| CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES |
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An Origin of Dzyaloshinskii–Moriya Interaction at Graphene-Ferromagnet Interfaces Due to the Intralayer RKKY/BR Interaction |
| Jin Yang1, Jian Li1, Liangzhong Lin2, and Jia-Ji Zhu1* |
1School of Science and Laboratory of Quantum Information Technology, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
2School of Information Engineering, Zhongshan Polytechnic, Zhongshan 528400, China
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| Cite this article: |
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Jin Yang, Jian Li, Liangzhong Lin et al 2020 Chin. Phys. Lett. 37 087501 |
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Abstract We present a theory of both the itinerant carrier-mediated RKKY interaction and the virtual excitations-mediated Bloembergen–Rowland (BR) interaction between magnetic moments in graphene induced by proximity effect with a ferromagnetic film. It is shown that the RKKY/BR interaction consists of the Heisenberg, Ising, and Dzyaloshinskii–Moriya (DM) terms. In the case of the nearest distance, we estimate the DM term from the RKKY/BR interaction is about $0.13$ meV for the graphene/Co interface, which is consistent with the experimental result of DM interaction $0.16\pm0.05$ meV. Our calculations indicate that the intralayer RKKY/BR interaction may be a possible physical origin of the DM interaction in the graphene-ferromagnet interface. This work provides a new perspective to comprehend the DM interaction in graphene/ferromagnet systems.
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Received: 28 June 2020
Published: 04 July 2020
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| PACS: |
75.30.Gw
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(Magnetic anisotropy)
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75.70.Ak
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(Magnetic properties of monolayers and thin films)
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75.70.Cn
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(Magnetic properties of interfaces (multilayers, superlattices, heterostructures))
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75.70.Tj
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(Spin-orbit effects)
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| Fund: Supported by the National Natural Science Foundation of China (Grant Nos. 11404043 and 1160041160), the Key Technology Innovations Project to Industries of Chongqing (Grant No. cstc2016zdcy-ztzx0067), and the Graduate Research Innovation Project of Chongqing (Grants No. CYS18253). |
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| [1] | Yazyev O V and Helm L 2007 Phys. Rev. B 75 125408 |
| [2] | Cervenka J, Katsnelson M I and Flipse C F J 2009 Nat. Phys. 5 840 |
| [3] | Ugeda M M, Brihuega I, Guinea F and Gómez-Rodríguez J M 2010 Phys. Rev. Lett. 104 096804 |
| [4] | Uchoa B, Kotov V N, Peres N M R and Castro Neto A H 2008 Phys. Rev. Lett. 101 026805 |
| [5] | Nair R R, Tsai I L, Sepioni M, Lehtinen O, Keinonen J, Krasheninnikov A V, Castro Neto A H, Katsnelson M I, Geim A K and Grigorieva I V 2013 Nat. Commun. 4 2010 |
| [6] | González-Herrero H, Gómez-Rodrı́guez J M, Mallet P, Moaied M, Palacios J J, Salgado C, Ugeda M M, Veuillen J Y, Yndurain F and Brihuega I 2016 Science 352 437 |
| [7] | Hu F M, Ma T, Lin H Q and Gubernatis J E 2011 Phys. Rev. B 84 075414 |
| [8] | Cao T, Li Z and Louie S G 2015 Phys. Rev. Lett. 114 236602 |
| [9] | Wang Y, Huang Y, Song Y, Zhang X Y, Ma Y F, Liang J J and Chen Y S 2009 Nano Lett. 9 220 |
| [10] | Sepioni M, Nair R R, Rablen S, Narayanan J, Tuna F, Winpenny R, Geim A K and Grigorieva I V 2010 Phys. Rev. Lett. 105 207205 |
| [11] | Nair R R, Sepioni M, Tsai I L, Lehtinen O, Keinonen J, Krasheninnikov A V, Thomson T, Geim A K and Grigorieva I V 2012 Nat. Phys. 8 199 |
| [12] | Son Y W, Cohen M L and Louie S G 2006 Nature 444 347 |
| [13] | Yazyev O V and Katsnelson M I 2008 Phys. Rev. Lett. 100 047209 |
| [14] | Magda G Z, Jin X Z, Hagymási I et al. 2014 Nature 514 608 |
| [15] | Stauber T, Peres N M R, Guinea F and Castro Neto A H 2007 Phys. Rev. B 75 115425 |
| [16] | Castro E V, Peres N M R, Stauber T and Silva N A P 2008 Phys. Rev. Lett. 100 186803 |
