We use nuclear magnetic resonance (NMR), high-resolution x-ray and neutron scattering to study structural and magnetic phase transitions in phosphorus-doped BaFe(AsP). 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 . However, we show that the tetragonal-to-orthorhombic structural () and paramagnetic to antiferromagnetic (AF, ) transitions in BaFe(AsP) are always coupled and approach to ( K) for before vanishing abruptly for . These results suggest that AF order in BaFe(AsP) disappears in a weakly first order fashion near optimal superconductivity, much like the electron-doped iron pnictides with an avoided QCP.

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