Doping effects on the hybridization gap and antiferromagnetic order in the Kondo semiconductor $\mathrm{CeO}{\mathrm{s}}_2\mathrm{A}{\mathrm{l}}_{10}$ studied by break-junction experiments

The Kondo semiconductors $\mathrm{Ce}{T}_2\mathrm{A}{\mathrm{l}}_{10}$ ($T=\mathrm{Ru}$ and Os) exhibit antiferromagnetic (AFM) orders at unexpectedly high temperatures $T_{\mathrm{N}}=27.0$ and 28.5 K, respectively, whose mechanism remains in debate. We report the break-junction experiments on $4f/5d$-hole and $5d$-electron doped $\mathrm{CeO}{\mathrm{s}}_2\mathrm{A}{\mathrm{l}}_{10}$ as well as nondoped $\mathrm{CeR}{\mathrm{u}}_2\mathrm{A}{\mathrm{l}}_{10}$. The differential conductance spectra $dI/dV$ for $T=\mathrm{Os}$ and Ru show three gap structures; two hybridization gaps $V_1, V_2$ and an AFM gap $V_{\mathrm{AF}}$, whose magnitudes for $T=\mathrm{Os}$ are $15-50\%$ larger than for $T=\mathrm{Ru}$. Doping of $4f/5d$ holes and $5d$ electrons in $\mathrm{CeO}{\mathrm{s}}_2\mathrm{A}{\mathrm{l}}_{10}$ changes the $dI/dV$ spectrum in very different ways. Nevertheless, in all cases, the suppression of $V_1$ is well correlated with those of $V_{\mathrm{AF}}$ and $T_{\mathrm{N}}$. Furthermore, the zero-bias conductance decreases on cooling below $T^{*}$ ($>T_{\mathrm{N}}$) only in the doping region where $V_1$ and $V_{\mathrm{AF}}$ coexist. This fact indicates that the unusual AFM order is preceded by the decrease in the density of states in the presence of $V_1$.

Figure 1

Temperature dependences of the electrical resistivity $\rho \left(T\right)$ normalized by the value at 300 K for single crystals along the orthorhombic $b$ axis of $\mathrm{C}{\mathrm{e}}_{1-z}\mathrm{L}{\mathrm{a}}_z\mathrm{O}{\mathrm{s}}_2\mathrm{A}{\mathrm{l}}_{10}$ ($z\le 0.35$) and $\mathrm{Ce}{\left(\mathrm{O}{\mathrm{s}}_{1-y}\mathrm{R}{\mathrm{e}}_y\right)}_2\mathrm{A}{\mathrm{l}}_{10}$ ($2y\le 0.2$).

Figure 2

Temperature dependences of the magnetic specific heat divided by temperature $C_m/T$ for $\mathrm{C}{\mathrm{e}}_{1-z}\mathrm{L}{\mathrm{a}}_z\mathrm{O}{\mathrm{s}}_2\mathrm{A}{\mathrm{l}}_{10}$ ($z\le 0.35$). The inset shows variations of $T_{\mathrm{N}}$ and the jump in $C_m/T$ at $T_{\mathrm{N}}$, where $T_{\mathrm{N}}$ is determined as the midpoint of the jump in $C/T$.

Figure 3

(a) Differential conductance spectra $dI/dV$ versus bias voltage $V$ at 4.4 K for $\mathrm{CeO}{\mathrm{s}}_2\mathrm{A}{\mathrm{l}}_{10}$ break junctions with various resistances $R_{\mathrm{J}}$, which is estimated as the inverse of the zero-bias conductance. (b) Peak-to-peak gap widths $V_1, V_2$, and $V_{\mathrm{AF}}$ for $\mathrm{CeO}{\mathrm{s}}_2\mathrm{A}{\mathrm{l}}_{10}$ break junctions as a function of the junction resistance $R_{\mathrm{J}}$ in a wide range of $9-800\mathrm{\Omega }$.

Figure 4

(a) Temperature variation of the $dI/dV$ spectra for $\mathrm{CeR}{\mathrm{u}}_2\mathrm{A}{\mathrm{l}}_{10}$ with $T_{\mathrm{N}}=27.0\mathrm{K}$. The values of $dI/dV$ are normalized by those at the bias voltage $V=-400\mathrm{mV}$. The gap widths $V_1, V_{\mathrm{AF}}$, and $V_2$ denote the widths between the shoulders, the peaks, and inner peaks of the spectra, respectively, which are indicated by the arrows. (b) Temperature dependences of bulk resistivity $\rho \left(T\right)$ and junction resistance $R_{\mathrm{J}}\left(T\right)$ normalized by the values at 4.4 K. (c) Normalized $dI/dV$ spectra for $\mathrm{Ce}{T}_2\mathrm{A}{\mathrm{l}}_{10}$ ($T=\mathrm{Fe}$, Ru, and Os) at 4.4 K.

