sufficiently large so that this is the case. In the context of strontium ruthenate, our results apply for the field along the $c$-axis (this is also true for the cobaltates when we are discussing spin-orbit coupling in hexagonal systems). For organic and cobaltate superconductors, our results apply for the field along any two-fold or higher symmetry axis of symmetry.

For non-chiral triplet order parameter symmetry, which is expected of the cobaltate Na$_x$CoO$_2 \cdot y$H$_2$O [@Nature.Physics.1.91] and organic superconductors [@organic], the spin pairing gap matrix takes the form $$\hat{\Delta}({\bf k})=f({\bf k})\left[
 \begin{array}{cc}
  \Delta_{\uparrow\uparrow}& 0 \\
  0 & \Delta_{\downarrow\downarrow}
  \end{array}
\right] \label{EQ:OP-nonchiral}$$ where the function $f({\bf k})$ depends on the specific odd angular momentum channel. The key simplifying feature is the the orbital dependence is described by a one-dimensional representation encoded by $f({\bf k})$. There has been suggestions that the cobaltate Na$_x$CoO$_2 \cdot y$H$_2$O has a spin-triplet pairing through $f$-wave channel [@Nature.Physics.1.91], although data from the Knight shift experiments remain controversial [@PhysRevB.73.180503; @JPSJ.77.073702]. In this case a common choice is $f({\bf k}) = k_x(k_x^2-3k_y^2)$. However, the precise form of $f({\bf k})$ is not needed for our results. For the organic superconductor (TMTSF)$_2$ClO$_4$, there is a strong case that the system becomes a 