Magnetism in two-dimensional (2D) van der Waals (vdW) materials has recently emerged as one of the most promising areas in condensed matter research, with many exciting emerging properties and significant potential for applications ranging from topological magnonics to low-power spintronics, quantum computing, and optical communications. In the brief time after their discovery, 2D magnets have blossomed into a rich area for investigation, where fundamental concepts in magnetism are challenged by the behavior of spins that can develop at the single layer limit. However, much effort is still needed in multiple fronts before 2D magnets can be routinely used for practical implementations. In this comprehensive review, prominent authors with expertise in complementary fields of 2D magnetism (i.e., synthesis, device engineering, magneto-optics, imaging, transport, mechanics, spin excitations, and theory and simulations) have joined together to provide a genome of current knowledge and a guideline for future developments in 2D magnetic materials research.

Intrinsic, two-dimensional (2D) ferromagnetic semiconductors are an important class of materials for spintronics applications. ${\mathrm{Cr}}_2{X}_2{\mathrm{Te}}_6(X=\text{Si}\text{and Ge})$ semiconductors show 2D Ising-like ferromagnetism, which is preserved in few-layer devices. The maximum magnetic entropy change associated with the critical properties around the ferromagnetic transition for ${\mathrm{Cr}}_2{\mathrm{Si}}_2{\mathrm{Te}}_6-\mathrm{\Delta }{S}_M^{\text{max}}\sim 5.05$ J ${\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$ is much larger than $-\mathrm{\Delta }{S}_M^{\text{max}}\sim 2.64$ J ${\mathrm{kg}}^{-1}{\mathrm{K}}^{-1}$ for ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ with an out-of-plane field change of 5 T. The rescaled $-\mathrm{\Delta }{S}_M(T,H)$ curves collapse onto a universal curve independent of temperature and field for both materials. This indicates similar critical behavior and 2D Ising magnetism, confirming the magnetocrystalline anisotropy that could preserve the long-range ferromagnetism in a few layers of ${\mathrm{Cr}}_2{X}_2{\mathrm{Te}}_6$.

Two-dimensional (2D) materials with intrinsic ferromagnetism provide unique opportunity to engineer new functionalities in nano-spintronics. One such material is CrI₃, showing long-range magnetic order in monolayer with the Curie temperature (T_c) of 45 K. Here we study detailed evolution of magnetic transition and magnetic critical properties in response to systematic reduction in crystal thickness down to 50 nm. Bulk T_c of 61 K is gradually suppressed to 57 K, however, the satellite transition at T ^* = 45 K is observed layer-independent at fixed magnetic field of 1 kOe. The origin of T ^* is proposed to be a crossover from pinning to depinning of magnetic domain walls. The reduction of thickness facilitates a field-driven metamagnetic transition around 20 kOe with out-of-plane field, in contrast to the continuous changes with in-plane field. The critical analysis around T_c elucidates the mean-field type interactions in microscale-thick CrI₃.

We present a comprehensive investigation of the anisotropic magnetic and magnetocaloric properties of quasi-two-dimensional weak itinerant ferromagnet trigonal ${\mathrm{Cr}}_5{\mathrm{Te}}_8$ single crystals. Magnetic-anisotropy-induced satellite transition $T^{*}$ is observed at low fields applied parallel to the $ab$ plane below the Curie temperature ($T_c\sim 230\mathrm{K}$). $T^{*}$ is featured by an anomalous magnetization downturn, similar to that in structurally related ${\mathrm{CrI}}_3$, which possibly stems from an in-plane antiferromagnetic alignment induced by out-of-plane ferromagnetic spins canting. Magnetocrystalline anisotropy is also reflected in magnetic entropy change $\mathrm{\Delta }{S}_M(T,H)$ and relative cooling power. Given the high Curie temperature, ${\mathrm{Cr}}_5{\mathrm{Te}}_8$ crystals are materials of interest for nanofabrication in basic science and applied technology.