Magnetic properties of $R$Rh$_6$Ge$_4$ ($R$ = Pr, Nd, Sm, Gd-Er) single crystals

TL;DR

This work addresses how 4f electrons in the RRh$_6$Ge$_4$ series (R = Pr, Nd, Sm, Gd–Er) drive diverse magnetic ground states through crystal-electric-field effects on a quasi-one-dimensional triangular lattice. The authors synthesize high-quality single crystals via Bi-flux and perform anisotropic magnetization, resistivity, and specific-heat measurements to map magnetic orderings and transitions, employing Curie-Weiss fits and CEF considerations. Nd and Sm emerge as new ferromagnets, Gd and Dy order antiferromagnetically, and Ho behaves as a ferrimagnet with a distinctive $M_s/3$ plateau, while Pr and Er remain paramagnetic down to 0.4 K; Dy further exhibits field-induced transitions and multiple magnetization plateaus along the $c$-axis. The results highlight the intricate interplay of RKKY exchange and single-ion CEF anisotropy in shaping ground states and magnetization textures, offering a platform for exploring frustration-related phenomena and potential quantum critical behavior under tuning.

Abstract

Single crystals of $R$Rh$_6$Ge$_4$ ($R$ = Pr, Nd, Sm, Gd - Er) were synthesized using a Bi flux and their physical properties were characterized by magnetization, resistivity, and specific heat measurements. These compounds crystallize in the noncentrosymmetric LiCo$_6$P$_4$-type structure (space group $P\bar{6}m2$), where rare-earth atoms form a triangular lattice in the $ab$-plane and chains along the $c$-axis. PrRh$_6$Ge$_4$ and ErRh$_6$Ge$_4$ do not exhibit magnetic transitions above 0.4 K. NdRh$_6$Ge$_4$ and SmRh$_6$Ge$_4$ are ferromagnets, while GdRh$_6$Ge$_4$ and DyRh$_6$Ge$_4$ show antiferromagnetic transitions, \red{whereas HoRh$_6$Ge$_4$ is a ferrimagnet}. In addition, DyRh$_6$Ge$_4$ shows multiple transitions and magnetization plateaus when a magnetic field is applied along the $c$-axis. In SmRh$_6$Ge$_4$, like the Ce counterpart, the crystalline-electric field (CEF) effect leads to an easy plane anisotropy, while in other compounds it gives rise to a pronounced uniaxial anisotropy.

Figures (13)

• Figure 1: (Color online) Crystal structure of $R$Rh$_6$Ge$_4$ ($R$ = Pr, Nd, Sm, Gd - Er), viewed (a) parallel, and (b) perpendicular to the chain direction ($c$ axis), where orange, gray, and blue represent $R$, Rh, and Ge atoms, respectively. (c) Single crystal XRD pattern of a GdRh$_6$Ge$_4$ crystal in the (0 h l) plane. (d) Lattice constants, (e) unit cell volume, and (f) $c/a$ ratio for $R$Rh$_6$Ge$_4$.
• Figure 2: (Color online) (a) Temperature dependence of the magnetic susceptibility $\chi(\rm T)$ (left axis) and 1/$\chi$ (right axis) of PrRh$_6$Ge$_4$ measured in $\mu_0H$ = 1 T for $H$$\Vert$$c$, where the solid line corresponds to fit to the modified Curie-Weiss law. Temperature dependence of the resistivity $\rho(\rm T)$ of (b) PrRh$_6$Ge$_4$ and (c) ErRh$_6$Ge$_4$. The insets show $\rho(\rm T)$ at low temperatures. Red lines show fitting using $\rho = \rho_0 + AT^2$.
• Figure 3: (Color online) Temperature dependence of the resistivity $\rho(\rm T)$ of (a) NdRh$_6$Ge$_4$ and (b) SmRh$_6$Ge$_4$. Insets show $\rho(\rm T)$ at low temperatures, where red arrows indicate the magnetic transitions.
• Figure 4: (Color online) (a) and (b) show the respective temperature dependence of the inverse magnetic susceptibility $1/\chi$ measured in $\mu_0H$ = 1 T for $H$$\Vert$$c$ (circles) and $H$$\Vert$$ab$ (squares), where the solid lines correspond to fits to the modified Curie-Weiss law. Insets show the magnetic susceptibility $\chi(\rm T)$measured upon field-cooling (FC) at low temperatures. (c) and (d) show the field dependence of the magnetization for $H$$\Vert$$c$ (circles) and $H$$\Vert$$ab$ (squares). The insets show the magnetization loops with hysteresis in the low-field region.
• Figure 5: (Color online) (a) Magnetic part of the specific heat $C_{\rm mag}/T$ of NdRh$_6$Ge$_4$ (black squares) and SmRh$_6$Ge$_4$ (red circles). The arrows show the magnetic transitions. The inset displays the total specific heat as $C/T$ of NdRh$_6$Ge$_4$ (black line), SmRh$_6$Ge$_4$ (red line) and LaRh$_6$Ge$_4$ (blue line). (b) Temperature dependence of the magnetic entropy $S_{\rm mag}$.