Suppression of long-range ferromagnetic order in the ${\mathrm{Ce}}_x{\mathrm{La}}_{1-x}{\mathrm{TiGe}}_3$ system

We report specific heat, magnetization, and resistivity measurements on single crystals of ${\mathrm{Ce}}_x{\mathrm{La}}_{1-x}{\mathrm{TiGe}}_3$ systems. When the Ce concentration $x$ is increased, the system changes from a single-ion Kondo system for $x=0.05$ into a ferromagnetic Kondo lattice for $x=1$, where the magnetic part of electrical resistivity reveals a single-ion scaling with $x$. The isoelectric substitution of Ce by La atoms causes a change of the relative strength of competing energy scales of Kondo and RKKY interaction and crystalline electric field (CEF). The substitutions induce the continuous evolution of the Kondo temperature $T_K$ and the linear variation of ferromagnetic ordering temperature $T_c$, which are accompanied by a change of the CEF level scheme of the Ce ions. The composition-temperature ($x\text{−}T$) phase diagram for ${\mathrm{Ce}}_x{\mathrm{La}}_{1-x}{\mathrm{TiGe}}_3$ is constructed by a combination of magnetization, specific heat, and resistivity measurements. The ferromagnetic ordering temperature is linearly suppressed as $x$ decreases and vanishes near the critical concentration $x_c=0.1$, but conventional quantum criticality is absent near $x_c$. The specific heat measurement for $x=0.05$ reveals the power law increase of the electronic specific heat coefficient $C_m/T\propto 1/T$ with a large value of $\sim 3.5$ J/mol ${\mathrm{K}}^2$ at $T=0.4\mathrm{K}$. The magnetic susceptibility for $x=0.05$ also shows a power law dependence $\chi \left(T\right)\propto 1/T$ below 10 K.

Figure 1

Variation of unit cell volume in ${\mathrm{Ce}}_x{\mathrm{La}}_{1-x}{\mathrm{TiGe}}_3$. Open symbols and star are taken from Refs. [13, 24]. Top inset shows lattice parameters $a$ (solid circles, left axis) and $c$ (open triangles, right axis). Bottom inset shows a photograph image of ${\mathrm{LaTiGe}}_3$.

Figure 2

Physical properties of ${\mathrm{LaTiGe}}_3$: (a) Specific heat in $H=0$ (symbols) and 90 kOe (solid line) for $H\parallel c$. Inset displays $C_p/T$ vs $T^2$ plot at low temperatures. Solid line represents a linear fit. (b) Magnetic susceptibility at $H=70$ kOe for $H\parallel c$. Inset shows the magnetization as a function of field at $T=1.8\mathrm{K}$ for $H\parallel c$. (c) Zero-field electrical resistivity. Inset shows the expanded view at low temperatures. (d) Transverse magnetoresistance at $T=1.8\mathrm{K}$. Inset shows the oscillatory component of the resistivity, subtracted background contributions using a polynomial fit.

Figure 3

(a) Temperature dependence of magnetic susceptibility ($M/H$) curves for ${\mathrm{Ce}}_x{\mathrm{La}}_{1-x}{\mathrm{TiGe}}_3$ system, measured at $H=1$ kOe for $H\parallel c$. The curves correspond to $x=1$, 0.8, 0.6, 0.5,0.4, 0.3, 0.2, 0.15, 0.1, 0.05 from top to bottom. (b) $M/H$ for $H\parallel ab$. Arrows indicate the local maximum in $\chi \left(T\right)$. For clarity the susceptibility curves for $x=0.4$ and $x=1$ are plotted only above the $T_c$. (c) Inverse magnetic susceptibility ($H/M$) for $H\parallel c$ below 10 K. The solid line is a guide to the eye. (d) $H/M$ for $H\parallel ab$ at $H=1$ kOe. Solid lines represent a Curie-Weiss fit to the data. The curves are shifted vertically for clarity.

Figure 4

(a) Effective magnetic moment ${\mu }_{\mathrm{eff}}$ as a function of $x$ in ${\mathrm{Ce}}_x{\mathrm{La}}_{1-x}{\mathrm{TiGe}}_3$. (b) Paramagnetic Curie temperature. (c) Curie temperature $T_c$ determined from $d\chi T/dT$ for $H\parallel c$. (d) $T_{\max }^{\chi }$ obtained from the maximum in $\chi \left(T\right)$ curve for $H\parallel ab$.

