Heat capacity proportional to $T^2$ induced by Ru substitution in ${\text{CaCu}}_3\left({\text{Ti}}_{4-x}{\text{Ru}}_x\right){\text{O}}_{12}$ $\left(x\approx 0.5\right)$

The effect of Ru substitution for Ti on the ground-state properties of three-dimensional antiferromagnet (AF) ${\text{CaCu}}_3{\text{Ti}}_4{\text{O}}_{12}$ is studied by means of magnetic susceptibility and heat-capacity measurements. A small amount of Ru substituted for Ti suppresses AF long-range order and induces a new intermediate state with $T^2$-proportional heat capacity, which shows a clear contrast to a simple spin-dilution effect demonstrated by the Zn substitution for Cu. Ru substitution also creates a finite density of state at the Fermi level while keeping nominal valence of Cu ions to be $2+$, which is essential to a novel insulator-to-metal crossover driven by an isovalent substitution of ${\text{Ru}}^{4+}$ for ${\text{Ti}}^{4+}$.

Figure 1

(Color online) (a) Temperature dependence of the dc magnetic susceptibility of ${\text{CaCu}}_3\left({\text{Ti}}_{4-x}{\text{Ru}}_x\right){\text{O}}_{12}$ measured at $H=100\text{Oe}$ with ZFC and FC processes. Inset shows $\chi \left(T\right)$ at $T\le 30\text{K}$. (b) ac susceptibility for $x=1.5$ at ${10}^{-1}–{10}^3\text{Hz}$. The amplitude of the ac magnetic field is 5 Oe. (c) $\chi \left(T\right)$ for $x=1.5$ at various magnetic fields. (d) The magnetic phase diagram deduced from the susceptibility.

Figure 2

(Color online) (a) Temperature dependence of the heat capacity of ${\text{CaCu}}_3\left({\text{Ti}}_{4-x}{\text{Ru}}_x\right){\text{O}}_{12}$ ($x=0$, 0.5, 1.5, 4.0). Inset shows the same data at the low-temperature region of $T\le 20\text{K}$. (b) $C/T$ vs $T^2$ plot and (c) $C/T$ vs $T$ plot for the same set of samples.

Figure 3

(Color online) (a) $C$ vs $T^2$ plot for the $x=0.5$ and 1.5 samples. (b) $C/T$ vs $T^2$ plot for the $x=0.5$ and 1.5 samples measured by ${}^3\text{H}\text{e}$ refrigerator. Solid lines are linear fit to the lowest part of the data for both the samples.

Figure 4

(Color online) (a) $\chi \left(T\right)$ (left axis, filled symbols) and $C\left(T\right)$ (right axis, open symbols) for $x=0$ and $z=0.5$. (b) $\chi \left(T\right)$ of $x=0$, $z=0.5$, and $x=0.5$ normalized per Cu mol. Inset shows the inverse of $\chi \left(T\right)$. For the Ru-free samples, ${\chi }^{-1}\left(T\right)$’s almost look straight, while the deviation from the straight line becomes obvious for $x=0.5$, indicating the evolution of ${\chi }_p$ by Ru substitution.

Figure 5

(Color online) (a)–(d) $x$ or $z$ dependence of $T_N$ $\left(T_{\text{peak}},T_{\text{SG}}\right)$, ${\theta }_W$, $C_{\text{Curie}}$, and ${\chi }_p$. Note that $C_{\text{Curie}}$ and ${\chi }_p$ is normalized per mol Cu. (e) $x$ dependence of ${\chi }_p$ and $\gamma$. All the data are normalized by mol formula unit, thus the ${\chi }_p$ is larger by 3 times than that shown in (d).

Figure 6

(Color online) Temperature dependence of entropy of magnetoeletronic contribution after subtraction of appropriate background. For $x=0$, the $S\left(T\right)$ tends to saturate to the value of $3R\text{ln}2$ above $T=60\text{K}$, indicating that the magnetic entropy is attributed to the localized $S=1/2$ spins on ${\text{Cu}}^{2+}$ ions. For finite $x$ (finite Ru substitution), such a saturation behavior is not observed, while the $S\left(T\right)$ keeps increasing toward $T=100\text{K}$, implying that the Ru substitution gives additional degrees of freedom to the system. Inset shows the background of phonon contribution used for the estimation of entropy. Data for $x=0$ and $x=4.0$, which are used to evaluate the phonon contribution, are also shown.

Figure 7

(Color online) Heat-capacity data of $x=0.5$ sample measured at $H=0$ and 4 T.