Study of the doubly Cabibbo-suppressed decay ${\mathit{D}}^{+}$→φ${\mathit{K}}^{+}$ and the singly Cabibbo-suppressed decay ${\mathit{D}}_{\mathit{s}}^{+}$→φ${\mathit{K}}^{+}$

We have searched for the doubly Cabibbo-suppressed decay ${\mathit{D}}^{\pm }$→φ ${\mathit{K}}^{\pm }$ and the singly Cabibbo-suppressed decay ${\mathit{D}}_{\mathit{s}}^{\pm }$→φ ${\mathit{K}}^{\pm }$ in data from the Fermilab photoproduction experiment E691. The ${\mathit{D}}^{\pm }$ decay mode is of particular interest because it cannot result from simple spectator decay. We observe a ${\mathit{D}}^{\pm }$ signal corresponding to a branching ratio of B(${\mathit{D}}^{\pm }$→φ${\mathit{K}}^{\pm }$)=(3.$3_{\mathrm{-}1.5}^{+1.8\mathrm{}}$±0.8)×${10}^{\mathrm{-}4}$. In the ${\mathit{D}}_{\mathit{s}}^{\pm }$ mode we measure an upper limit B(${\mathit{D}}_{\mathit{s}}^{\pm }$→φ${\mathit{K}}^{\pm }$)<0.2%.