  The magnetization, magnetic susceptibility, and specific heat of the single
crystalline sample SmRh$_2$Zn$_{20}$ were measured. The valence of Sm ions in
SmRh$_2$Zn$_{20}$ was found to be trivalent. No evidence of valence
fluctuations was detected. SmRh$_2$Zn$_{20}$ is an antiferromagnet with $T_{\rm
N}=$ 2.46 K. The observed $C(T,H)$ curves showed that $T_{\rm N}$ splits into
two in the external field $H$ along the [001] and [101]directions. On the other
hand, $T_{\rm N}$ in $H$ along the [111] direction did not split, decreasing to
2.20 K at $H=7$ T. At 2 K, the magnetization $M_{111}$ in $H$ along the [111]
direction increased linearly with increasing field, while $M_{001}$ and
$M_{101}$ deviated upward slightly from the linear dependence. We analyzed the
observed magnetic and thermal properties of SmRh$_2$Zn$_{20}$ taking into
account the crystalline-electric-field effect, the Zeeman energy, and the
exchange interaction. The theoretical calculation well reproduced the
experimental $\chi(T)$, $M(H)$, $C(T,H)$ and $T_{\rm N}(H)$. The sublattice
magnetic moments are expected to be along the $\langle 111\rangle$ direction
below $T_{\rm N}$ at $H=0$ T. Variations of the magnetic structures induced by
the external magnetic fields in a narrow temperature region around $T_{\rm N}$
are inferred on the basis of theoretical calculations.
