  We use nuclear magnetic resonance (NMR), high-resolution x-ray and neutron
scattering to study structural and magnetic phase transitions in
phosphorus-doped BaFe$_2$(As$_{1-x}$P$_x$)$_2$. Previous transport, NMR,
specific heat, and magnetic penetration depth measurements have provided
compelling evidence for the presence of a quantum critical point (QCP) near
optimal superconductivity at $x=0.3$. However, we show that the
tetragonal-to-orthorhombic structural ($T_s$) and paramagnetic to
antiferromagnetic (AF, $T_N$) transitions in BaFe$_2$(As$_{1-x}$P$_x$)$_2$ are
always coupled and approach to $T_N\approx T_s \ge T_c$ ($\approx 29$ K) for
$x=0.29$ before vanishing abruptly for $x\ge 0.3$. These results suggest that
AF order in BaFe$_2$(As$_{1-x}$P$_x$)$_2$ disappears in a weakly first order
fashion near optimal superconductivity, much like the electron-doped iron
pnictides with an avoided QCP.
