Two-dimensional Weyl nodal-line semimetal in a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>d</mml:mi><mml:mn>0</mml:mn></mml:msup></mml:math> ferromagnetic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="normal">K</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mi mathvariant="normal">N</mml:mi></mml:math> monolayer with a high Curie temperature
Lei Jin, Xiaoming Zhang, Ying Liu, Xuefang Dai, Xunan Shen, Liying Wang, Guodong Liu
Abstract
Nodal-line semimetals in two-dimensional (2D) materials have attracted intense attention recently. From fundamental physics and spintronic application points of view, high Curie temperature ferromagnetic (FM) ones with nodal lines robust against spin-orbit coupling (SOC) are extremely desirable. Here, we propose that the FM ${\mathrm{K}}_{2}\mathrm{N}$ monolayer is such a Weyl nodal-line semimetal. We show that the ${\mathrm{K}}_{2}\mathrm{N}$ monolayer is dynamically stable and has a FM ground magnetic state with out-of-plane [001] magnetization. It shows two nodal lines in the low-energy band structures. Both nodal lines are robust against SOC, under the protection of mirror symmetry. We construct an effective Hamiltonian, which can well characterize the nodal lines in the system. Remarkably, the nodal-line semimetal proposed here is distinct from the previously studied ones in that the ${\mathrm{K}}_{2}\mathrm{N}$ monolayer is a 2D ${d}^{0}$-type ferromagnet with the magnetism arising from the partially filled the $p$ orbitals of the N atom, which can bring special advantages in spintronic applications. In addition, the Curie temperature in the ${\mathrm{K}}_{2}\mathrm{N}$ monolayer is estimated to be 942 K, which is significantly higher than previous FM nodal-line materials. We also find that specific tensile strains can transform the nodal line from type-I to type-II, making its nodal-line characteristics even more interesting.