Structural and physical properties of the chiral antiferromagnet CeRhC$_2$

We report a study of the structural, magnetic, transport, and thermodynamic properties of polycrystalline samples of CeRhC$_2$. CeRhC$_2$ crystallizes in a tetragonal structure with space group $P4_1$ and it orders antiferromagnetically below $T_\textrm{N1} \approx$ 1.8 K. Powder neutron diffraction measurements reveal a chiral magnetic structure with a single propagation vector $Q_m = (1/2,1/2,0.228(5))$, indicating an antiferromagnetic arrangement of Ce magnetic moments in the $ab$-plane and incommensurate order along the $c$-axis with a root-mean-square ordered moment of $m_\textrm{ord}$= 0.68 $\mu_\textrm{B}$/Ce. Applying a magnetic field suppresses the N\'{e}el temperature $T_\textrm{N1}$ to zero near $\mu_0H_\textrm{c1}\sim$0.75 T. A second antiferromagnetic phase ($T_\textrm{N2}$), however, becomes apparent in electrical resistivity, Hall and heat capacity measurements in fields above 0.5 T and extrapolates to zero temperature at $\mu_0H_\textrm{c2}\sim$ 1 T. Electrical resistivity measurements reveal that LaRhC$_2$ is a semiconductor with a bandgap of $E_\textrm{g}\sim24$ meV; whereas, resistivity and Hall measurements indicate that CeRhC$_2$ is a semimetal with a low carrier concentration of $n\sim10^{20}$ cm$^{-3}$. With applied hydrostatic pressure, the zero-field antiferromagnetic transition of CeRhC$_2$ is slightly enhanced and CeRhC$_2$ becomes notably more metallic up to 1.36 GPa. The trend toward metallicity is in line with density-functional calculations that indicate that both LaRhC$_2$ and CeRhC$_2$ are semimetals, but the band overlap is larger for CeRhC$_2$, which has a smaller unit cell volume that its La counterpart. This suggests that the bandgap closes due to a lattice contraction when replacing La with Ce in RRhC$_2$ (R = rare-earth), in agreement with experimental results.