[1] Dzyaloshinsky I 1958 J. Phys. Chem. Solids 4 241 [2] Moriya T 1960 Phys. Rev. 120 91 [3] Fert A and Lévy P M 1980 Phys. Rev. Lett. 44 1538 [4] Yu X Z, Kanazawa N, Onose Y, Kimoto K, Zhang W Z, Ishiwata S, Matsui Y and Tokura Y 2011 Nat. Mater. 10 106 [5] Fert A, Reyren N and Cros V 2017 Nat. Rev. Mater. 2 17031 [6] Shen L C, Xia J, Zhang X C, Ezawa M, Tretiakov O A, Liu X X, Zhao G P and Zhou Y 2020 Phys. Rev. Lett. 124 037202 [7] Thiaville A, Rohart S, Jué É, Cros V and Fert A 2012 Europhys. Lett. 100 57002 [8] Cui Q R, Liang J H, Zhu Y M, Yao X and Yang H X 2023 Chin. Phys. Lett. 40 037502 [9] Iacocca E and Heinonen O 2017 Phys. Rev. Appl. 8 034015 [10] Li Y M 2023 Phys. Rev. Res. 5 033026 [11] Kanazawa N, Onose Y, Arima T, Okuyama D, Ohoyama K, Wakimoto S, Kakurai K, Ishiwata S and Tokura Y 2011 Phys. Rev. Lett. 106 156603 [12] Li Y F, Kanazawa N, Yu X Z, Tsukazaki A, Kawasaki M, Ichikawa M, Jin X F, Kagawa F and Tokura Y 2013 Phys. Rev. Lett. 110 117202 [13] Jonietz F, Mühlbauer S, Pfleiderer C, Neubauer A, Münzer W, Bauer A, Adams T, Georgii R, Böni P, Duine R A, Everschor K, Garst M and Rosch A 2010 Science 330 1648 [14] Yu X Z, Kanazawa N, Zhang W Z, Nagai T, Hara T, Kimoto K, Matsui Y, Onose Y and Tokura Y 2012 Nat. Commun. 3 988 [15] Nagaosa N and Tokura Y 2013 Nat. Nanotechnol. 8 899 [16] Fert A, Cros V and Sampaio J 2013 Nat. Nanotechnol. 8 152 [17] Luo S J, Song M, Li X, Zhang Y, Hong J, Yang X F, Zou X C, Xu N and You L 2018 Nano Lett. 18 1180 [18] Luo S J and You L 2021 APL Mater. 9 050901 [19] Yu D X, Yang H X, Chshiev M and Fert A 2022 Natl. Sci. Rev. 9 nwac021 [20] Song K M, Jeong J S, Pan B, Zhang X C, Xia J, Cha S, Park T E, Kim K, Finizio S, Raabe J, Chang J, Zhou Y, Zhao W S, Kang W, Ju H and Woo S 2020 Nat. Electron. 3 148 [21] Yu G Q, Upadhyaya P, Shao Q M, Wu H, Yin G, Li X, He C L, Jiang W J, Han X F, Amiri P K and Wang K L 2017 Nano Lett. 17 261 [22] Sheng Y, Wang W Y, Deng Y C, Ji Y, Zheng H Z and Wang K Y 2023 Natl. Sci. Rev. 10 nwad093 [23] Wang L M, Ga Y L, Cui Q R, Li P, Liang J H, Zhou Y, Wang S G and Yang H X 2023 Phys. Rev. B 108 214404 [24] Huang K, Shao D F and Tsymbal E Y 2022 Nano Lett. 22 3349 [25] Sun W, Wang W X, Li H, Zhang G B, Chen D, Wang J L and Cheng Z X 2020 Nat. Commun. 11 5930 [26] Yang H X, Thiaville A, Rohart S, Fert A and Chshiev M 2015 Phys. Rev. Lett. 115 267210 [27] Liang J H, Wang W W, Du H F, Hallal A, Garcia K, Chshiev M, Fert A and Yang H X 2020 Phys. Rev. B 101 184401 [28] Ga Y L, Yu D X, Wang L M, Li P, Liang J H and Yang H X 2023 2D Mater. 