Figure 5

(a) Magnetic field dependences of magnetization $M\left(H\right)$ curves for $H\parallel c$ at $T=1.8$ K. (b) Extended plot in the low field region of $M\left(H\right)$ curves for $H\parallel c$. Solid symbols and open symbols are up- and down-sweep of magnetic fields, respectively. Arrows indicate the critical fields. (c) $M\left(H\right)$ curves of ${\mathrm{Ce}}_{0.05}{\mathrm{La}}_{0.95}{\mathrm{TiGe}}_3$ at $T=1.8$ K for both $H\parallel ab$ and $H\parallel c$. (d) Magnetization values for $H\parallel c$ at $T=1.8$ K as a function of $x$. Solid circle and triangular symbols are taken at $H=70$ kOe and at the critical fields, respectively.

Figure 6

Specific heat curves for ${\mathrm{Ce}}_x{\mathrm{La}}_{1-x}{\mathrm{TiGe}}_3$. Inset shows the expanded plot below 20 K in log-log scale.

Figure 7

(a) Magnetic part of specific heat $C_m$ curves for ${\mathrm{Ce}}_x{\mathrm{La}}_{1-x}{\mathrm{TiGe}}_3$, where $x=1$, 0.8, 0.6, 0.5, 0.4, 0.3, 0.2, 0.15, 0.1, and 0.05 from top to bottom. (b) $C_m/T$ curves. Vertical arrows indicate the peak position in $C_m$. (c) Magnetic entropy $S_m$ curves. (d) The broad local maximum $T_{\max }^{C_m}$ and the phase transition temperature $T_c$ as a function of $x$.

Figure 8

Electrical resistivity $\rho \left(T\right)$ curves, normalized to 300 K, for ${\mathrm{Ce}}_x{\mathrm{La}}_{1-x}{\mathrm{TiGe}}_3$.

Figure 9

(a) $\rho \left(T\right)$ curves for ${\mathrm{Ce}}_x{\mathrm{La}}_{1-x}{\mathrm{TiGe}}_3$ below 16 K. Arrows indicate the peak position in $\mathrm{d}\rho \left(T\right)/\mathrm{d}T$. (b) Resistivity value at 300 K as a function of $x$. Error bars represent the geometry (dimensional) error. Dashed line is a guide to the eye. (c) Resistivity value at 0.4 K for $x\le 0.4$ and at 1.8 K for $x>0.5$ (left axis) and residual resistivity ratio RRR (right axis) as a function of $x$. (d) Local maximum $T_{\max }^{\rho }$ and $T_c$ as a function of $x$. See details in text.

Figure 10

The magnetic contribution to the resistivity ${\rho }_m$ for $x>$ 0, where $x=0$ curve is plotted together for comparison. Down arrows indicate a local maximum developed at high temperatures and up arrows indicate the position of a local maximum in the low temperature side.

Figure 11

(a) $x\text{−}T$ phase diagram for ${\mathrm{Ce}}_x{\mathrm{La}}_{1-x}{\mathrm{TiGe}}_3$. The symbols are obtained from $\mathrm{d}\rho \left(T\right)/\mathrm{d}T$, $\mathrm{d}\chi T/\mathrm{d}T$, and the maximum in $C_p\left(T\right)$. Dotted line is a guide to the eye. (b) $C_m$ and $\mathrm{d}\rho \left(T\right)/\mathrm{d}T$ for $x=0.15$. Arrows indicate the determined phase transition temperature. (c) Onset temperatures reaching $Rln\left(2\right)$ and $0.4Rln\left(2\right)$ magnetic entropy. (d) $C_m/T$ at $T=0.4$ K for $x<0.4$ and at 1.8 K for $x\ge 0.4$ (left axis) and magnetic entropy $S_m/Rln\left(2\right)$ at $T_c$ (right axis).

Figure 12

Local maximum temperatures developed in the magnetic susceptibility, specific heat, and electrical resistivity and the Weiss temperatures ${\theta }_p$ along $H\parallel ab$ and $H\parallel c$. The solid line indicates a phase boundary between PM and FM, presented in Fig. 11.

Figure 13

$C_m$ curves for $x=0.05$ and 0.1. The solid and dash-dotted line represent the $J=1/2$ C-S model with $T_0=0.45$ K and $J=3/2$ C-S model with $T_0=0.85$ K, respectively [29]. The dotted line is based on the two level Schottky contribution with ${\mathrm{\Delta }}_{\mathrm{CEF}}\sim 28$ K.

Figure 14

$C_m/T$ of ${\mathrm{Ce}}_x{\mathrm{La}}_{1-x}{\mathrm{TiGe}}_3$ for $x=0.2$, 0.15, 0.1, and 0.05, plotted as a function of $1/T$. Solid line is guide to the eye.