  The low efficiency of conventional liquefaction technologies based on the
Joule-Thomson expansion makes liquid hydrogen currently not attractive enough
for large-scale energy-related technologies that are important for the
transition to a carbon-neutral society. Magnetocaloric hydrogen liquefaction
has great potential to achieve higher efficiency and is therefore a crucial
enabler for affordable liquid hydrogen. Cost-effective magnetocaloric materials
with large magnetic entropy and adiabatic temperature changes in the
temperature range of 77 $\sim$ 20 K under commercially practicable magnetic
fields are the foundation for the success of magnetocaloric hydrogen
liquefaction. Heavy rare-earth-based magnetocaloric intermetallic compounds
generally show excellent magnetocaloric performances, but the heavy rare-earth
elements (Gd, Tb, Dy, Ho, Er, and Tm) are highly critical in resources. Yttrium
and light rare-earth elements (La, Ce, Pr, and Nd) are relatively abundant, but
their alloys generally show less excellent magnetocaloric properties. A dilemma
appears: higher performance or lower criticality? In this review, we study how
cryogenic temperature influences magnetocaloric performance by first reviewing
heavy rare-earth-based intermetallic compounds. Next, we look at light
rare-earth-based, "mixed" rare-earth-based, and Gd-based intermetallic
compounds with the nature of the phase transition order taken into
consideration, and summarize ways to resolve the dilemma.
