The radio spectral turnover of radio-loud quasars at $z>5$
We present Karl G. Jansky Very Large Array (VLA) S- (2--4 GHz), C- (4--8 GHz), and X-band (8--12 GHz) continuum observations toward seven radio-loud quasars at $z>5$. This sample has previously been found to exhibit spectral peaks at observed-frame frequencies above $\sim$1 GHz. We also present upgraded Giant Metrewave Radio Telescope (uGMRT) band-2 (200 MHz), band-3 (400 MHz), and band-4 (650 MHz) radio continuum observations toward eight radio-loud quasars at $z>5$, selected from our previous GMRT survey, in order to sample their low-frequency synchrotron emission. Combined with archival radio continuum observations, all ten targets show evidence for spectral turnover. The turnover frequencies are $\sim$1--50 GHz in the rest frame, making these targets gigahertz-peaked-spectrum (GPS) or high-frequency-peaker (HFP) candidates. For the nine well-constrained targets with observations on both sides of the spectral turnover, we fit the entire radio spectrum with absorption models associated with synchrotron self-absorption and free-free absorption (FFA). Our results show that FFA in an external inhomogeneous medium can accurately describe the observed spectra for all nine targets, which may indicate an FFA origin for the radio spectral turnover in our sample. As for the complex spectrum of J114657.79+403708.6 at $z=5.00$ with two spectral peaks, it may be caused by multiple components (i.e., core-jet) and FFA by the high-density medium in the nuclear region. However, we cannot rule out the spectral turnover origin of variability. Based on our radio spectral modeling, we calculate the radio loudness $R_{2500\rm\, Å}$ for our sample, which ranges from 12$^{+1}_{-1}$ to 674$^{+61}_{-51}$.