Magnetic order induced by Fe substitution of Al site in the heavy-fermion systems $\alpha$-YbAlB${}_4$ and $\beta$-YbAlB${}_4$

$\beta$-YbAlB${}_4$ is a heavy-fermion superconductor that exhibits a quantum criticality without tuning at zero field and under ambient pressure. We have succeeded in substituting Fe for Al in $\beta$-YbAlB${}_4$ as well as the polymorphous compound $\alpha$-YbAlB${}_4$, which in contrast has a heavy Fermi-liquid ground state. Full structure determination by single-crystal x-ray diffraction confirmed no change in crystal structure for both $\alpha$- and $\beta$-YbAlB${}_4$, in addition to volume contraction with Fe substitution. Our measurements of the magnetization and specific heat indicate that both $\alpha$-YbAl${}_{0.93}$Fe${}_{0.07}$B${}_4$ and $\beta$-YbAl${}_{0.94}$Fe${}_{0.06}$B${}_4$ exhibit a magnetic order, most likely of a canted antiferromagnetic type, at $7\sim 9$ K. The increase in the entropy as well as the decrease in the antiferromagnetic Weiss temperature with the Fe substitution in both systems indicates that the chemical pressure due to the Fe substitution suppresses the Kondo temperature and induces the magnetism.

Figure 1

(a) Temperature dependence of the $ab$-plane and $c$-axis susceptibility of $\alpha$-YbAlB${}_4$ (open circle), $\alpha$-YbAl${}_{0.93}$Fe${}_{0.07}$B${}_4$ (closed circle) measured under a field of 10 mT, and of $\alpha$-LuAl${}_{0.79}$Fe${}_{0.21}$B${}_4$ (open triangle) under 1 T. (b) Temperature dependence of the $ab$-plane and $c$-axis susceptibility of $\beta$-YbAlB${}_4$ (open square), $\beta$-YbAl${}_{0.97}$Fe${}_{0.03}$B${}_4$ (closed triangle) and $\beta$-YbAl${}_{0.94}$Fe${}_{0.06}$B${}_4$ (closed square) measured under a field of 10 mT, and of $\beta$-LuAl${}_{0.96}$Fe${}_{0.04}$B${}_4$ under 1 T. For all measurements, both zero-field-cooling and field-cooling sequences are employed. The inset of each panel shows the magnetic field dependence of the magnetization $M$ of $\alpha$-YbAl${}_{0.93}$Fe${}_{0.07}$B${}_4$ and $\beta$-YbAl${}_{0.94}$Fe${}_{0.06}$B${}_4$ under a field up to 7 T along the $ab$ plane at 2 K.

Figure 2

Temperature dependence of (a) the specific heat divided by temperature $C_P/T$ and (b) the entropy of $\alpha$-YbAlB${}_4$ (open circle), $\alpha$-YbAl${}_{0.93}$Fe${}_{0.07}$B${}_4$ (closed circle), $\beta$-YbAlB${}_4$ (open square), $\beta$-YbAl${}_{0.94}$Fe${}_{0.06}$B${}_4$ (closed square), and $\beta$-YbAl${}_{0.95}$Fe${}_{0.05}$B${}_4$ (closed triangle). The panel (a) inset is the temperature dependence of $C_P/T$ near the transition temperature under 0 T (closed circle for $\alpha$-YbAl${}_{0.93}$Fe${}_{0.07}$B${}_4$ and closed square for $\beta$-YbAl${}_{0.94}$Fe${}_{0.06}$B${}_4$) and 9 T (open circle for $\alpha$-YbAl${}_{0.93}$Fe${}_{0.07}$B${}_4$ and open square for $\beta$-YbAl${}_{0.94}$Fe${}_{0.06}$B${}_4$) along the $c$ axis.