Magnetic Field Dependent Optical Studies of a Layered Antiferromagnet Pr$$Sr${}_{1\mathrm{/}2}$MnO${}_3$

Magnetic field ($H$)-dependent optical conductivity spectra $\sigma (\omega )$ and dielectric constant spectra $ϵ(\omega )$ of a layered antiferromagnet ($A$-type) Pr${}_{1\mathrm{/}2}$Sr${}_{1\mathrm{/}2}$MnO${}_3$ were presented. At 0.0 T in 4.2 K, the $\sigma (\omega )$ showed a small Drude-like peak in the far-infrared region and a broad absorption peak in the mid-infrared region. With increasing $H$, large spectral weights were transferred from high to low energy regions with increase of the Drude-like peak. We found that a polaron picture could explain most of the $H$-dependent spectral changes. By comparing with the $H$-dependent spectral weight changes and $ϵ(\omega )$ of Nd${}_{1\mathrm{/}2}$Sr${}_{1\mathrm{/}2}$MnO${}_3$, which has the $CE$-type spin ordering, we showed that a dimensional crossover from a 2-dimensional to a 3-dimensional metal occurs in Pr${}_{1\mathrm{/}2}$Sr${}_{1\mathrm{/}2}$MnO${}_3$.