Quantum criticality and development of antiferromagnetic order in the quasikagome Kondo lattice $\mathrm{CeR}{\mathrm{h}}_{1-x}\mathrm{P}{\mathrm{d}}_x\mathrm{Sn}$

CeRhSn with a quasikagome lattice of Ce atoms in the hexagonal $c$ plane has been expected to be in close vicinity to a zero-field quantum criticality derived from magnetic frustration. We have studied how the ground state changes with substitution of Pd for Rh in $\mathrm{CeR}{\mathrm{h}}_{1-x}\mathrm{P}{\mathrm{d}}_x\mathrm{Sn}$ $\left(x\le 0.75\right)$ by measuring the specific heat $C$, magnetic susceptibilities ${\chi }_{\mathrm{dc}}$ and ${\chi }_{\mathrm{ac}}$, magnetization $M$, electrical resistivity ρ, and magnetoresistance. For $x=0$, the field dependence of ${\chi }_{\mathrm{ac}}$ at $T=0.03\mathrm{K}$ shows a peak at $B\parallel a=3.5\mathrm{T}$, confirming the spin-flop crossover in the field applied along the hard axis. The temperature dependence of ${\chi }_{\mathrm{ac}}$ shows a broad maximum at 0.1 K whereas $C/T$ continues to increase down to 0.08 K. For $x\geqq 0.1,\rho \left(T\right)$ is dominated by incoherent Kondo scattering and both $C/T$ and ${\chi }_{\mathrm{ac}}\left(T\right)$ exhibit peaks, indicating the development of an antiferromagnetic order. The ordering temperature rises to 2.5 K as $x$ is increased to 0.75. Our results indicate that the ground state in the quasikagome Kondo lattice $\mathrm{CeR}{\mathrm{h}}_{1-x}\mathrm{P}{\mathrm{d}}_x\mathrm{Sn}$ leaves the quantum critical point at $x=0$ with increasing $x$ as a consequence of suppression of both the magnetic frustration and Kondo effect.

Figure 1

Hexagonal lattice parameters $a$ and $c$ of $\mathrm{CeR}{\mathrm{h}}_{1-x}\mathrm{P}{\mathrm{d}}_x\mathrm{Sn}$ as a function of $x$. The data except for $x=0.1$ are derived from Ref. [28]. The inset shows the unit cell of CeRhSn.

Figure 2

Temperature dependence of electrical resistivity normalized to the value at 300 K for polycrystalline samples of $\mathrm{CeR}{\mathrm{h}}_{1-x}\mathrm{P}{\mathrm{d}}_x\mathrm{Sn}$.

Figure 3

Temperature dependence of the inverse of the averaged magnetic susceptibility of $\mathrm{CeR}{\mathrm{h}}_{1-x}\mathrm{P}{\mathrm{d}}_x\mathrm{Sn}$ (see text). Solid lines are the fits with the modified Curie-Weiss form $\chi -{\chi }_0=C/(T-{\theta }_p)$ to the data at temperatures above 100 K.

Figure 4

Isothermal magnetization curves $M(B\parallel )$ of polycrystalline samples of $\mathrm{CeR}{\mathrm{h}}_{1-x}\mathrm{P}{\mathrm{d}}_x\mathrm{Sn}$ as a function of the magnetic field at 1.8 K. The data except for $x=0.1$ are derived from Ref. [28]. The inset shows the temperature dependence of the magnetic susceptibility for $x=0.75$ below 5 K.

Figure 5

(a) Specific heat of polycrystalline samples of $\mathrm{CeR}{\mathrm{h}}_{1-x}\mathrm{P}{\mathrm{d}}_x\mathrm{Sn}$ $\left(0\le x\le 0.75\right)$ plotted as $C/T$ vs logT. (b) The ac magnetic susceptibility vs $\log T$ for single crystals with $x=0$ and 0.1 and polycrystals with 0.2, 0.3, and 0.4.

Figure 6

Isothermal ac susceptibility of the CeRhSn single crystal as a function of magnetic field $B$ applied parallel to the $a$ and $c$ axes, respectively. The data are vertically shifted for clarity.

Figure 7

Temperatures at the maximum in $C/T$ $(\blacksquare )$ and ${\chi }_{\mathrm{ac}}\left(T\right)$ $(○)$ for $\mathrm{CeR}{\mathrm{h}}_{1-x}\mathrm{P}{\mathrm{d}}_x\mathrm{Sn}$ vs x.

Figure 8

Magnetic entropy of $\mathrm{CeR}{\mathrm{h}}_{1-x}\mathrm{P}{\mathrm{d}}_x\mathrm{Sn}$ as a function of temperature. The dashed line represents the value of $0.65R\ln 2$.

Figure 9

Electrical resistivity of single crystals $\mathrm{CeR}{\mathrm{h}}_{1-x}\mathrm{P}{\mathrm{d}}_x\mathrm{Sn}$ with $x=0$ and 0.1 for the current $I$ parallel to the $a$ and $c$ axes, respectively. The data for $x=0$ are derived from Ref. [24]. The inset shows the magnetic contribution to the resistivity vs $\log T$.

Figure 10

The dc magnetic susceptibility of single crystals of $\mathrm{CeR}{\mathrm{h}}_{1-x}\mathrm{P}{\mathrm{d}}_x\mathrm{Sn}$ with $x=0$ and 0.1 for $B\parallel a$ and $B\parallel c$, respectively. The inset shows the isothermal magnetization for $B\parallel a$ and $B\parallel c$ at 0.3 K. The data for $x=0$ are derived from Ref. [24].

Figure 11

Normalized magnetoresistance for single crystals $\mathrm{CeR}{\mathrm{h}}_{1-x}\mathrm{P}{\mathrm{d}}_x\mathrm{Sn}$ with $x=0$ (a) and $x=0.1$ (b) at 0.08 K in applied fields $B\parallel a$ and $B\parallel c$ for the longitudinal and transverse configurations.