  We report a comprehensive investigation of the structural, magnetic,
transport and thermodynamic properties of a single crystal PrAlSi, in
comparison to its nonmagnetic analogue LaAlSi. PrAlSi exhibits a ferromagnetic
transition at $T_C$ = 17.8 K which, however, is followed by two weak phase
transitions at lower temperatures. Based on the combined dc and ac magnetic
susceptibility measurements, we propose the two reentrant magnetic phases below
$T_C$ to be spin glasses or ferromagnetic cluster glasses. When the magnetic
glassy states are suppressed by small field, several remarkable features
appear. These include a linear, nonsaturating magnetoresistance as a function
of field that is reminiscent of a topological or charge-compensated semimetal,
and a large anomalous Hall conductivity amounting to $\sim$2000 $\Omega
^{-1}$cm$^{-1}$. Specific-heat measurements indicate a non-Kramers doublet
ground state and a relatively low crystal electric field splitting of the
Pr$^{3+}$ multiplets of less than 100 K. Shubnikov-de Hass oscillations are
absent in LaAlSi, whereas they are clearly observed below about 25 K in PrAlSi,
with an unusual temperature dependence of the dominating oscillation frequency
$F$. It increases from $F$ = 18 T at 25 K to $F$ = 33 T at 2 K, hinting at an
emerging Fermi pocket upon cooling into the ordered phase. These results
suggest that PrAlSi is a new system where a small Fermi pocket of likely
relativistic fermions is strongly coupled to magnetism. Whether hybridization
between $f$ and conduction band is also involved remains an intriguing open
problem.
