-(Zn,Cr)S(111)表面上的Dzyaloshinsky-Moriya作用:第一性原理计算

李小影; 黄灿; 朱岩; 李晋斌; 樊济宇; 潘燕飞; 施大宁; 马春兰

doi:10.7498/aps.67.20180342

摘要

根据密度泛函理论的第一性原理计算了具有非中心反演对称的异质结-（Zn，Cr）S（111）体系的原子结构和电子结构.Cr原子之间通过第一层S原子传递磁性相互作用.结合广义布洛赫条件，又进一步计算了反方向的自旋螺旋能量与波矢的色散关系E（q）与E（-q）.E（q）与E（-q）能量之差反映了-（Zn，Cr）S（111）的S层与Cr层之间空间反演对称性破缺引起的DMI的大小.通过海森伯相互作用（HBI）模型与Dzyaloshinsky-Moriya作用（DMI）模型拟合第一性原理计算值，得到了Cr原子间各近邻的HBI参数J1-J4与DMI参数d1，d2.在-（Zn，Cr）S（111）中，Cr原子间的耦合为M型反铁磁.DMI参数d1为-0.53 meV，为顺时针手性DMI，在-（Zn，Cr）S（111）界面上有可能会产生斯格明子.本文计算表明，磁性和非磁性半导体界面有可能存在DMI，为理论研究和磁存储技术的进步开拓一个新的方向.

关键词:

Abstract

According to density functional theory calculations, we elucidate the atomic and electronic structure of -(Zn, Cr)S(111) surface. The magnetic interaction between Cr atoms is via S atoms close to the Cr layer. This interaction is shown by the analysis of spin charge contour plot and partial density of states (DOS) of each atom. The DOSs of other S atoms are non magnetic and have no magnetic exchange with the Cr layer. E(q) and E(-q) are the dispersions between energy E and wave vector q of spin spiral in the opposite directions. They are calculated with generalized Bloch equations and all the magnetic moments of Cr atoms are arranged in the plane perpendicular to the -(Zn, Cr)S(111) film. The differences between E(q) and E(-q) are caused by the interface of -(Zn, Cr)S(111), where the symmetry of space perpendicular to the film is broken. Effective Heisenberg exchange interaction (HBI) and Dzyaloshinsky-Moriya interaction (DMI) parameters between different neighbors (Ji and di) are derived by well fitting the ab initio spin spiral dispersion E(q) to HBI with DMI model and E(q)-E(-q) to DMI model, respectively. The J2 plays a major role with a large negative value of -9.04 meV. The J1 is about 2/5 of J2, and J3 is about 1/4 of J2 with positive value. The DMI d1 is -0.53 meV, and d2 is 0.07 meV. With these HBI parameters, E(0) is the largest one at which -(Zn, Cr)S(111) has no ferromagnetic interface. The E(q) has its lowest energy with the q at M=b1/2 in the first Brillouin zone. Hence, -(Zn, Cr)S(111) is an M-type antiferromagnetic (AFM) material. In this type of AFM configuration, magnetic moments of Cr atom in a line along b2 are parallel to each other, and antiparallel to the magnetic moments in adjacent lines. The E(q) at K=b1/2+ b2/2 is almost as large as that at point. The value of DMI parameter d1 is about 1/5 of that on Co/Pt3 interface and 1/2 of Co/graphene. However, it is a negative number, which shows the clockwise chirality. The -(Zn, Cr)S(111) interface has obvious DMI, and skyrmion may be formed at this transition-metal/semiconductor (TM/S) interface. It is a good option to search for DMI in different kinds of TM/S heterojunctions. The material that combines the advantage of heterojunction, and DMI may have new magnetic phenomenon, which is usefulfor the magnetic storage. This paper enriches the research on DMI.

Keywords:

作者及机构信息

1.
南京航空航天大学理学院物理系, 南京 210006;

2.
苏州科技大学数理学院物理科学与技术系, 苏州 215009

通信作者: 朱岩, yzhu@nuaa.edu.cn

基金项目: 国家自然科学基金（批准号：11204131，11374159）、江苏省高等学校自然科学研究重大项目（批准号：17KJA140001）和江苏省六大人才高峰高层次人才项目（批准号：XCL-078）资助的课题.

