5d过渡金属原子掺杂六方氮化铝单层的磁性及自旋轨道耦合效应:可能存在的二维长程磁有序

Electronic structures, magnetic properties and spin-orbital coupling effects of aluminum nitride monolayers doped by 5d transition metal atoms:possible two-dimensional long-range magnetic orders

采用基于密度泛函理论的第一性原理计算方法,研究了5d过渡金属原子(Hf,Ta,W,Re,Os,Ir,Pt,Au和Hg)取代六方氮化铝单层中的Al原子的几何结构、电子结构、磁性性质、铁磁态与反铁磁态能量差(EFM-EAFM)以及自旋轨道耦合效应导致的磁各向异性.研究发现Hg掺杂的体系中,5d金属原子和最邻近的N原子的键长最大,平均值为2.093?,之后依次是Au,Hf,Pt,Ta和Ir.态密度结果显示掺杂体系的禁带中出现明显的杂质能级,给出了掺杂体系的总磁矩以及自旋密度的分布.对于EFM-EAFM,Hf,Re,Pt和Au四种原子的掺杂在4×8超胞中到达最大值,分别为-187.2563,286.2320,-48.0637和-61.7889 meV.磁各向异性结果中,Re掺杂的磁各向异性最大,达到11.622 meV.结合以上结果,我们预测5d过渡金属原子掺杂六方氮化铝单层可能存在二维长程磁有序.

The magnetism of two-dimensional material is an important research topic.In particular,the long-range magnetic order of two-dimensional material is of great significance in theoretical research and practical application.According to the Mermin-Wagner theory,the isotropic Heisenberg model in a two-dimensional system cannot produce long-range magnetic orders at non-vanishing temperatures.Considering the existence of strong magnetic anisotropy,possible twodimensional long-range magnetic orders may exist in 5d atom doped two-dimensional aluminum nitride（Al N） monolayer.This research is performed by first-principles calculations based on the density functional theory.Geometries,electronic structures,magnetic properties,and magnetic anisotropy energies from spin-orbital coupling effects in Al N monolayers doped by 5d transition metal atoms（Hf,Ta,W,Re,Os,Ir,Pt,Au,and Hg） are calculated.Four kinds of supercells are used in the calculation,i.e,2×2,3×3,4×4,and 5×5,with one aluminum atom substituted by one 5d atom.Projection augmented wave method is used to describe the interaction between the valence electrons and the ions.The plane wave is used to expand the wave function of the valence electron.For an optimized geometry,the bond length between the5 d metal atom and the nearest N atom is the largest in Hg-doped supercells,which is 2.093 ？,followed by the Au,Hf,Pt,Ta,and Ir according to the order of bond length magnitude.For the densities of states（DOSs）,obvious impurity energy levels appear in the forbidden bands.For all the supercells,spin-up and spin-down DOSs of Ta and Ir doped systems are symmetric,indicating non-magnetic states.DOSs of Hf,W,Re,and Os doped systems are asymmetric,indicating magnetic states.For Pt,Au,and Hg,DOSs are symmetric in 2 × 2 supercells,but asymmetric in the 3 × 3,4 × 4,and 5 × 5 supercells.Total magnetic moments and the spin densities are also given.In 5 × 5 supercells,they are 1.00,0.00,0.39,1.99,1.17,0.00,1.00,2.00,and 1.00 for Hf,Ta,W,Re,Os,Ir,Pt,Au,and Hg,respectively.The magnetic moment is mainly concentrated in the vicinity of the 5d atoms.The energy differences between ferromagnetic and antiferromagnetic states are calculated.For Hf,Re,Pt and Au systems,the differences in 4 × 8 supercells reach the maximum values of-187.2563 meV,286.2320 meV,-48.0637 meV and-61.7889 meV,respectively.The results indicate that there is a strong interaction between the magnetic centers.Magnetic anisotropy energy originating from spin-orbital effect is calculated in the 4 × 4 supercells.For the Re system,it is the highest,reaching 11.622 meV.For W,Os,and Au,the values are larger than 1 meV,showing strong magnetic anisotropies.The magnetic anisotropy can produce a spin wave energy gap,resulting in long-range magnetic orders.Based on the results above,it is predicted that with appropriate 5d atoms and suitable doping concentration,two-dimensional long-range magnetic orders may exist in5 d transition metal atom doped Al N monolayers.