CrN中原子位移的第一性原理计算研究

王倩倩; 赵振杰; 李欣; 谢文辉

doi:10.3969/j.issn.1000-5641.201922002

CrN中原子位移的第一性原理计算研究

doi: 10.3969/j.issn.1000-5641.201922002

华东师范大学物理与电子科学学院, 上海　200241

基金项目: 国家自然科学基金(51572086, 11574084, 11774091)

详细信息

通讯作者:
谢文辉, 男, 副教授, 研究方向为计算材料学. E-mail: whxie@phy.ecnu.edu.cn

中图分类号: O411.3
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- 文章访问数: 123
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- PDF下载量: 3
- 被引次数: 0
出版历程
- 收稿日期: 2019-01-22
- 网络出版日期: 2019-12-25
- 刊出日期: 2020-01-01

Atomic distortion in CrN: A first-principle investigation

School of Physics and Electronic Science, East China Normal University, Shanghai　200241, China

摘要

摘要: 采用第一性原理计算方法研究了氮化铬（Chromium Nitride，CrN)的正交(Orthorhombic)相, 发现其中的Cr原子和N原子均沿着正交结构的[100]方向移动, 均偏离其高对称位置, 且在结构中形成锯齿形的原子链, 这个现象在过去的计算研究中一直没有被考虑. 结果表明, 在正交相中, 原子位移可以使总能降低0.125 eV, 因而更加稳定；考虑原子位移后, 计算得到的晶格长度等结构参数与实验符合得更好；计算得到的体弹性模量 K₀ 数值明显减小, 更加接近实验值. 正交相的磁基态是层间不对称的反铁磁结构, 原子位移是由正交相中层间不对称的磁应力所驱动, 同时原子位移可以补偿层间的磁相互作用力. 此外, 原子位移不改变CrN的莫特绝缘体特性, 但是会轻微减小带隙.
- CrN /
- 原子位移 /
- 磁性质 /
- 电子结构
Abstract: First principle calculations indicate that Cr and N atoms in the orthorhombic phase of CrN (Chromium Nitride) tend to shift from their ideal positions along the [100] direction. This shift can induce zigzag Cr-N-Cr chains in the orthorhombic phase; these atomic distortions have not been taken into account in previous studies. The atomic distortions may decrease the total energy of the orthorhombic phase by 0.125 eV/formula unit and make the structure more stable. Lattice constants, moreover, may also be in better agreement with experiment results when considering these atomic distortions. Further, the bulk modulus K₀ decreases significantly when considering the atomic distortions and is closer to the experimental value. The atomic distortions are induced by the asymmetric magnetic forces between asymmetric magnetic layers in the special antiferromagnetic order of the orthorhombic phase, which compensates for the magnetic forces between the layers. The atomic distortions would not change the Mott-insulator property of the orthorhombic phase but may reduce the band gap slightly.
- CrN /
- atomic distortion /
- magnetic properties /
- electronic structure

HTML全文

图 1 AFM2磁构型的正交结构 , 红色箭头表示自旋向上, 绿色箭头表示自旋向下：(a) 没有原子位移的结构; (b) 有原子位移的结构

Fig. 1 The structure of AFM2 orthorhombic phase, the red arrows represent the spin up and the green arrows represent the spin down, respectively: (a) without atomic distortions and (b) with atomic distortions, respectively

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图 2 CrN的能量曲线与a/b的关系, (a) PBE计算结果, (b) LDA+U (U=3.7 eV, J=0.94 eV)计算结果; AFM2磁构型中原子位移随a/b的变化, (c)PBE计算结果, (d)LDA+U计算结果

Fig. 2 The total energy of CrN for different a/b ratios and different magnetic states, the results calculated by PBE and LDA+U are shown in (a) and (b), respectively; the atomic distortion values of the AFM2 state of CrN calculated by PBE and LDA+U are shown in (c) and (d), respectively

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图 3 正交相AFM2磁构型的分波态密度(PDOS)的 LDA+U(U=3.7 eV, J=0.94 eV)计算结果：(a)不考虑原子位移的PDOS; (b)考虑原子位移的PDOS

Fig. 3 The partial density of states (PDOS) of the orthorhombic AFM2 phase calculated with the LDA+U (U=3.7 eV，J=0.94 eV) method: (a) the PDOS of the structure without atomic distortions; (b) the PDOS of the structure with atomic distortions

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图 4 正交相AFM2磁构型的能带结构的LDA+U(U=3.7 eV, J=0.94 eV)计算结果: (a)不考虑原子位移的结果; (b)考虑原子位移的结果

Fig. 4 The band structure of the orthorhombic AFM2 phase calculated with the LDA+U (U = 3.7 eV, J = 0.94 eV) method: (a) the band structure without atomic distortions; (b) the band structure with atomic distortions

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表 1 正交相中原子位移前后的Cr原子和N原子坐标、晶格常数、原子畸变值( ΔCr/ΔN, 单位为分数坐标), 以及[100]面内Cr-N-Cr的屈曲角度 (U = 3.7 eV, J = 0.94 eV)

Tab. 1 The atomic coordinates of Cr and N atoms of orthorhombic phase, the lattices constants(Å), the atomic distortion values (in fractional coordinates) and the angles (in degree) of Cr-N-Cr in the [100] plane (U = 3.7 eV, J = 0.94 eV)

	x(a)	y(b)	z(c)	ΔCr/ΔN	Cr-N-Cr
实验值^[7]	5.757	2.964	4.134	0.013/0.01	*
原子位移前
晶格常数(PBE)	5.672	2.986	4.165
晶格常数(LDA+U)	5.736	2.962	4.152
Cr₁	0.037 5	0.75	0.75	0	180
Cr₂	0.062 5	0.25	0.25	0	180
N₁	0.037 5	0.75	0.25	0	180
N₂	0.062 5	0.25	0.75	0	180
原子位移后(PBE)
晶格常数	5.732	3.001	4.098
Cr₁’	0.039 5	0.75	0.75	0.021	167.6
Cr₂’	0.060 4	0.25	0.25	0.021	167.6
N₁’	0.035 9	0.75	0.25	0.015	167.6
N₂’	0.064 1	0.25	0.75	0.015	167.6
原子位移后(LDA+U)
晶格常数	5.750	2.971	4.129
Cr₁’	0.061 3	0.25	0.25	0.013	171.6
Cr₂’	0.038 8	0.75	0.75	0.013	171.6
N₁’	0.036 1	0.75	0.25	0.013	171.6
N₂’	0.063 9	0.25	0.75	0.013	171.6

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表 2 原子位移前后CrN正交相计算得到的弹性模量

Tab. 2 The bulk modulus K₀ of the Orthorhombic phase without atomic distortions and

		K₀ /GPa
		PBE	LDA+U
实验值	(190 ± 50) Gpa^[24]
计算值	位移前	255^[27]	279
计算值	位移后	239	268

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