  We present the low-frequency radio spectra of 9 high-redshift quasars at $5.6
\leq z \leq 6.6$ using the Giant Metre Radio Telescope band-3, -4, and -5
observations ($\sim$300-1200 MHz), archival Low Frequency Array (LOFAR; 144
MHz), and Very Large Array (VLA; 1.4 and 3 GHz) data. Five of the quasars in
our sample have been discovered recently, representing some of the highest
redshift radio bright quasars known at low-frequencies. We model their radio
spectra to study their radio emission mechanism and age of the radio jets by
constraining the spectral turnover caused by synchrotron self-absorption (SSA)
or free-free absorption (FFA). Besides J0309+2717, a blazar at $z=6.1$, our
quasars show no sign of a spectral flattening between 144 MHz and a few GHz,
indicating there is no strong SSA or FFA absorption in the observed frequency
range. However, we find a wide range of spectral indices between $-1.6$ and
$0.05$, including the discovery of 3 potential ultra-steep spectrum quasars.
Using further archival VLBA data, we confirm that the radio SED of the blazar
J0309+2717 likely turns over at a rest-frame frequency of 0.6-2.3 GHz (90-330
MHz observed frame), with a high-frequency break indicative of radiative ageing
of the electron population in the radio lobes. Ultra-low frequency data below
50 MHz are necessary to constrain the absorption mechanism for J0309+2717 and
the turnover frequencies for the other high-$z$ quasars in our sample. A
relation between linear radio jet size and turnover frequency has been
established at low redshifts. If this relation were to hold at high redshifts,
the limits on the turnover frequency of our sample suggest the radio jet sizes
must be more extended than the typical sizes observed in other radio-bright
quasars at similar redshift. To confirm this deep radio follow-up observations
with high spatial resolution are required.
