Borderline magnetism in Sr$_{4}$Ru$_{3}$O$_{10}$: Impact of dilute La and Ca doping on itinerant metamagntism and ferromagnetism

The triple-layered Sr$_{4}$Ru$_{3}$O$_{10}$ features ferromagnetic behavior with Tc=105 K along the c-axis (interlayer) and a first-order metamagnetic transition below 50 K in the basal plane [1]. The coexistence of ferromagnetism and metamagnetism suggests Sr$_{4}$Ru$_{3}$O$_{10}$ be on the borderline that separates its closest neighbors: the itinerant ferromagnet SrRuO$_{3}$ and the enhanced paramagnet Sr$_{3}$Ru$_{2}$O$_{7}$. We report our results on Sr$_{4}$Ru$_{3}$O$_{10 }$with Sr slightly substituted by La and Ca ions. The La doping drastically changes the magnetic and transport properties. In particular, it effectively suppresses Tc along the c-axis, but simultaneously induces ferromagnetic behavior in the basal plane with Tc=30 K, entirely different from that of the c-axis. Associated with these changes, the metamagnetism disappears in the basal plane but appears along the c-axis. In sharp contrast, the Ca doping significantly enhances the ferromagnetism along c-axis but drastically weakens the magnetic ordering in the basal plane where an unusual T$^{3/2}$-power law for the resisitivity is developed. The vastly different responses to the La and Ca doping, despite similar ionic radii of La$^{3+}$ and Ca$^{2+}$, highlight the role of the extra electron from the La ion added to the t$_{2g}$ orbitals. [1] G. Cao, et al., Phys. Rev. B \textbf{68} 174409 (2003)