with smaller load lines.