Magnetic percolation and giant spontaneous Hall effect in ${\mathrm{La}}_{1-x}{\mathrm{Ca}}_x{\mathrm{CoO}}_3$ $(0.2\mathrm{}<~x<~0.5)$

We report an unprecedentedly large spontaneous Hall effect in ferromagnetic ${\mathrm{La}}_{1-x}{\mathrm{Ca}}_x{\mathrm{CoO}}_3$ $(0.2\mathrm{}<~x<~0.5)$ epitaxial films. The effect exceeds existing theoretical predictions for the value of the spontaneous Hall resistivity ${\rho }_{\mathrm{xy}}$ by several orders of magnitude. The Hall effect is the strongest for $x$=0.2, which is at a doping level nearest to the ferromagnetic percolation threshold in ${\mathrm{La}}_{1-x}{\mathrm{Ca}}_x{\mathrm{CoO}}_3$. We suggest that the coexistence of high- and low-spin configurations in the perovskite cobaltites, together with the magnetic percolation behavior, may be responsible for the giant Hall effect.