Ca$_{1+\varepsilon }$Co$_{4}$B$_{4}$ and Ca$_{1+\varepsilon }$Ru$_{4}$B$_{4}$: New Borides with One-Dimensional Channel Structures

We discovered two novel borides Ca$_{1+\varepsilon }$Co$_{4}$B$_{4}$ (\textit{$\varepsilon $} $\sim $0.10) and Ca$_{1+\varepsilon }$Ru$_{4}$B$_{4}$ (\textit{$\varepsilon $} $\sim $0.18) as the first members of Gd$_{1+\varepsilon }$Fe$_{4}$B$_{4}$- and Pr$_{1+\varepsilon }$Re$_{4}$B$_{4}$-type ternary borides with a divalent metal at the rare earth sites. In these compounds, tetrahedral chains of transition metals and boron form tetragonal channel structures, which contain single atomic chains of Ca. These are composite structures of Ca sublattice and CoB/RuB sublattice, with common $a$-axis lengths and independent $c$-axis lengths. The two structural types are distinguished by configurations of the tetrahedral chains. Resistivity and magnetization measurements showed that these compounds are paramagnetic metals down to 2 K. Preliminary first-principle calculations indicated the presence of covalent bonds between transition metals and boron, and electrical conductivity originating from the $d$-bands of the transition metals.