Magnetic properties and complex magnetic phase diagram in non centrosymmetric EuRhGe$_3$ and EuIrGe$_3$ single crystals

We report the magnetic properties of two Eu based compounds, single crystalline EuIrGe$_3$ and EuRhGe$_3$, inferred from magnetisation, electrical transport, heat capacity and $^{151}$Eu M\"{o}ssbauer spectroscopy. These previously known compounds crystallise in the non-centrosymmetric, tetragonal, $I4mm$, BaNiSn$_3$-type structure. Single crystals of EuIrGe$_3$ and EuRhGe$_3$ were grown using high temperature solution growth method using In as flux. EuIrGe$_3$ exhibits two magnetic orderings at $T_{\rm N1}$ = 12.4 K, and $T_{\rm N2}$ = 7.3 K. On the other hand EuRhGe$_3$ presents a single magnetic transition with a $T_{\rm N}$ = 12 K. $^{151}$Eu M\"{o}ssbauer spectra present evidence for a cascade of transitions from paramagnetic to incommensurate amplitude modulated followed by an equal moment antiferromagnetic phase at lower temperatures in EuIrGe$_3$, the transitions having a substantial first order character. On the other hand the $^{151}$Eu M\"{o}ssbauer spectra at 4.2 and 9 K in EuRhGe$_3$ present evidence of a single magnetic transition. In both compounds a superzone gap is observed for the current density $J\parallel$ [001], which enhances with transverse magnetic field. The magnetisation measured up to 14 T shows the occurrence of field induced transitions, which are well documented in the magnetotransport data as well. The magnetic phase diagram constructed from these data is complex, revealing the presence of many phases in the $H-T$ phase space.