Perhaps I have misunderstood some part of your attachement.
If I replace your NDSolve and the plots that follow it with this
f = First[f/.NDSolve[{f''[\[Xi]]-1/f[\[Xi]]^3+1/eo f[\[Xi]] phir[\[Xi]] 10^7==0, f[0]==1, f'[0]==0}, f,{\[Xi],0,1}]];
Plo], {\[Xi], 0, 1},
AxesOrigin->{0,0}, PlotStyle->{Thickness[0.006]}, AxesLabel->{\[Xi]}, PlotRange->All]
then it seems to find the desired function f and it then uses that f to evaluate your next expression.
I am concerned that in your attachment you seem to want that next expression to equal zero, but from the second plot that does not seem possible.
If I have made some mistake and you can explain what that was then I will see if I can correct it.