Antiferromagnetic order in the honeycomb Kondo lattice $\mathrm{Ce}{\mathrm{Pt}}_6{\mathrm{Al}}_3$ induced by Pd substitution

The cerium-based compound $\mathrm{Ce}{\mathrm{Pt}}_6{\mathrm{Al}}_3$, in which Ce atoms form a honeycomb lattice hosting magnetic frustration, has a heavy-fermion ground state. We have observed development of magnetic order in partially Pd-substituted $\mathrm{Ce}{\left({\mathrm{Pt}}_{1-x}{\mathrm{Pd}}_x\right)}_6{\mathrm{Al}}_3$ series up to $x$ = 0.3 by the measurements of magnetic susceptibility, electrical resistivity ρ, and specific heat $C$. In the whole range of $x$, the unit cell volume remains unchanged within 0.2%, and the effective magnetic moment stays at $2.4{\mu }_B/\mathrm{Ce}$. For $x$ = 0.05, both $C/T$ and $\rho \left(T\right)$ jump on cooling at $T_m=1.8\mathrm{K}$. With increasing $x$ to 0.2, $T_m$ increases to 3.8 K, where $C/T$ shows a pronounced λ-type anomaly. Application of magnetic fields suppresses $T_m$, which is indicative of an antiferromagnetic (AFM) ordered state. Thus, a long-range AFM order is induced by the substitution of isovalent Pd for Pt in $\mathrm{Ce}{\mathrm{Pt}}_6{\mathrm{Al}}_3$ without carrier doping and chemical pressure. We attribute the emergence of AFM order in $\mathrm{Ce}{\left({\mathrm{Pt}}_{1-x}{\mathrm{Pd}}_x\right)}_6{\mathrm{Al}}_3$ to the randomness in the spin-orbit interaction in the Pt-Pd sublattice, which weakens both the coherent Kondo effect and magnetic frustration in the honeycomb Kondo lattice.

Figure 1

(a) Layers of Ce (red) honeycombs with Pt (green) triangles on the center which are stacked along the $c$ axis in $\mathrm{Ce}{\mathrm{Pt}}_6{\mathrm{Al}}_3$ of the trigonal $\mathrm{Nd}{\mathrm{Pt}}_6{\mathrm{Al}}_3$-type structure [13]. ${\mathrm{Pt}}_9{\mathrm{Al}}_6$ blocks between the ${\mathrm{Ce}}_2{\mathrm{Pt}}_3$ layers are omitted for clarity. Intralayer Ce-Ce distances are denoted as $d_1$ and $d_2$ and the interlayer distance as $d_3$ (see text). (b) Trigonal lattice parameters $a$ and $c$ and (c) the ratio $c/a$ and the unit cell volume $V$ for $\mathrm{Ce}{\left({\mathrm{Pt}}_{1-x}{\mathrm{Pd}}_x\right)}_6{\mathrm{Al}}_3$ as a function of the Pd concentration $x$.

Figure 2

Temperature dependence of the inverse of magnetic susceptibility of $\mathrm{Ce}{\left({\mathrm{Pt}}_{1-x}{\mathrm{Pd}}_x\right)}_6{\mathrm{Al}}_3$ in a field of 1 T. The solid line is an example of the fit with the modified Curie-Weiss form $\chi =C/(T-{\theta }_p)+{\chi }_0$ to the data for $x$ = 0 at temperatures $>100\mathrm{K}$. The inset shows the effective magnetic moment ${\mu }_{\mathrm{eff}}$ and paramagnetic Curie temperature ${\theta }_p$ as a function of the Pd concentration $x$. The horizontal broken line represents the value ${\mu }_{\mathrm{eff}}=2.54{\mu }_B$ expected for a free ${\mathrm{Ce}}^{3+}$ ion.

Figure 3

Temperature dependence of the magnetic susceptibility χ of $\mathrm{Ce}{\left({\mathrm{Pt}}_{1-x}{\mathrm{Pd}}_x\right)}_6{\mathrm{Al}}_3$ in a field of 1 T. Arrows indicate the bends in $\chi \left(T\right)$ at $T_m$. The lower inset shows the decrease in $T_m$ for $x$ = 0.2 with increasing the applied magnetic field to 5 T. The upper inset shows the temperature dependence of alternating current (AC) magnetic susceptibility ${\chi }_{\mathrm{AC}}\left(T\right)$ for $x$ = 0, 0.02, and 0.05 in an AC field of 300 μT at a frequency of 4000 Hz. The data are shifted vertically for clarity.

Figure 4

Temperature dependence of electrical resistivity $\rho \left(T\right)$ normalized to the value at 300 K for $\mathrm{Ce}{\left({\mathrm{Pt}}_{1-x}{\mathrm{Pd}}_x\right)}_6{\mathrm{Al}}_3$.

Figure 5

(a) Magnetic part of specific heat $C_m$ divided by temperature $T$ and (b) electrical resistivity $\rho \left(T\right)$ for $\mathrm{Ce}{\left({\mathrm{Pt}}_{1-x}{\mathrm{Pd}}_x\right)}_6{\mathrm{Al}}_3$ as a function of temperature. Arrows indicate the midpoint of jump in $C_m/T$ and the anomaly in $\rho \left(T\right)$, revealing magnetic transitions at $T_m$. The inset shows the $\rho \left(T\right)$ data for $x$ = 0.05 on an expanded scale.

Figure 6

Magnetic field vs temperature phase diagram for $\mathrm{Ce}{\left({\mathrm{Pt}}_{1-x}{\mathrm{Pd}}_x\right)}_6{\mathrm{Al}}_3$ constructed from anomalies in magnetic susceptibility (open squares), specific heat (open circles), and electrical resistivity (open triangles).

Figure 7

Magnetic entropy $S_m$ normalized by $R$ln2 for $\mathrm{Ce}{\left({\mathrm{Pt}}_{1-x}{\mathrm{Pd}}_x\right)}_6{\mathrm{Al}}_3$ as a function of temperature. The open circles represent the values of $S_m\left(T\right)/R\ln 2$ at $T=T_m$. The inset shows the values of $S_m/Rln2$ at 5 K as a function of the Pd concentration $x$.

Figure 8

Variations of physical properties of $\mathrm{Ce}{\left({\mathrm{Pt}}_{1-x}{\mathrm{Pd}}_x\right)}_6{\mathrm{Al}}_3$ as a function of the Pd concentration $x$. (a) Magnetic transition temperatures $T_m$ which are taken from anomalies in alternating current (AC) magnetic susceptibility (open circles), direct current (DC) magnetic susceptibility (open squares), specific heat (closed circles), and electrical resistivity (open triangles). SR, AF I, and AF II denote the short-range ordered state, spin-density wave (SDW) state, and antiferromagnetic (AFM) ordered state, respectively. (b) Specific heat divided by temperature $C/T$ at 0.4 K. (c) Kondo temperature $T_K$ estimated from the temperature-dependent magnetic entropy (see text). (d) Magnetic frustration parameter $f=-{\theta }_p/T_m$, where ${\theta }_p$ and $T_m$ denote the paramagnetic Curie temperature and magnetic transition temperature, respectively. The marks have the same meanings as in (a).