Is this a half-sort?
J, 20 18 15 14 bytes

-1 thanks to Jonah.

Goes the other way around: sorts the string ('node' -> 'deno'), rotates it back ('deno' -> 'node') and checks if this equals the input. Fits better J trains. 

-:&lt;.@-:@#|./:~


Try it online!

How it works

-:&lt;.@-:@#|./:~
           /:~  sort input
  &lt;.@-:@#       length of input, halved and floored
         |.     rotate sorted input by that amount
-:              input equal to that?