Magnetisation: Diamagnetism, Paramagnetism and Ferromagnetism
Magnetisation is magnetic moment per unit volume. Diamagnetic and paramagnetic materials usually respond weakly in opposite directions. Below its Curie temperature, a ferromagnet has ordered domains and can retain magnetisation after an applied field is removed. Differently directed domains can also cancel, leaving a sample unmagnetised.
What a learner can do afterwards
- Classifies diamagnetic, local-moment paramagnetic and ferromagnetic responses using induced opposition, partial alignment and cooperative domain order
- Explains why an iron core can greatly increase a solenoid's field while a copper core changes it only slightly at the same coil current
- Interprets B-H loop area and zero crossings, relating them to hysteresis loss per volume per complete cycle and B-coercivity
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Magnetisation is magnetic moment per unit volume. An applied field induces an opposing diamagnetic response. Copper has a small net response of this kind. In a nonuniform field, a diamagnetic sample tends to move toward weaker-field regions. A uniform field alone does not give this translational force. Stronger effects can hide the diamagnetic contribution in other materials.
In a local-moment paramagnet, atoms or ions have permanent magnetic moments. Without an applied field, the moments point in many directions, giving zero average magnetisation. A field produces partial alignment and weak attraction toward stronger-field regions. At fixed applied field, warming generally reduces the alignment because thermal motion competes with it.
Exchange interactions favour parallel neighbouring moments in a ferromagnet. Below the Curie temperature, moments align within domains without an applied field. Differently directed domains can cancel. A coil field changes domain sizes and directions, increasing net magnetisation. At fixed coil current, iron can greatly increase a solenoid's field; copper slightly reduces it. Iron's response depends on field strength and magnetic history.
To magnetise an iron or steel nail, stroke it with the same magnet pole in one direction. Lift the magnet and return through the air before repeating. An opposite contact pass can reduce net alignment. Compare how many similar paper clips the nail lifts before and after. Do not heat or strike the nail. High-temperature demonstrations require laboratory equipment and protection from burns.
Above its Curie temperature, iron loses spontaneous ferromagnetic order and becomes paramagnetic. An applied field can still produce magnetisation, but removing it leaves no spontaneous magnetisation. A mechanical shock can change domain patterns and reduce a magnet's strength without destroying its underlying ferromagnetic order.
On a B-H loop, B is flux density and H is magnetising field. The branches record magnetic history. The reverse H needed to reach B = 0 defines B-coercivity. For a symmetric loop, each zero crossing has magnitude HcB; their separation is 2HcB. With slow field changes and negligible eddy-current loss, loop area gives hysteresis energy lost per volume per full cycle, in J/m^3.
Example: crossings at -20 and +20 A/m give B-coercivity 20 A/m. This line shows H coordinates, not the B-H loop.
Transformer cores reverse magnetisation repeatedly. Compare hysteresis loss at equal core volume, cycle frequency and peak B: the smaller B-H loop area gives less heating. Small coercivity often accompanies low loss, but width alone does not determine area. Eddy currents add another loss, so hysteresis alone does not predict total core heating. In the example, A loses 20 J/m^3 per full cycle and B loses 50 J/m^3.
The bars compare hysteresis energy losses per cubic metre per complete cycle. They do not show loop shapes.
Diamagnetism opposes the field; paramagnetism weakly aligns. Ferromagnets have ordered domains below the Curie temperature. B-H loop area gives hysteresis loss per volume per complete cycle.
Lesson, questions and flashcards written for this dataset. Scientific background was studied in OpenStax's Magnetism in Matter and Ferromagnets and Electromagnets sections; their prose and figures are not reproduced.
Readings and flashcards written for this dataset. Video records credited to Khan Academy: Ferromagnetism & curie temperature and Paramagnetism & diamagnetism. Video licenses are not specified.
More to read
Classifying a magnetic response
A sample can contain magnetic moments and still have zero magnetisation. Magnetisation measures their net magnetic moment per unit volume. Contributions in different directions can cancel, so a zero result does not tell you that every microscopic moment is absent.
To classify a response, compare the induced magnetisation with the applied field. Copper develops a small opposing response, called diamagnetism. In a field that varies across space, it tends to move toward a weaker-field region. A uniform field does not provide that same force test.
A local-moment paramagnet contains permanent moments whose directions average out before a field is applied. The field biases their directions, producing partial alignment. At fixed field, warming generally reduces this bias because thermal motion competes with alignment.
Iron below its Curie temperature has a different starting point: moments already align within domains. The directions of different domains may cancel. Changing their sizes and directions can produce a much larger net magnetisation than the weak response of a paramagnet. A diamagnetic contribution can still be present beneath these stronger effects.
What a core remembers
Keeping a coil's current fixed lets you compare its field with different cores. An iron core can add a large contribution as its domains respond. Copper gives only a small opposing contribution. The difference is a magnetic response, not extra electrical current supplied by the core. Iron's response also depends on the field it experienced earlier.
Switching off the coil need not erase the core's magnetisation. Some net alignment can remain. Permanent magnets resist changes to their magnetic state, but their domains are not immovable.
A B-H hysteresis loop records flux density B against magnetising field H through a complete cycle. Earlier fields affect which branch is followed. The reverse H needed to reach B = 0 defines B-coercivity. For a symmetric loop, the two B = 0 crossings are separated by twice this magnitude.
For slow changes with negligible eddy-current loss, enclosed area gives hysteresis energy lost per cubic metre per complete cycle. Equal-volume cores operating at equal frequency and peak B can be compared using these areas. Width alone does not give area, and eddy currents contribute additional heating.
Comparing a nail before and after magnetising
First test an iron or steel nail with similar paper clips and record how many it lifts. Then use one pole of a magnet to make repeated passes along the nail in one direction. After each pass, lift the magnet away and return through the air to the starting end. Test the nail again with the same clips.
Keeping the nail, magnet pole and direction unchanged makes the comparison easier to interpret. The field can change the balance of domains and leave a net alignment. An opposite contact pass can reduce the effect of earlier passes, which is why the return movement stays away from the nail.
The number of clips is a practical comparison, not a direct measurement of magnetisation. Nail composition, magnet strength and clip shape affect the result.
Do not heat or strike the nail during this test. A shock can alter domain patterns without removing ferromagnetic order. Heating iron above its Curie temperature destroys spontaneous ferromagnetic order, but demonstrating that transition requires laboratory equipment and protection from burns. A change in clip count alone does not establish that a Curie transition occurred.
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