  We are witnessing a great transition towards a society powered by renewable
energies to meet the ever-stringent climate target. Hydrogen, as an energy
carrier, will play a key role in building a climate-neutral society. Although
liquid hydrogen is essential for hydrogen storage and transportation,
liquefying hydrogen is costly with the conventional methods based on
Joule-Thomas effect. As an emerging technology which is potentially more
efficient, magnetocaloric hydrogen liquefaction is a "game-changer". In this
work, we have investigated the rare-earth-based Laves phases ${\rm R}Al_2$ and
${\rm R}Ni_2$ for magnetocaloric hydrogen liquefaction. We have noticed an
unaddressed feature that the magnetocaloric effect of second-order
magnetocaloric materials can become "giant" near the hydrogen boiling point.
This feature indicates strong correlations, down to the boiling point of
hydrogen, among the three important quantities of the magnetocaloric effect:
the maximum magnetic entropy change $\Delta S_{m}^{max}$, the maximum adiabatic
temperature change $\Delta T_{ad}^{max}$, and the Curie temperature $T_C$. Via
a comprehensive literature review, we interpret the correlations for a
rare-earth intermetallic series as two trends: (1) $\Delta S_{m}^{max}$
increases with decreasing $T_C$; (2) $\Delta T_{ad}^{max}$ decreases near room
temperature with decreasing $T_C$ but increases at cryogenic temperatures.
Moreover, we have developed a mean-field approach to describe these two trends
theoretically. The dependence of $\Delta S_{m}^{max}$ and $\Delta T_{ad}^{max}$
on $T_C$ revealed in this work helps us quickly anticipate the magnetocaloric
performance of rare-earth-based compounds, guiding material design and
accelerating the discoveries of magnetocaloric materials for hydrogen
liquefaction.
