The interplay between double exchange, super-exchange, and Lifshitz localization in doped manganites

Considering the disorder caused in manganites by the substitution of Mn by Fe or Ga, we accomplish a systematic study of doped manganites begun in previous papers. To this end, a disordered model is formulated and solved using the Variational Mean Field technique. The subtle interplay between double exchange, super-exchange, and disorder causes similar effects on the dependence of T_C on the percentage of Mn substitution in the cases considered. Yet, in La${}_{2\mathrm{/}3}$Ca${}_{1\mathrm{/}3}$Mn${}_{1-y}$Ga${}_y$O${}_3$ our results suggest a quantum critical point (QCP) for $y\approx 0.1-0.2$, associated to the localization of the electronic states of the conduction band. In the case of La${}_x$Ca${}_x$Mn${}_{1-y}$Fe${}_y$O${}_3$ (with $x=1\mathrm{/}3,3\mathrm{/}8$) no such QCP is expected.