Authors and contacts

1.
College of Science, Nanjing University of Aeronautics and Astronautics, Najing 210006, China;

2.
School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou 215009, China

Corresponding author: Zhu Yan, yzhu@nuaa.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11204131, 11374159), NSF of Jiangsu Higher Education Institutions, China (Grant No. 17KJA140001), and Six Talent Peaks Project of Jiangsu, China (Grant No. XCL-078).

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施引文献

[1]	Mhlbauer S, Binz B, Jonietz F, Pfleiderer C, Rosch A, Neubauer A, Georgii R, Bni P 2009 Science 323 915
[2]	Yu X Z, Kanazawa N, Onose Y, Kimoto K, Zhang W Z, Ishiwata S, Matsui Y, Tokura Y 2011 Nat. Mater. 10 106
[3]	Yu X Z, DeGrave J P, Hara T, Hara Y, Jin S, Tokura Y 2013 Nano Lett. 13 3755
[4]	Du H F, DeGrave J P, Xue F, Liang D, Ning W, Yang J Y, Tian M L, Zhang Y H, Jin S 2014 Nano Lett. 14 2026
[5]	Skyrme T H R A 1962 Nucl. Phys. 31 556
[6]	Honolka J, Lee T Y, Kuhnke K, Enders A, Skomski R, Bornemann S, Mankovsky S, Minr J, Staunton J, Ebert H, Hessler M, Fauth K, Schtz G, Buchsbaum A, Schmid M, Varga P, Kern K 2009 Phys. Rev. Lett. 102 067207
[7]	Heinze S, von Bergmann K, Menzel M, Brede J, Kubetzka A, Wiesendanger R, Bihlmayer G, Blgel S 2011 Nat. Phys. 7 713
[8]	Romming N, Hanneken C, Menzel M, Bickel J, Wolter B, Bergmann K V, Kubetzka A, Wiesendanger R 2013 Science 341 636
[9]	Sun L, Cao R X, Miao B F, Feng Z, You B, Wu D, Zhang W, Hu A, Ding H F 2013 Phys. Rev. Lett. 110 167201
[10]	Pollard S D, Garlow J A, Yu J, Wang Z, Zhu Y, Yang H 2017 Nat. Commun. 8 14761
[11]	Wells A W J, Shepley P M, Marrows C H, Moore T A 2017 Phys. Rev. B 95 054428
[12]	Hellman F, Hoffmann A, Tserkovnyak Y, Beach G S D, Fullerton E E, Leighton C, MacDonald A H, Ralph D C, Arena D A, Drr H A, Fischer P, Grollier J, Heremans J P, Jungwirth T, Kimmel A V, Koopmans B, Krivorotov I N, May S J, Petford-Long A K, Rondinelli J M, Samarth N, Schuller I K, Slavin A N, Stiles M D, Tchernyshyov O, Thiaville A, Zink B L 2017 Rev. Mod. Phys. 89 025006
[13]	Nagaosa N, Tokura Y 2013 Nat. Nanotech. 8 899
[14]	Dzyaloshinskii I 1958 J. Phys. Chem. Solids 4 241
[15]	Moriya T 1960 Phys. Rev. 120 91
[16]	Shu L, Chen Y G, Chen H 2002 Acta Phys. Sin. 51 902 (in Chinese) [殳蕾,陈宇光,陈鸿 2002 物理学报 51 902]
[17]	Cai Z, Lu W B, Liu Y J 2008 Acta Phys. Sin. 57 7267 (in Chinese) [蔡卓,陆文彬,刘拥军 2008 物理学报 57 7267]
[18]	Zhang Y L, Zhou B 2011 Acta Phys. Sin. 60 120301 (in Chinese) [张丽英,周斌 2011 物理学报 60 120301]
[19]	Luo Y M, Zhou C, Won C, Wu Y Z 2014 AIP Adv. 4 047136
[20]	Fert A, Cros V, Sampaio J 2013 Nat. Nanotech. 8 152
[21]	Mnzer W, Neubauer A, Adams T, Mhlbauer S, Franz C, Jonietz F, Georgii R, Bni P, Pedersen B, Schmidt M, Rosch A, Pfleiderer C 2010 Phys. Rev. B 81 041203
