  A key question in high temperature iron-based superconductivity is the
mechanism by which the paired electrons minimize their strong mutual Coulomb
repulsion. While electronically paired superconductors generally avoid the
Coulomb interaction through the formation of nodal, higher angular momentum
pairs, iron based superconductors appear to form singlet s-wave (s$^{\pm}$)
pairs. By taking the orbital degrees of freedom of the iron atoms into account,
here we argue that the s$^{\pm}$ state in these materials possesses internal
d-wave structure, in which a relative d-wave ($L=2$) motion of the pairs
entangles with the ($I=2$) internal angular momenta of the d-orbitals to form a
low spin $J=L+I=0$ singlet. We discuss how the recent observation of a nodal
gap with octahedral structure in KFe$_{2}$As$_{2}$ can be understood as a high
spin ($J=L+I=4$) configuration of the orbital and isospin angular momenta; the
observed pressure-induced phase transition into a fully gapped state can then
interpreted as a high-to-low spin phase transition of the Cooper pairs.
