第一性原理研究half-Heusler合金VLiBi和CrLiBi的半金属铁磁性

构建只含有一种过渡金属元素的half-Heusler合金VLiBi和CrLiBi.采用第一性原理的全势能线性缀加平面波方法计算half-Heusler合金VLiBi和CrLiBi的电子结构.计算结果表明，VLiBi和CrLiBi是半金属性铁磁体，它们的半金属隙分别是0.25 eV和0.46 eV，晶胞总磁矩分别为3.00 μ_B和4.00 μ_B.磁性计算结果显示，晶胞总磁矩主要来源于V和Cr的原子磁矩，Li和Bi的原子磁矩较弱，而且Bi的原子磁矩为负值.利用平均场近似方法计算合金的居里温度T_C，VLiBi和CrLiBi的居里温度（T_C）的估算值分别为1401 K和1551 K.使晶格常数在±10%的范围内变化，分别计算VLiBi和CrLiBi的电子结构.计算研究表明，晶格常数在-5.6%–10%和-6.9%–10%的范围内变化时VLiBi和CrLiBi仍具有半金属性，并且晶胞总磁矩稳定于3.00 μ_B和4.00 μ_B.采用局域密度近似（LDA）+U（电子库仑相互作用项）的方法计算VLiBi和CrLiBi的电子结构，当U的取值增大到5 eV时VLiBi和CrLiBi仍保持半金属性.此外，采用考虑自旋-轨道耦合（spin-orbit coupling，SOC）效应的广义梯度近似（GGA）+SOC方法计算VLiBi和CrLiBi的电子结构，计算结果显示有微弱的自旋向下能带穿过费米能级，此时VLiBi和CrLiBi在费米面处的自旋极化率分别为98.8%和94.3%，它们的晶胞总磁矩分别为3.03 μ_B和4.04 μ_B.VLiBi的半金属性几乎不受SOC效应的影响，而CrLiBi在费米面处仍有较高的自旋极化率.

First-principles study on half-metallic ferromagnetism of half-Heusler alloys VLiBi and CrLiBi

The hypothetical half-Heusler alloys VLiBi and CrLiBi containing only one transition metal element are constructed. The electronic structure and magnetic properties of VLiBi and CrLiBi are investigated by using the first-principles full-potential linearized augmented plane wave method based on density functional theory. The spin-polarized calculations of electronic structure for the half-Heusler alloys VLiBi and CrLiBi are performed. The calculation results reveal that VLiBi and CrLiBi are half-metallic ferromagnets with the half-metallic gaps of 0.25 eV and 0.46 eV and the total magnetic moments of 3.00 μ_B and 4.00 μ_B per formula unit, respectively. The total magnetic moments mainly originate from the magnetic moment on V or Cr atom. Li and Bi have small atomic magnetic moments, where the atomic magnetic moment of Bi is negative. The mean field approximation method is used to estimate the Curie temperatures of the alloys. The calculated results show that the values of Curie temperature for VLiBi and CrLiBi are 1401 K and 1551 K, respectively. To study the robustness of the half-metallicity with the change of lattice constant, the electronic structures of VLiBi and CrLiBi are also calculated under their lattice constant changing from-10% to +10% relative to the equilibrium lattice constant. It is found that the VLiBi and CrLiBi can maintain their half-metallicity and retain their total magnetic moments of 3.00 μ_B and 4.00 μ_B per formula unit even when their lattice constants change from-5.6% to 10.0% and from-6.9% to 10.0%, respectively. To discuss the effect of strongly correlated interaction on the half-metallicity, the electronic structure of VLiBi and CrLiBi are calculated by the LDA+U method with U for V-3d and Cr-3d orbital. The calculation results indicate that VLiBi and CrLiBi can keep their half-metallicity and integer total magnetic moments of 3.00 μ_B and 4.00 μ_B when the value of U reaches to 5 eV. Also, the electronic structure of VLiBi and CrLiBi are recalculated by the GGA+SOC method. The calculated results show that 1) there are some spin-down bands crossing the Fermi level, 2) the spin polarizations of VLiBi and CrLiBi at the Fermi level are 98.8% and 94.3%, respectively, and 3) total magnetic moments of VLiBi and CrLiBi are 3.03 μ_B and 4.04 μ_B per formula unit, respectively. The spin-orbit coupling has a weak effect on the half-metallic of half-Heusler alloy VLiBi and the spin polarization is still high for the half-Heusler alloy CrLiBi. The half-Heusler alloys VLiBi and CrLiBi may be useful in spintronics and other applications.