  Two-dimensional magnets could potentially revolutionize information
technology, but their potential application to cooling technology and
magnetocaloric effect (MCE) in a material down to the monolayer limit remain
unexplored. Herein, we reveal through multiscale calculations the existence of
giant MCE and its strain tunability in monolayer magnets such as CrX$_3$ (X=F,
Cl, Br, I), CrAX (A=O, S, Se; X=F, Cl, Br, I), and Fe$_3$GeTe$_2$. The maximum
adiabatic temperature change ($\Delta T_\text{ad}^\text{max}$), maximum
isothermal magnetic entropy change, and specific cooling power in monolayer
CrF$_3$ are found as high as 11 K, 35 $\mu$Jm$^{-2}$K$^{-1}$, and 3.5
nWcm$^{-2}$ under a magnetic field of 5 T, respectively. A 2% biaxial and 5%
$a$-axis uniaxial compressive strain can remarkably increase $\Delta
T_\text{ad}^\text{max}$ of CrCl$_3$ and CrOF by 230% and 37% (up to 15.3 and
6.0 K), respectively. It is found that large net magnetic moment per unit area
favors improved MCE. These findings advocate the giant-MCE monolayer magnets,
opening new opportunities for magnetic cooling at nanoscale.
