Charge density wave, enhanced mobility, and large nonsaturating magnetoresistance across the magnetic states of ${\mathrm{HoNiC}}_2$ and ${\mathrm{ErNiC}}_2$

We report on magnetotransport and thermoelectric properties of two ternary carbides ${\mathrm{HoNiC}}_2$ and ${\mathrm{ErNiC}}_2$ hosting both charge density wave and long-range magnetic order. In the charge density wave state, both compounds show relatively large magnetoresistance MR $\approx$ 150% in ${\mathrm{HoNiC}}_2$ and $\approx 70$% in ${\mathrm{ErNiC}}_2$ at a magnetic field of 9 T and temperature as low as 2 K. This positive field-linear magnetoresistance shows no signatures of saturation. Our combined analysis of diagonal and off-diagonal transport responses reveals electronic mobility values on the order of ${10}^3{\mathrm{cm}}^2{V}^{-1}{s}^{-1}$ at 2 K. Both the elevated mobility and related enhanced magnetoresistance persist in the zero-field antiferromagnetic ground state and survive the field-induced crossovers through metamagnetic to field-aligned ferromagnetic states. The robustness of the high-mobility Fermi surface pockets across the magnetically ordered states suggests that the charge density wave is not suppressed but coexists with long-range magnetism in the entire dome of the magnetically ordered states.