Coupling between magnetic and thermodynamic properties in $R{\mathrm{Rh}}_2{\mathrm{Si}}_2(R$ = Dy, Ho)

Single crystals of ${\mathrm{DyRh}}_2{\mathrm{Si}}_2$ and ${\mathrm{HoRh}}_2{\mathrm{Si}}_2$ were investigated by thermal expansion and magnetostriction. The different types of magnetic order can clearly be seen in these measurements, particularly the canting of the moments away from the crystallographic $c$ direction below about 12 K and the spin flip for magnetic field applied along the $c$ direction. For ${\mathrm{HoRh}}_2{\mathrm{Si}}_2$, an additional transition just below $T_N$ is analyzed by means of the Grüneisen ratio and is likely caused by a change in the magnetic structure. Our results nicely corroborate findings from other magnetic and thermodynamic measurements on these materials and provide further evidence suggesting the formation of magnetic domains.