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The four decay modes $D^{0}\to\phi\pi^{0}$, $D^{0}\to\phi\eta$,$D^{+}\to\phi\pi^{+}$, and $D^{+}\to\phi K^{+}$ are studied by using a datasample taken at the centre-of-mass energy $\sqrt{s} = 3.773$~GeV~with theBESIII detector, corresponding to an integrated luminosity of 2.93 fb$^{-1}$.The branching fractions of the first three decay modes are measured to be${\cal B}(D^{0}\to\phi\pi^{0})=(1.168\pm0.028\pm0.028)\times10^{-3}$, ${\calB}(D^{0}\to\phi\eta)=(1.81\pm0.46\pm0.06)\times10^{-4}$, and ${\calB}(D^{+}\to\phi\pi^{+})=(5.70\pm0.05\pm0.13)\times10^{-3}$, respectively, wherethe first uncertainties are statistical and the second are systematic. Nosignificant signal is observed of the decay $D^+\to\phi{K^+}$ and the upperlimit of its branching fraction is set for the first time, to be$2.1\times10^{-5}$ at the $90\%$ confidence level. The ratio of ${\calB}(D^0\to\phi\pi^0)$ to $\cal B(D^+\to\phi\pi^+)$ is calculated to be$(20.49\pm0.50\pm0.45)\%$, which is consistent with the theoretical predictionbased on isospin symmetry between these two decay modes.

Measurement of branching fractions for $D$ meson decaying into $\phi$ meson and a pseudoscalar meson