Optical probes of symmetry breaking in magnetic and superconducting BaFe$_{2}$(As$_{1-x}$P$_{x})_{2}$

The discovery of iron pnictide superconductors has opened promising new directions in the effort to fully understand the phenomenon of high-$T_{c}$, with a focus on the connections between superconductivity, magnetism, and electronic nematicity. The BaFe$_{2}$(As$_{1-x}$P$_{x})_{2}$ (P:Ba122) system in particular has received attention because isovalent substitution of As for P generates less disorder than doping on the Fe site. The phase diagram of P:Ba122 is characterized by a line of simultaneous antiferromagnetic (AF) and tetragonal-to-orthorhombic transitions, $T_{s}(x)$, that penetrates the superconducting dome at x$=$0.28, just below optimal doping ($x_{opt}=$0.30). In this work, we use spatially-resolved optical polarimetry and photomodulated reflectance to detect linear birefringence and therefore breaking of 4-fold rotational (C$_{4})$ symmetry. In underdoped ($x$\textless 0.28) samples, birefringence appears at $T $\textgreater $T_{s} $and grows continuously with decreasing $T$ . The birefringence is unidirectional in a large (300 $\mu $m x300 $\mu $m) field of view, suggesting that C$_{4}_{\, }$breaking in this range of $T$ is caused by residual strain that couples to a diverging nematic susceptibility. Birefringence maps just below $T_{s}(x)$ show the appearance of domains, indicating the onset of spontaneous symmetry breaking to an AF ground state. Surprisingly, in samples with $x$\textgreater 0.28, in which the low $T$ phase is superconducting/ tetragonal rather than AF/orthorhombic, C$_{4}_{\, }$breaking is observed as well, with an abrupt onset and domain formation at 55 K. We tentatively associate these features with a transition to an AF phase induced by residual strain, as previously proposed [H.-H. Kuo et al. Phys. Rev. B86, 134507 (2012)] to account for structure in resistivity vs. $T$. Time-resolved photomodulation allow us to follow the amplitude of the AF order with time following pulsed photoexcitation. Below $T_{c}$ the AF order at first weakens , but then strengthens in response to the photoinduced weakening of superconductivity. This complex time evolution is accounted for quantitatively by a model based on the coexistence and competition of AF and superconducting order.