Unconventional magnetic order emerging from competing energy scales in the new $R{\mathrm{Rh}}_3{\mathrm{Si}}_7$ intermetallics ($R$ = Gd-Yb)

The competition between Ruderman-Kittel-Kasuya-Yosida (RKKY), crystal electric field (CEF), and Kondo energy scales has recently emerged at the heart of complex magnetism in several Ce- or Yb-based intermetallics. Hard axis magnetic order has been observed in a handful of these compounds, independent of the crystal symmetry, size of the ordered moment, or the relative scale of the Kondo and magnetic ordering temperatures. This raises the question of the role of each energy scale in driving the ground state properties. In focusing on a single class of compounds, the rhombohedral R${\mathrm{Rh}}_3{\mathrm{Si}}_7$, we compare the anisotropy and magnetic ground states in members of this series with only RKKY interactions (R = Gd), or RKKY and CEF effects (R = Tb-Tm), with the behavior of the R = Yb compound, where all three energy scales (RKKY, CEF, Kondo) are at play. Moreover, we extend the comparison to two other isostructural Kondo systems ${\mathrm{YbIr}}_3{\mathrm{Si}}_7$ and ${\mathrm{YbIr}}_3{\mathrm{Ge}}_7$, where hard axis magnetic order is also observed. The non-Kondo compounds R${\mathrm{Rh}}_3{\mathrm{Si}}_7$ (R = Tb-Tm) lack the complexity of magnetic order along the hard CEF axis, pointing to the dominant role of the Kondo effect in driving this magnetic order. However, the CEF-RKKY competition is still responsible for complex magnetic ground states, and it appears that the electronic and magnetic degrees of freedom are entangled in all magnetic members of this series of compounds.

Figure 1

(a) Powder x-ray diffraction (symbols) and Rietveld refinement (black line) at 300 K for ${\mathrm{TbRh}}_3{\mathrm{Si}}_7$, with an image of a ${\mathrm{TbRh}}_3{\mathrm{Si}}_7$ crystal in the inset. (b) Crystal structure of R${\mathrm{Rh}}_3{\mathrm{Si}}_7$ (R = Gd-Tm). (c) Unit cell volume V vs ionic radius of R${}^{3+}$ for R${\mathrm{Rh}}_3{\mathrm{Si}}_7$ (R = Gd-Lu), with the dashed line showing the expected lanthanide contraction [34].

Figure 2

Temperature-dependent magnetic susceptibility with ${\mu }_{0}H=0.1T$ for $H\parallel a$ (full symbols) and $H\parallel c$ (open symbols) of R${\mathrm{Rh}}_3{\mathrm{Si}}_7$ (R = Gd-Tm).

Figure 3

Inverse magnetic susceptibility $H/M_{\mathrm{ave}}$ (symbols) of R${\mathrm{Rh}}_3{\mathrm{Si}}_7$ (R = Gd-Tm) for ${\mu }_{0}H=0.1T$. Solid lines are Curie-Weiss fits.

Figure 4

Field-dependent magnetization measured at $T$ = 1.8 K for $H\parallel a$ (full symbols) and $H\parallel c$ (open symbols) for R${\mathrm{Rh}}_3{\mathrm{Si}}_7$ (R = Gd-Tm). Horizontal dashed lines indicate the saturated moments of the ${\mathrm{R}}^{3+}$ ions calculated from Hund's rules.

Figure 5

Zero-field specific heat for R${\mathrm{Rh}}_3{\mathrm{Si}}_7$. The insets in (b), (d), and (e) show the lower temperature range of the corresponding specific heat curve. The dashed line indicates the specific heat of the nonmagnetic analog ${\mathrm{LuRh}}_3{\mathrm{Si}}_7$

Figure 6

Magnetic entropy $S_m$ for R${\mathrm{Rh}}_3{\mathrm{Si}}_7$ (R = Gd-Tm). The vertical arrows indicate the ordering temperatures defined by the sharp peak in specific heat measurement, as discussed in the main text.

Figure 7

(a)–(f) Zero-field resistivity for R${\mathrm{Rh}}_3{\mathrm{Si}}_7$ (R = Gd-Tm) with $i\parallel c$. (g) Semilog plot of the normalized resistivity $\rho /\rho \left(300K\right)$ for R${\mathrm{Rh}}_3{\mathrm{Si}}_7$, including the data for R = Yb (light blue) and Lu (dashed line)[30], and the respective curves for the isostructural Kondo compounds ${\mathrm{YbIr}}_3{\mathrm{Ge}}_7$[29] and ${\mathrm{YbIr}}_3{\mathrm{Si}}_7$[12].

Figure 8

Hard axis ordering of ${\mathrm{YbIr}}_3{\mathrm{Si}}_7$, ${\mathrm{YbIr}}_3{\mathrm{Ge}}_7$ and ${\mathrm{YbRh}}_3{\mathrm{Si}}_7$. $H\parallel a$ (full symbols) and $H\parallel c$ (open symbols). The dashed lines indicate the magnetic ordering temperature.