= Magnetic compensation temperature
{title2=$T_{\rm comp}$}
= Magnetization compensation temperature
{synonym}
At a <magnetic compensation temperature>, $M_A=M_B\ne0$: an ordered <ferrimagnet> has zero net <magnetization>. Such cancellation need not occur in every material.<Magnetism and the local molecular field by Louis Néel>[§8, Fig.7; §§11–12, pp.335–338: cancellation within an ordered phase]{ref}
For an original stipulated example, let $t=T/T_C$, with $0\le t\le1$, and prescribe sublattice magnitudes per common <volume> by
$$
M_A(t)=M_0(1-t),\qquad M_B(t)=\frac32M_0(1-t)^2,\qquad M_0>0.
$$
Take 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:
$$
M_z(t)=M_A-M_B=\frac{M_0}{2}(1-t)(3t-1).
$$
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>.
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