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I'm wondering whether ferrimagnetic materials have a Néel or Curie temperature (or both) and whether it depends on the material. They would be temperatures at which the material undergoes a magnetic phase transition, from ferrimagnetism to paramagnetism.

From what I gathered, Wikipedia claims

The Néel temperature (...) is the temperature above which an antiferromagnetic material becomes paramagnetic.

The article on ferrimagnetism talks about a Curie temperature, no mention of a Néel one. However the Oxford dictionary and Wolfram Physics claim

The transition temperature for an antiferromagnetic or ferrimagnetic substance, above which it is paramagnetic (analogous to the Curie temperature for ferromagnetics).

and

The temperature at which ferrimagnetic and antiferromagnetic materials become paramagnetic.

respectively. So they favor the Néel temperature over the Curie one.

The book "Introduction to the theory of ferromagnetism" by Amikam Aharoni, page 29 claims that

(...) Tc is called the ferrimagnetic Curie point.

The Ph.D. thesis (page 21) "The Application of Environmental Magnetism to Archaeological Prospection" by N. T. Linford claims that there are the two temperatures and that they are different:

Above the ferrimagnetic Curie point Tc the magnetisation of each sublattice will behave as a paramagnet with a separate Curie constant. However below Tc a ferrimagnetic Néel temperature exists at which non-zero values of the sublattice magnetisations MA and MB can occur for zero applied field.

I am therefore left extremely confused. For ferrimagnetic materials, are the Néel and Curie temperatures different? Or are they equivalent and/or equal? If they're different, what is their difference(s)? Is there some "hidden physics" that differentiate them?

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In a ferrimagnet, the temperature at which the sublattice magnetizations cancel is generally called the compensation temperature. There is a nice series of these in the rare-earth iron garnets. It is not a phase transition.

I had never seen the term Néel temperature for this before. That is for the phase transition to the paramagnetic state.

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The Neel temperature is a phase transition for antiferromagnetic materials. This link has a good figure explaining the difference.

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In my experience the magnetic ordering temperature is called Néel temperature only for antiferromagnets. For other types of order, including ferrimagnetism, it is called Curie temperature.

However, as Néel was rewarded with the Nobel price for describing both antiferromagnets and ferrimagnets, I suppose that is why the official sources claim that "Néel temperature" should be also used in the ferrimagnets' case.

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The term Curie temperature is generally applied to ferro- and ferrimagnets, while the term Neel temperature is applied to antiferromagnets. Both terms refer to the temperature at which a phase transition from the paramagnetic to magnetically ordered state takes place.

The PhD thesis that you quote is grossly incorrect. The compensation point occurs below the Curie temperature of a ferrimagnet. In contrast to the Curie temperature, the compensation point, indeed, is not a phase transition. It is caused by different anisotropies of two magnetic sublattices, whereas the sublattice with smaller magnetic moments develops its magnetization faster than the sublattice with higher magnetic moments. At some point, dubbed the compensation point by Neel, the higher-moment sublattice takes over and zero magnetization is observed, after which the magnetization increases in the opposite direction as the temperature is lowered. Note that such behavior is observed only in the specific cases for which the higher-moment sublattice is more anisotropic, i.e., it is more difficult to align its moments with the applied magnetic field.

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