Two-dimensional (2D) intrinsic ferromagnetic (FM) semiconductors are crucial to develop low-dimensional spintronic devices. Using density functional theory, we show that single-layer chromium trihalides (SLCTs) (CrX3, X = F, Cl, Br and I) constitute a series of stable 2D intrinsic FM semiconductors. A free-standing SLCT can be easily exfoliated from the bulk crystal, due to a low cleavage energy and a high in-plane stiffness. Electronic structure calculations using the HSE06 functional indicate that both bulk and singlelayer CrX3 are half semiconductors with indirect gaps and their valence and conduction bands are fully spin-polarized in the same spin direction. The energy gaps and absorption edges of CrBr3 and CrI3 are found to be in the visible frequency range, which implies possible opto-electronic applications. Furthermore, SLCTs are found to possess a large magnetic moment of 3 mu(B) per formula unit and a sizable magnetic anisotropy energy. The magnetic exchange constants of SLCTs are then extracted using the Heisenberg spin Hamiltonian and the microscopic origins of the various exchange interactions are analyzed. A competition between a near 90 degrees FM superexchange and a direct antiferromagnetic (AFM) exchange results in a FM nearest-neighbour exchange interaction. The next and third nearestneighbour exchange interactions are found to be FM and AFM, respectively, and this can be understood by the angle-dependent extended Cr-X-X-Cr superexchange interaction. Moreover, the Curie temperatures of SLCTs are also predicted using Monte Carlo simulations and the values can be further increased by applying a biaxial tensile strain. The unique combination of robust intrinsic ferromagnetism, half semiconductivity and large magnetic anisotropy energies renders the SLCTs as promising candidates for next-generation semiconductor spintronic applications.
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