In case of mixed valent perovskite manganites some Mn ions are in +3 oxidation states and some are in +4 oxidation state.What is the fraction of Mn3+ and Mn4+ ions for which double-exchange interactions are maximum?
Double exchange takes place between two sites if the hole exist there to overcome the correlation.
However, considering the equal amount of Mn3+ and Mn4+ there is high probability for double exchange to occur.
But precisely at this concentration the temperature of the system should ne high enough to prevent the charge localization which eventually makes the charge ordering case and double exchange ger fail.
The mixed-valence manganites (R1-xAxMnO3) displays double exchange ferromagnetic interaction showing long range ferromagnetic ordering.The mixed-valence manganites having maximum Curie-temperature show maximum double exchange interaction. The mixed-valence manganites having compositions in the range 0.3 ≤ x ≤ 0.5 often show maximum double exchange interaction. You can follow following article:
Article Anomalous magnetic properties and magnetic phase diagram of ...
Besides the ratio of Mn4+/Mn3+ ions,the double-exchange interactions are dominated by some other facts,including Crystal field effect, J-T distortion,A-site ionic radius,Lattice defects,etc. So it is impossible to give a precise ratio.