  We calculate the critical current of a
superconductor/ferromagnetic/superconductor (S/FM/S) Josephson junction in
which the FM layer has a conical magnetic structure composed of an in-plane
rotating antiferromagnetic phase and an out-of-plane ferromagnetic component.
In view of the realistic electronic properties and magnetic structures that can
be formed when conical magnets such as Ho are grown with a polycrystalline
structure in thin-film form by methods such as direct current sputtering and
evaporation, we have modeled this situation in the dirty limit with a large
magnetic coherence length ($\xi_f$). This means that the electron mean free
path is much smaller than the normalized spiral length $\lambda/2\pi$ which in
turn is much smaller than $\xi_f$ (with $\lambda$ as the length a complete
spiral makes along the growth direction of the FM). In this physically
reasonable limit we have employed the linearized Usadel equations: we find that
the triplet correlations are short ranged and manifested in the critical
current as a rapid oscillation on the scale of $\lambda/2\pi$. These rapid
oscillations in the critical current are superimposed on a slower oscillation
which is related to the singlet correlations. Both oscillations decay on the
scale of $\xi_f$. We derive an analytical solution and also describe a
computational method for obtaining the critical current as a function of the
conical magnetic layer thickness.