[22]	Tonomura A, Yu X, Yanagisawa K, Matsuda T, Onose Y, Kanazawa N, Park H S, Tokura Y 2012 Nano Lett. 12 1673
[23]	Miao B F, Sun L, Wu Y W, Tao X D, Xiong X, Wen Y, Cao R X, Wang P, Wu D, Zhan Q F, You B, Du J, Li R W, Ding H F 2014 Phys. Rev. B 90 174411
[24]	Dai Y Y, Wang H, Tao P, Yang T, Ren W J, Zhang Z D 2013 Phys. Rev. B 88 054403
[25]	Xie K X, Sang H 2014 J. Appl. Phys. 116 223901
[26]	Jiang W J, Upadhyaya P, Zhang W, Yu G Q, Pear J E 2015 Science 349 283
[27]	Luchaire C M, Moutafis C, Reyren N, Sampaio J, Vaz C A F, van Horne N, Bouzehouane K, Garcia K, Deranlot C, Warnicke P, Wohlhter P, George J M, Weigand M, Raabe J, Cros V, Fert A 2016 Nat. Nanotech. 11 444
[28]	Boulle O, Vogel J, Yang H X, Pizzini S, Chaves D D S, Locatelli A, Menteș T O, Sala A, Buda-Prejbeanu L D, Klein O, Belmeguenai M, Roussign Y, Stashkevich A, Chrif S M, Aballe L, Foerster M, Chshiev M, Auffret S, Miron I M, Gaudin G 2016 Nat. Nanotech. 11 449
[29]	Woo S, Litzius K, Krger B, Im M Y, Caretta L, Richter K, Mann M, Krone A, Reeve R M, Weigand M, Agrawal P, Lemesh I, Mawass M A, Fischer P, Klui M, Beach G S D 2016 Nat. Mater. 15 501
[30]	Fert A, Reyren N, Cros V 2017 Nat. Rev. Mater. 2 17031
[31]	Yang H X, Chen G, Cotta A A C, Alpha T, Diaye N, Nikolaev S A, Soares E A, Macedo W A A, Schmid A K, Fert A, Chshiev M 2017 ArXiv 1704 09023
[32]	Sanvito S, Hill N A 2001 Phys. Rev. Lett. 87 267202
[33]	Fan S W, Yao K L, Liu Z L 2009 Appl. Phys. Lett. 94 152506
[34]	Saito H, Zayets V, Yamagata S, Ando K 2003 Phys. Rev. Lett. 90 207202
[35]	Kresse G, Joubert D 1999 Phys. Rev. B 59 1758
[36]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[37]	Yang H X, Boulle O, Cros V, Fert A, Chshiev M 2016 ArXiv 1603 01847
[38]	Zhu Y, Ma C L, Shi D N, Zhang K C 2014 Phys. Lett. A 378 2234
[39]	Yang H, Thiaville A, Rohart S, Fert A, Chshiev M 2015 Phys. Rev. Lett. 115 267210
[40]	Pan Y, Zhu Y, Shi D N, Wei X Y, Ma C L, Zhang K C 2015 J. Alloys Compd. 644 341
[41]	Marsman M, Hafner J 2002 Phys. Rev. B 66 224409
[42]	Hobbs D, Kresse G, Hafner J 2000 Phys. Rev. B 62 11556
[43]	Mryasov O N, Lichtenstein A I, Sandratskii L M, Gubanov V A 1991 J. Phys. Condens. Matter 3 8565
[44]	Knpfle K, Sandratskii L M, Kbler J 2000 Phys. Rev. B 62 5564
[45]	Emori S, Bauer U, Ahn S M, Martinez E, Beach G S 2013 Nat. Mater. 12 611
[46]	Zhang X, Zhou Y, Ezawa M 2016 Sci. Rep. 6 24795
[47]	Barker J, Tretiakov O A 2016 Phys. Rev. Lett. 116 147203
[48]	Dup B, Hoffmann M, Paillard C, Heinze S 2014 Nat. Commun. 5 4030
[49]	Hu X X, Zhao J, Gao W 2017 Chin.Phys. B 26 079101
[50]	Shang J X, Liu K, Wang F H 2017 Acta Phy. Sin. 66 216801

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