I have a matrix whose eigenvalues have to be plotted. I am using two techniques but they are not the same. Please guide me on this.  

Here is first command or code used for plotting the eigenvalues(two in my case)

    a := 1;
    SM[j1_, j2_, k_] := {{0, -(j1 + j2*Exp[I*k*a])}, {-(j1 + (j2*Exp[-I*k*a])), 
        0}};
    eigenen[j1_, j2_, k_] := Module[{EV1}, EV1 = Eigenvalues[SM[j1, j2, k]];
      Plot[EV1, {k, -\[Pi]/a, \[Pi]/a}, PlotLegends -> "Expressions"]]
    Manipulate[eigenen[j1, j2, k], {j1, 0.1, 1}, {j2, 0.1, 1}]
Result is (j1>j2, you can take j1=0.3, j2=0.1)
[![enter image description here][1]][1]

Second used code

    a:=1;
    PowerExpand[FullSimplify[Eigenvalues[ {{0, -(j1 + j2*Exp[I*ka])},{-(j1 + j2*Exp[-I*ka]), 0}} ]]]
    
    Out:= {-Sqrt[j1^2 + j2^2 + 2 j1 j2 Cos[ka]], Sqrt[j1^2 + j2^2 + 2 j1 j2 Cos[ka]]}
    Manipulate[Plot[{Sqrt[(j1^2 + j2^2 + 2 j1 j2 Cos[k*a])], -Sqrt[(j1^2 + j2^2 + 2 j1 j2 Cos[k*a])]}, {k, -\[Pi]/a, \[Pi]/a}, 
      PlotLegends -> "Expressions"], {j1, 0.1, 1}, {j2, 0.1, 1}]

For this result is (j1>j2, you can take j1=0.3, j2=0.1)
[![enter image description here][2]][2]

I have no idea about the difference but I will be using first code more often as I later have to deal with large matrices(40$\times$ 40), where I can't simply write the eigenvalues. Or there is any effective or similar code where this problem can be resolved.  

My queries(to summarise):  
(i) Reason(s) for the difference in the plots.  
(ii) Anyway the second code can be resolved to give similar results as Ist one(those are expected ones), not the IInd ones.

  [1]: https://i.sstatic.net/DISVo.jpg
  [2]: https://i.sstatic.net/TEOn5.jpg