 Magnetic compensation temperature

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.