couplings while the latter (a combination of  dominant CEF and weaker dipolar and anisotropic exchange forces) by an easy-axis anisotropy field $\vec{H}_{a}$:[@Kittel-SpinWave] this $\vec{H}_{a}$ representation is convenient for spin-wave calculation and is valid for the low-temperature orthorhombic-distorted equal-amplitude collinear AF or squared-up phases of borocarbides (see Sec.V). Considering the above mentioned magnetic arrangement and the crystal symmetry, the magnetic couplings can be conveniently divided into two classes: $J_{ij}^{A}$ that couples moments $i$ and $j$ within the same layer (denoted as $A$ or $B$) and $J_{ij}^{AB}$ that couples moments from different layers. Then at zero external field, the following Hamiltonian is expected to capture most of their low-temperature  properties: $$\mathcal{H}=-\sum_{<ij>,L\in A,B}J_{ij}^{L}\overrightarrow{S_{i}^{L}}.\overrightarrow{S_{j}^{L}}+\sum_{<ij>A,B}J_{ij}^{AB}\overrightarrow
{S_{i}^{A}}.\overrightarrow{S_{j}^{B}}-g\mu_{B}\vec{H_{a}}\sum_{j\in
A}\overrightarrow{S_{j}^{A}}+g\mu_{B}\vec{H_{a}}.\sum_{j\in B}\overrightarrow
{S_{j}^{B}} \label{H}$$ The first and second sum represent, respectively, interactions within the same layer and among different layers. The last two terms represent the anisotropic interactions. By standard spin-wave analysis, we obtained the following dispersion relation: $$\hbar\omega_{k}=\sqrt{\left[  SJ_{\bot}(0)-SJ_{\bot}(k)+SJ_{\Vert}(0)+g\mu
_{B}H_{a}\right]  ^{2}-\left[  SJ_{\Vert}(k)\right]  ^{2}} \label{dispersion}$$ where $J(k)=\sum J_{ij}\exp(ik(r_{i}-r_{j})).$ $J_{\Vert}$ ($J_{\bot}$) represents the Fourier-transform parallel (perpendicular) to the c-axis. The energy gap, $\Delta=\hbar\omega_{k=0},$ is: $$\Delta=\sqrt{\left(  g\mu_{B}H_{a}\right)  ^{2}+2J_{\Vert}(0)g\mu_{B}SH_{a}}
\label{gap}$$ which defines an AF resonance frequency similar to the uniform mode of ordinary AFs.[@Kubo-SpinWave; @Eisele-Keffer-SpinWave; @Kittel-SpinWave; @Walker-SpinWave] Evidently, (i) $\Delta$ is zero 