Specific heat study of the magnetic superconductor ${\mathrm{HoNi}}_2{\mathrm{B}}_2\mathrm{C}$

The complex magnetic transitions and superconductivity of ${\mathrm{HoNi}}_2{\mathrm{B}}_2\mathrm{C}$ were studied via the dependence of the heat capacity on temperature and in-plane field angle. We provide an extended, comprehensive magnetic phase diagram for $B\Vert \left[100\right]$ and $B\Vert \left[110\right]$ based on the thermodynamic measurements. Three magnetic transitions and the superconducting transition were clearly observed. The 5.2 K transition ${(T}_N)$ shows a hysteresis with temperature, indicating the first-order nature of the transition at $B=0\mathrm{}\mathrm{T}.$ The 6 K transition $T_M,$ namely the onset of the long-range ordering, displays a dramatic in-plane anisotropy: $T_M$ increases with increasing magnetic field for $B\Vert \left[100\right]$ while it decreases with increasing field for $B\Vert \left[110\right].$ The anomalous anisotropy in $T_M$ indicates that the transition is related to the a-axis spiral structure. The 5.5 K transition $T^{*}$ shows similar behavior to the 5.2 K transition, i.e., a small in-plane anisotropy and scaling with Ising model. This last transition is ascribed to the change from $a^{*}$ dominant phase to $c^{*}$ dominant phase.