Thermodynamic properties of mixed-valent Eu ions and nonmetallicity in Eu3Bi2S4F4 single crystals

New ${\mathrm{BiS}}_{2}$-based layered compound ${\mathrm{Eu}}_{3}{\mathrm{Bi}}_{2}{\mathrm{S}}_{4}{\mathrm{F}}_{4}$ has recently been reported to exhibit superconductivity with a transition temperature of 1.5 K using polycrystalline samples. Here we report measurements of electrical resistivity $\ensuremath{\rho}$, magnetization $M$, and specific heat $C$ of ${\mathrm{Eu}}_{3}{\mathrm{Bi}}_{2}{\mathrm{S}}_{4}{\mathrm{F}}_{4}$ single crystals. At the antiferromagnetic transition temperature of 2.17 K, $C(T)$ shows a sharp $\ensuremath{\lambda}$-type peak, suggesting the existence of strong Eu magnetic moment fluctuations due to the quasi-two-dimensional nature of the Eu-ion lattice in ${\mathrm{Eu}}_{3}{\mathrm{F}}_{4}$ block layers. The average Eu-ion valence of $+2.19$, determined from the Schottky-type $4f$-electron contribution to $C(T)$ and $M(T,H)$, indicates the self-doped electron density in ${\mathrm{BiS}}_{2}$ layers due to the Eu mixed valence to be 0.285 electrons per Bi site. It has been revealed, however, that $\ensuremath{\rho}(T)$ shows an anomalous nonmetallic behavior with $\ensuremath{\sim}1/{T}^{3}$ dependence without any sign of superconductivity, in marked contrast to a metallic behavior in the polycrystals. This behavior suggests an unconventional electron-localization mechanism working in the single crystals, possibly caused by ${\mathrm{Eu}}^{2+}/{\mathrm{Eu}}^{3+}$ distribution (or fluctuations) and/or lattice instabilities inherent to ${\mathrm{BiS}}_{2}$ layers.