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Two-dimensional (2D) ferromagnetic charge density wave (CDW), an exoticquantum state for exploring the intertwining effect between correlated chargeand spin orders in 2D limit, has not been discovered in the experiments yet.Here, we propose a feasible strategy to realize 2D ferromagnetic CDWs underexternal fields, which is demonstrated in monolayer VSe$_2$ usingfirst-principles calculations. Under external tensile strain, two novelferromagnetic CDWs ($\sqrt{3}$$\times$$\sqrt{3}$ and 2$\times2\sqrt{3}$ CDWs)can be generated, accompanied by distinguishable lattice reconstructions ofmagnetic V atoms. Remarkably, because the driving forces for generating thesetwo ferromagnetic CDWs are strongly spin-dependent, fundamentally differentfrom that in conventional CDWs, the $\sqrt{3}$$\times$$\sqrt{3}$ and2$\times2\sqrt{3}$ CDWs can exhibit two dramatically different half-metallicphases under a large strain range, along with either a flat band or a Diraccone around Fermi level. Our proposed strategy and material demonstration mayopen a door to generate and manipulate correlation effect between collectivecharge and spin orders via external fields.

Generating Two-dimensional Ferromagnetic Charge Density Waves via External Fields