Ordering wave vectors of metamagnetic states in ${\mathrm{HoNi}}_2{\mathrm{B}}_2\mathrm{C}:$ One dimension is not enough

Elastic neutron-diffraction measurements have been preformed in each of the metamagnetic states of ${\mathrm{HoNi}}_2{\mathrm{B}}_2\mathrm{C}$ for an applied field applied in the tetragonal basal plane making an angle of approximately $15°$ with the $\left[110\right]$ axis. Whereas these data are in excellent quantitative agreement with earlier thermodynamic studies of the $H_{\mathrm{app}}-\theta$ phase diagram of ${\mathrm{HoNi}}_2{\mathrm{B}}_2\mathrm{C},$ the magnetic wave vector of the metamagnetic state, $\approx {4/7a}^{\star },$ is in stark contradiction with the predictions of two, one-dimensional theoretical models developed for this system. On the other hand, simple energetic arguments which are consistent with the existence of the $a^{\star }$ phase are presented.