Multiple magnetic phase transitions in single-crystal $({\mathrm{Sr}}_{1-x}{\mathrm{Ca}}_x{)}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ for $0<~x<~1.0$

${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ is a highly correlated narrow $d$-band metallic ferromagnet with a Curie temperature $T_C=105\mathrm{}\mathrm{K}.$ ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7,$ which is isomorphic to ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7,$ becomes antiferromagnetic and remains metallic below $T_N=56\mathrm{}\mathrm{K}$ and exhibits a lower-temperature transition at $T_M=48\mathrm{}\mathrm{K}$ into a nonmetallic antiferromagnetic phase. Both systems have the ${\mathrm{Sr}}_3{\mathrm{Ti}}_2{\mathrm{O}}_7$ staggered double-layered body-centered-tetragonal structure, ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ being less ideal because of the smaller Ca ionic radius. Both systems demonstrate a very high degree of anisotropy of the magnetic and electrical properties. Magnetization and magnetic susceptibility studies for $2<T<\mathrm{}400\mathrm{}\mathrm{K}$ and $0<H<\mathrm{}7\mathrm{}\mathrm{T},$ electrical resistivity for $1<T<\mathrm{}300\mathrm{}\mathrm{K},$ and heat capacity measurements for $1<T<\mathrm{}20\mathrm{}\mathrm{K}$ are presented on as-grown single crystals of $({\mathrm{Sr}}_{1-x}{\mathrm{Ca}}_x{)}_3{\mathrm{Ru}}_2{\mathrm{O}}_7,$ spanning the full concentration range $0<~x<~\mathrm{1.0.}$ The results show multiple magnetic phases, from ferromagnetism for $x<\mathrm{}0.4\mathrm{}$ to antiferromagnetism for $x>\mathrm{}\mathrm{0.4.}\mathrm{}$ The transition from ferromagnetism to antiferromagnetism precedes a crossover from metallic conductivity at low temperatures to nonmetallic conductivity for $x>\mathrm{}0.7\mathrm{}$ and $T<~40\mathrm{K}.$ In all cases the resistivity at room temperature is large $(\rho \approx 0.02–0.04\Omega \mathrm{cm}),$ but with a metallic temperature dependence $(d\rho /dT>\mathrm{}0),$ indicating the materials are probably “bad” metals. Resistivity anomalies at the transition temperatures suggest the opening of a gap at the Fermi surface for the metallic antiferromagnetic phase $\mathrm{}(0.4<x<\mathrm{}0.7\mathrm{}).$ The gap appears to evolve smoothly with increasing Ca content and may be relevant to a Mott-like metal to nonmetal transition for Ca-rich samples, $x<~\mathrm{1.0.}$ Magnetic anisotropy measurements show that the easy axis ($c$ axis for $x=0\mathrm{}$) rotates into the $\mathrm{ab}$ plane with increasing Ca concentration and a lower-temperature canted magnetic structure is suppressed as the system becomes antiferromagnetic. The electronic component of the heat capacity, which is large for the end members of the $({\mathrm{Sr}}_{1-x}{\mathrm{Ca}}_x{)}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ series, $\gamma =77\mathrm{}{\mathrm{m}\mathrm{J}/\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{}\mathrm{K}}^2$ for $x=0\mathrm{}$ and $\gamma =35\mathrm{}{\mathrm{m}\mathrm{J}/\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{}\mathrm{K}}^2$ for $x=1.0,$ is even larger for most of the mixed systems, $x\ne 0,1.0.$ The data are discussed relative to the physics of bad metals and to the highly correlated nature of the Ru-dominated narrow $4d$ bands. The results are compared with a recent analogous study of metallic ferromagnetism in single-crystal ${\mathrm{Sr}}_{1-x}{\mathrm{Ca}}_x{\mathrm{RuO}}_3.$ Included in this paper is a discussion of the strikingly strong variation between the magnetic and electrical properties of single-crystal materials compared to similar data from isostructural polycrystalline materials.