limit, namely $C_{M}(T>\Delta)$ =0.058$T^{3}$ J/moleK (see Fig.1). Thirdly, the substitution of $\theta$ into the Molecular Field relation:[@Kubo-SpinWave] $$T_{N}=\frac{1}{3}\theta(S+1)\label{Tn-cal}$$ gives $T_{N}$ = 18.8$\pm$0.3 K which is in reasonable agreement with the experimentally determined value of $T_{N}$.

TbNi$_{2}$B$_{2}$C
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A longitudinal SDW, accompanied by an orthorhombic distortion, sets-in at $T_{N}$.[@Dervenagas-Tb-structure-anistropy-WeakFM; @Song-Tb-dichroism-HRMXRD] The magnitude of the modulation vector decreases from 0.551$\overset{\ast}{a}$ near $T_{N}$ to 0.545$\overset{\ast}{a}$ at 2.3 K.[@Dervenagas-Tb-structure-anistropy-WeakFM] A weak ferromagnetic component develops below $T_{WF}\approx$ 8 K and at lower temperature a squaring-up of the modulated state was observed.[@Dervenagas-Tb-structure-anistropy-WeakFM]

$C_{M}(T)$ of single crystal TbNi$_{2}$B$_{2}$C (Fig.2) shows the magnetic ordering at $T_{N}=14.5$ K and the WF-associated anomaly that peaks around 5.5 K. These features are in agreement with those reported by Tommy et al.[@Tommy-Tb-reorientation]  Similar to the case of GdNi$_{2}$B$_{2}$C, no attempt was made to analyze $C_{M}(T)$ within the amplitude modulated state spanning the range $5$ K$<T<T_{N}$. Below 5 K, where the orthorhombic-distorted squared-up state is expected, $C_{M}(T)$ follows convincingly the prediction of Eq.\[Cm-bessel\] with $\theta$=$21.5\pm$0.2 K and $\Delta$=7.0$\pm$0.5 K.

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[magnon-Fig2.eps]{}

DyNi$_{2}$B$_{2}$C
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This compound develops a commensurate AF structure below $T_{N}$ with moments arranged in an identical manner as that of HoNi$_{2}$B$_{2}$C. [@Lynn-RNi2B2C-mag-xrd; @Dervenagas-Dy-structure] Moreover, superconductivity coexists with this AF order below 