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We study the temperature dependence as well as anisotropy of opticalconductivity ($\sigma_1$) in the pseudocubic single crystalPr$_{0.5}$Ca$_{1.5}$MnO$_{4}$ using spectrocopic ellipsometry. Three transitiontemperatures are observed and can be linked to charge-orbital ($T_{\rm CO/OO}$$\sim$ 320 K), two-dimensional-antiferromagnetic (2D-AFM) ($\sim$ 200 K), andthree-dimensional AFM ($T_{\rm N} \sim$ 125 K) orderings. Below $T_{\rmCO/OO}$, $\sigma_1$ shows a charge ordering peak ($\sim$0.8 eV) with asignificant blue shift as the temperature decreases. Calculations based on amodel that incorporates a static Jahn-Teller distortion and assumes theexistence of a local charge imbalance between two different sublattices supportthis assignment and explain the blue shift. This view is further supported bythe partial spectral weight analysis showing the onset of optical anisotropy at$T_{\rm CO/OO}$ in the charge-ordering region ($0.5-2.5$ eV). Interestingly, inthe charge-transfer region ($2.5-4$ eV), the spectral weight shows anomaliesaround the $T_{\rm 2D-AFM}$ that we attribute to the role of oxygen-$p$orbitals in stabilizing the CE-type magnetic ordering. Our result shows theimportance of spin, charge, and lattice degrees of freedom in this layeredmanganite.

Temperature-dependent and anisotropic optical response of layered Pr$_{0.5}$Ca$_{1.5}$MnO$_{4}$ probed by spectroscopic ellipsometry