Dzyaloshinsky-Moriya interaction in -(Zn, Cr)S(111) surface: First principle calculations

Li Xiao-Ying; Huang Can; Zhu Yan; Li Jin-Bin; Fan Ji-Yu; Pan Yan-Fei; Shi Da-Ning; Ma Chun-Lan

doi:10.7498/aps.67.20180342

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:

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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[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
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[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

Cited By

[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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