| [17] | Wang Z, Tang C, Sachs R, Barlas Y and Shi J 2015 Phys. Rev. Lett. 114 016603 |
| [18] | Wei P, Lee S, Lemaitre F, Pinel L, Cutaia D, Cha W, Katmis F, Zhu Y, Heiman D, Hone J, Moodera J S and Chen C T 2016 Nat. Mater. 15 711 |
| [19] | Dedkov Y S, Fonin M, Rudiger U and Laubschat C 2008 Phys. Rev. Lett. 100 107602 |
| [20] | Peralta M, Medina E and Mireles F 2019 Phys. Rev. B 99 195452 |
| [21] | Ruderman M A and Kittel C 1954 Phys. Rev. 96 99 |
| [22] | Kasuya T 1956 Prog. Theor. Phys. 16 45 |
| [23] | Yosida K 1957 Phys. Rev. 106 893 |
| [24] | Brey L, Fertig H A and Das Sarma S 2007 Phys. Rev. Lett. 99 116802 |
| [25] | Saremi S 2007 Phys. Rev. B 76 184430 |
| [26] | Kogan E 2011 Phys. Rev. B 84 115119 |
| [27] | Sherafati M and Satpathy S 2011 Phys. Rev. B 83 165425 |
| [28] | Zhang S H, Zhu J J, Yang W and Chang K 2017 2D Mater. 4 035005 |
| [29] | Black-Schaffer A M 2010 Phys. Rev. B 81 205416 |
| [30] | Parkin S S P, Hayashi M and Thomas L 2008 Science 320 190 |
| [31] | Fert A, Cros V and Sampaio J 2013 Nat. Nanotechnol. 8 152 |
| [32] | Cho J, Kim N H, Lee S, Kim J S, Lavrijsen R, Solignac A, Yin Y, Han D S, van Hoof N J J, Swagten H J M, Koopmans B and You C Y 2015 Nat. Commun. 6 7635 |
| [33] | Dzyaloshinsky I 1958 J. Phys. Chem. Solids 4 241 |
| [34] | Moriya T 1960 Phys. Rev. 120 91 |
| [35] | Sergienko I A and Dagotto E 2006 Phys. Rev. B 73 094434 |
| [36] | Dmitrienko V E, Ovchinnikova E N, Collins S P, Nisbet G, Beutier G, Kvashnin Y O, Mazurenko V V, Lichtenstein A I and Katsnelson M I 2014 Nat. Phys. 10 202 |
| [37] | Je S G, Kim D H, Yoo S C, Min B C, Lee K J and Choe S B 2013 Phys. Rev. B 88 214401 |
| [38] | Di K, Zhang V L, Lim H S, Ng S C, Kuok M H, Yu J, Yoon J, Qiu X and Yang H 2015 Phys. Rev. Lett. 114 047201 |
| [39] | Yang H, Thiaville A, Rohart S, Fert A and Chshiev M 2015 Phys. Rev. Lett. 115 267210 |
| [40] | Nembach H T, Shaw J M, Weiler M, Jue E and Silva T J 2015 Nat. Phys. 11 825 |
| [41] | Yang H X, Chen G, Cotta A A C, N'Diaye A T, Nikolaev S A, Soares E A, Macedo W A A, Liu K, Schmid A K, Fert A and Chshiev M 2018 Nat. Mater. 17 605 |
| [42] | Yang B, Cui Q, Liang J, Chshiev M and Yang H 2020 Phys. Rev. B 101 014406 |
| [43] | Zhang D, Lou W, Miao M, Zhang S C and Chang K 2013 Phys. Rev. Lett. 111 156402 |
| [44] | Miao M S, Yan Q, Van de Walle C G, Lou W K, Li L L and Chang K 2012 Phys. Rev. Lett. 109 186803 |
| [45] | Marchenko D, Sánchez-Barriga J, Scholz M R, Rader O and Varykhalov A 2013 Phys. Rev. B 87 115426 |
| [46] | Rader O, Varykhalov A, Sánchez-Barriga J, Marchenko D, Rybkin A and Shikin A M 2009 Phys. Rev. Lett. 102 057602 |
| [47] | Marchenko D, Varykhalov A, Scholz M R, Bihlmayer G, Rashba E I, Rybkin A, Shikin A M and Rader O 2012 Nat. Commun. 3 1232 |
| [48] | Fert A and Levy P M 1980 Phys. Rev. Lett. 44 1538 |
| [49] | Vedmedenko E Y, Riego P, Arregi J A and Berger A 2019 Phys. Rev. Lett. 122 257202 |
| [50] | Bloembergen N and Rowland T J 1955 Phys. Rev. 97 1679 |
| [51] | Dugaev V K, Litvinov V I and Barnas J 2006 Phys. Rev. B 74 224438 |
| [52] | Min H, Hill J E, Sinitsyn N A, Sahu B R, Kleinman L and MacDonald A H 2006 Phys. Rev. B 74 165310 |
| [53] | Zhu J J, Yao D X, Zhang S C and Chang K 2011 Phys. Rev. Lett. 106 097201 |
| [54] | Duan H J, Zheng S H, Fu P H, Wang R Q, Liu J F, Wang G H and Yang M 2018 New J. Phys. 20 103008 |
| [55] | Chang H R, Zhou J, Wang S X, Shan W Y and Xiao D 2015 Phys. Rev. B 92 241103 |
| [56] | Hosseini M V and Askari M 2015 Phys. Rev. B 92 224435 |
| [57] | Mastrogiuseppe D, Sandler N and Ulloa S E 2014 Phys. Rev. B 90 161403 |
| [58] | Murakami S, Nagosa N and Zhang S C 2004 Phys. Rev. B 69 235206 |
| [59] | Deacon R S, Chuang K C, Nicholas R J, Novoselov K S and Geim A K 2007 Phys. Rev. B 76 081406 |
| [60] | Sichau J, Prada M, Anlauf T, Lyon T J, Bosnjak B, Tiemann L and Blick R H 2019 Phys. Rev. Lett. 122 046403 |
| [61] | Zhang S H, Zhu J J, Yang W, Lin H Q and Chang K 2016 Phys. Rev. B 94 085408 |
| [62] | Eom D, Prezzi D, Rim K T, Zhou H, Lefenfeld M, Xiao S, Nuckolls C, Hybertsen M S, Heinz T F and Flynn G W 2009 Nano Lett. 9 2844 |
| [63] | Dedkov Y S, Fonin M, Rudiger U and Laubschat C 2008 Appl. Phys. Lett. 93 022509 |
| [64] | Zakeri K, Zhang Y, Prokop J, Chuang T H, Sakr N, Tang W X and Kirschner J 2010 Phys. Rev. Lett. 104 137203 |
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