Two-dimensional (2D) intrinsic ferromagnetic (FM) semiconductors are crucialto develop low-dimensional spintronic devices. Using density functional theory,we show that single-layer chromium trihalides (SLCTs) (CrX$_3$,X=F, Cl, Br andI) constitute a series of stable 2D intrinsic FM semiconductors. Afree-standing SLCT can be easily exfoliated from the bulk crystal, due to a lowcleavage energy and a high in-plane stiffness. Electronic structurecalculations using the HSE06 functional indicate that both bulk andsingle-layer CrX$_3$ are half semiconductors with indirect gaps and theirvalence bands and conduction bands are fully spin-polarized in the same spindirection. The energy gaps and absorption edges of CrBr$_3$ and CrI$_3$ arefound to be in the visible frequency range, which implies possibleopt-electronic applications. Furthermore, SLCTs are found to possess a largemagnetic moment of 3$\mu_B$ per formula unit and a sizable magnetic anisotropyenergy. The magnetic exchange constants of SLCTs are then extracted using theHeisenberg spin Hamiltonian and the microscopic origins of the various exchangeinteractions are analyzed. A competition between a near 90$^\circ$ FMsuperexchange and a direct antiferromagnetic (AFM) exchange results in a FMnearest-neighbour exchange interaction. The next and third nearest-neighbourexchange interactions are found to be FM and AFM respectively and this can beunderstood by the angle-dependent extended Cr-X-X-Cr superexchange interaction.Moreover, the Curie temperatures of SLCTs are also predicted using Monte Carlosimulations and the values can further increase by applying a biaxial tensilestrain. The unique combination of robust intrinsic ferromagnetism, halfsemiconductivity and large magnetic anisotropy energies renders the SLCTs aspromising candidates for next-generation semiconductor spintronic applications.
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