Emergence of Orbital Nematicity in the Tetragonal Phase of BaFe$_2$(As$_{1-x}$P$_x$)$_2$

We report on $^{75}$As-NMR measurements in single crystalline BaFe$_{2}$(As$_{0.96}$P$_{0.04}$)$_{2}$ for magnetic fields parallel to the orthorhombic $[110]_{\rm o}$ and $[100]_{\rm o}$ directions above the structural transition temperature $T_{\rm S}\simeq121$ K. A large difference in the linewidth between the two field directions reveals in-plane anisotropy of the electric field gradient, even in the tetragonal phase. This provides microscopic evidence of population imbalance between As-$4p_{x}$ and $4p_{y}$ orbitals, which reaches $|n_x-n_y|/|n_x+n_y| \sim 15$\% at $T\rightarrow T_{\rm S}$ and is a natural consequence of the orbital ordering of Fe-3$d_{xz}$ and $d_{yz}$ electrons. Surprisingly, this orbital polarization is found to be already static near room temperature, suggesting that it arises from the pinning of anisotropic orbital fluctuations by disorder. The effect is found to be stronger below $\sim 160$ K, which coincides with the appearance of nematicity in previous torque and photoemission measurements. These results impose strong constraints on microscopic models of the nematic state.