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Antiferromagnetism is ordered compensation of magnetic moments. In the collinear two-sublattice model, ${\mathbf{M}}_A=-{\mathbf{M}}_B\ne 0$: net magnetization vanishes but staggered magnetization remains. Louis Néel developed this possibility.^[ref]

For an original local energy check, perturb the antiparallel pair in exchange interaction by writing $\theta =\pi -\delta$. ThenFor $J>0$, a small relative rotation costs positive energy. This verifies a pair's preference; it does not prove a bulk ordering temperature. A whole crystal must satisfy many bonds simultaneously, and thermal fluctuations and quantum effects matter. The Heisenberg antiferromagnet and antiferromagnetic Ising model specify different assumptions about those collective degrees of freedom.

Why is the distinction useful? A measurement of zero magnetization cannot decide between an ordered alternating arrangement, a disordered ensemble, and oppositely magnetized magnetic domains. A spatial probe such as magnetic neutron diffraction tests the pattern directly. The manganese monoxide neutron diffraction experiment is a particularly clear example: the order adds a new periodic scattering signal even though the net magnetic moment cancels.

Ferrimagnetism has opposing, generally unequal ordered magnetic sublattices, with net magnetization $|M_A-M_B|$ in a collinear model. Louis Néel used it to explain magnetic oxides.^[ref]

The counting example in magnetic sublattice gives $3(2m_0)-3(m_0)=3m_0$. Unequal populations also suffice: four sites carrying $+m_0$ and two carrying $-m_0$ give $2m_0$, even with identical individual magnitudes. Thus one must compare total sublattice contributions per common volume, rather than merely asking whether two atomic species carry different magnetic moments.

Both ferromagnetism and ferrimagnetism can produce a macroscopic magnet. Their internal organization differs: the latter retains opposing contributions. This makes ferrimagnetism a useful bridge between net magnetization and microscopic magnetic order: reducing one opposing contribution can increase the net sum, even though the total sum of moment magnitudes decreases.

At a magnetic compensation temperature, $M_A=M_B\ne 0$: an ordered ferrimagnet has zero net magnetization. Such cancellation need not occur in every material.^[ref]

For an original stipulated example, let $t=T/T_C$, with $0\le t\le 1$, and prescribe sublattice magnitudes per common volume byTake A along $+z$ and B along $-z$, retaining a fixed sublattice orientation convention. These are toy functions, not measured curves or a self-consistent mean-field approximation. Their difference factors exactly:At $t=0$, $M_z=-M_0/2$. At $t=1/3$, both magnitudes equal $2M_0/3$ and $M_z=0$: this is compensation with finite order. At $t=1/2$, $M_z=M_0/8>0$. At $t=1$, both magnitudes vanish: that endpoint represents the stipulated Curie temperature, not another compensation point. For $t>1$ stipulate both ordered magnitudes zero; do not extrapolate the polynomials into negative sublattice magnitudes.

The sign change refers to the net component relative to the fixed A direction. A freely reorienting specimen in an applied magnetic field need not display this signed branch directly. The example isolates the cancellation mechanism; it predicts neither a material's transition temperature nor its response to magnetic domains or an applied magnetic field.

The Néel temperature marks loss of long-range antiferromagnetism. A Curie temperature concerns ferromagnetism or ferrimagnetism; magnetic compensation temperature instead denotes cancellation within an ordered ferrimagnet.^[ref]

In the simple collinear description, compare $|\mathbf{L}|$ across $T_N$, rather than expecting $|\mathbf{M}|$ to switch from nonzero to zero. Zero-field magnetization may be zero on both sides. A nonzero magnetic susceptibility is also compatible with antiferromagnetism: an applied magnetic field can disturb the cancellation. The uniform response of a two-sublattice Ising antiferromagnet provides a model calculation.