Figure 5

Temperature dependences of (a) the gap widths and (b) the square root of the normalized zero-bias conductance ${\left[\mathrm{NZBC}\right]}^{1/2}$ for $\mathrm{Ce}{T}_2\mathrm{A}{\mathrm{l}}_{10}$ ($T=\mathrm{Fe}$, Ru, and Os).

Figure 6

Temperature variations of the $dI/dV$ spectra for $4f$-hole doped system $\mathrm{C}{\mathrm{e}}_{1-z}\mathrm{L}{\mathrm{a}}_z\mathrm{O}{\mathrm{s}}_2\mathrm{A}{\mathrm{l}}_{10}$ for $z=0$, 0.05, 0.2, and 0.35 with $T_{\mathrm{N}}=28.5$, 25.5, 11.6, and $<2.0\mathrm{K}$, respectively. The gap widths $V_1, V_{\mathrm{AF}}$, and $V_2$ are shown by horizontal arrows. Curves are vertically shifted for clarity.

Figure 7

Temperature variations of the $dI/dV$ spectra for $\mathrm{CeO}{\mathrm{s}}_2\mathrm{A}{\mathrm{l}}_{10}$ with $T_{\mathrm{N}}=28.5\mathrm{K}$ and for $5d$-hole doped system $\mathrm{Ce}{\left(\mathrm{O}{\mathrm{s}}_{1-y}\mathrm{R}{\mathrm{e}}_y\right)}_2\mathrm{A}{\mathrm{l}}_{10}$ for $2y=0.04$ and 0.2 with $T_{\mathrm{N}}=23.0, <2.0\mathrm{K}$, and $5d$-electron doped system $\mathrm{Ce}{\left(\mathrm{O}{\mathrm{s}}_{1-x}\mathrm{I}{\mathrm{r}}_x\right)}_2\mathrm{A}{\mathrm{l}}_{10}$ for $2x=0.08$ and 0.3 with $T_{\mathrm{N}}=26.5$ and 7.0 K, respectively. The horizontal arrows mark the gap widths $V_1$ and $V_{\mathrm{AF}}$, respectively. Curves are offset vertically for clarity.

Figure 8

Temperature dependences of $V_1, V_{\mathrm{AF}}$, and ${\left[\mathrm{NZBC}\right]}^{1/2}$ for the doped samples of $\mathrm{C}{\mathrm{e}}_{1-z}\mathrm{L}{\mathrm{a}}_z\mathrm{O}{\mathrm{s}}_2\mathrm{A}{\mathrm{l}}_{10}, \mathrm{Ce}{\left(\mathrm{O}{\mathrm{s}}_{1-y}\mathrm{R}{\mathrm{e}}_y\right)}_2\mathrm{A}{\mathrm{l}}_{10}$, and $\mathrm{Ce}{\left(\mathrm{O}{\mathrm{s}}_{1-x}\mathrm{I}{\mathrm{r}}_x\right)}_2\mathrm{A}{\mathrm{l}}_{10}$, where ${\left[\mathrm{NZBC}\right]}^{1/2}$ is the normalized square root of zero-bias conductance $dI/dV$ ($V=0$).

Figure 9

Variations of (a) gap widths $V_1$ and $V_{\mathrm{AF}}$, (b) $T^{*}$ and $T_{\mathrm{N}}$, and (c) ${\left[\mathrm{NZBC}\right]}^{1/2}$ at 4.4 K as functions of $z, 2y$, and $2x$ in $\mathrm{C}{\mathrm{e}}_{1-z}\mathrm{L}{\mathrm{a}}_z\mathrm{O}{\mathrm{s}}_2\mathrm{A}{\mathrm{l}}_{10}, \mathrm{Ce}{\left(\mathrm{O}{\mathrm{s}}_{1-y}\mathrm{R}{\mathrm{e}}_y\right)}_2\mathrm{A}{\mathrm{l}}_{10}$, and $\mathrm{Ce}{\left(\mathrm{O}{\mathrm{s}}_{1-x}\mathrm{I}{\mathrm{r}}_x\right)}_2\mathrm{A}{\mathrm{l}}_{10}$, respectively. The NZBC is the normalized zero-bias conductance, $T^{*}$ is the onset temperature where ${\left[\mathrm{NZBC}\right]}^{1/2}$ decreases on cooling, and $T_{\mathrm{N}}$ is the Néel temperature.