of the $H-T$ phase diagram of ErNi$_{2}$B$_{2}$C are $\ $[@Lynn-RNi2B2C-mag-xrd; @Canfield-Er-HT-diagram; @Choi-ErNi2B2C-neutron; @Kawano-ErNi2B2C-neutron]: the onset of the incommensurate transversely polarized SDW state with *k*$_{a}$=0.553$a^{\ast}$ at $T_{N}=$5.94 K, and the onset of weak ferromagnetism (WF) at $T_{WF}=$2.2 K. These two events (none is able to quench superconductivity, $T_{c}=10.5$ K) are well evident in $C_{M}(T)$ of Fig.6. $T_{WF}$, in particular, is evident as a change of slope that separates two distinct thermal evolutions:[@Massalami-Cm-ErNi2B2C] $C_{M}(T)$ within the amplitude-modulated state $T_{WF}<T<T_{N}$ and that within the squared-up state at $T<T_{WF}$. In the latter region, $C_{M}(T<T_{WF})$ is well described by Eq.\[Cm-bessel\] with $\ \theta=$7.4$\pm$0.2 K and $\Delta=$5.4$\pm$0.3 K.

\[ptbh\]

[magnon-Fig6.eps]{}

TmNi$_{2}$B$_{2}$C
------------------

Superconductivity sets-in at 11 K and, below $T_{N}=1.52\pm0.05$ K, coexists with a transversely polarized SDW state wherein the spins are pointing along the c-axis and the modulation vector is (0.093,0.093,0).[@Lynn-RNi2B2C-mag-xrd; @Movshovich-TmNi2B2C] At lower temperatures, the incommensurate SDW state squares up.[@Lynn-RNi2B2C-mag-xrd] The magnetic specific heat of single crystal TmNi$_{2}$B$_{2}$C was measured by Movshvich et al [@Movshovich-TmNi2B2C] and was shown to follow Eq.\[Cm-2d\] with $J_{\bot}\approx$0.8 K, $J_{\Vert
}\approx$0.2 K.

Discussion and Conclusions
==========================

On a linearized spin-wave (non interacting magnon gas) approach, one is always limited to the low-temperature region of the ordered state which in 