10 035020 [29] Li P, Yu D X, Liang J H, Ga Y L and Yang H X 2023 Phys. Rev. B 107 054408 [30] Cui Q R, Liang J H, Shao Z J, Cui P and Yang H X 2020 Phys. Rev. B 102 094425 [31] Zhu Y M, Cui Q R, Liang J H, Ga Y L and Yang H X 2022 2D Mater. 9 045030 [32] Liang J H, Cui Q R and Yang H X 2020 Phys. Rev. B 102 220409 [33] Xu C S, Chen P, Tan H X, Yang Y R, Xiang H J and Bellaiche L 2020 Phys. Rev. Lett. 125 037203 [34] Wang L M, Ga Y L, Li P, Yu D X, Jiang J W, Liang J H, Wang S G and Yang H X 2023 Phys. Rev. B 108 054440 [35] Ga Y L, Yu D X, Li Y, Jiang J W, Wang L M, Li P, Liang J H, Feng H, Shi Y G and Yang H X 2024 Phys. Rev. B 109 L060402 [36] Edström A, Amoroso D, Picozzi S, Barone P and Stengel M 2022 Phys. Rev. Lett. 128 177202 [37] Ga Y L, Cui Q R, Liang J H, Yu D X, Zhu Y M, Wang L M and Yang H X 2022 Phys. Rev. B 106 054426 [38] Jiang J W, Ga Y L, Li P, Cui Q R, Wang L M, Yu D X, Liang J H and Yang H X 2024 Phys. Rev. B 109 014402 [39] Tong Q J, Liu F, Xiao J and Yao W 2018 Nano Lett. 18 7194 [40] Xiao F P, Chen K Q and Tong Q J 2021 Phys. Rev. Res. 3 013027 [41] Yang H X, Boulle O, Cros V, Fert A and Chshiev M 2018 Sci. Rep. 8 12356 [42] Cho J, Kim N H, Lee S, Kim J S, Lavrijsen R, Solignac A, Yin Y X, Han D S, Van Hoof N J J, Swagten H J M, Koopmans B and You C Y 2015 Nat. Commun. 6 7635 [43] Tacchi S, Troncoso R E, Ahlberg M, Gubbiotti G, Madami M, Åkerman J and Landeros P 2017 Phys. Rev. Lett. 118 147201 [44] Gusev N S, Sadovnikov A V, Nikitov S A, Sapozhnikov M V and Udalov O G 2020 Phys. Rev. Lett. 124 157202 [45] Feng C, Meng F, Wang Y D, Jiang J, Mehmood N, Cao Y, Lv X W, Yang F, Wang L, Zhao Y K, Xie S, Hou Z P, Mi W B, Peng Y, Wang K Y, Gao X S, Yu G H and Liu J M 2021 Adv. Funct. Mater. 31 2008715 [46] Zhu Y M, Cui Q R, Liu B, Zhou T J and Yang H X 2023 Phys. Rev. B 108 134438 [47] Dai B Q, Wu D, Razavi S A, Xu S J, He H, Shu Q Y, Jackson M, Mahfouzi F, Huang H S, Pan Q J, Cheng Y, Qu T, Wang T Y, Tai L X, Wong K, Kioussis N and Wang K L 2023 Sci. Adv. 9 eade6836 [48] Wu J X, Yuan H T, Meng M M, Chen C, Sun Y, Chen Z Y, Dang W H, Tan C W, Liu Y J, Yin J B, Zhou Y B, Huang S Y, Xu H Q, Cui Y, Hwang H Y, Liu Z F, Chen Y L, Yan B H and Peng H L 2017 Nat. Nanotechnol. 12 530 [49] Wu M H and Zeng X C 2017 Nano Lett. 17 6309 [50] Ghosh T, Samanta M, Vasdev A, Dolui K, Ghatak J, Das T, Sheet G and Biswas K 2019 Nano Lett. 19 5703 [51] Sun Y, Zhang J, Ye S, Song J and Qu J L 2020 Adv. Funct. Mater. 30 2004480 [52] Li T R, Tu T, Sun Y W, Fu H X, Yu J, Xing L, Wang Z A, Wang H M, Jia R D, Wu J X, Tan C W, Liang Y, Zhang Y C, Zhang C C, Dai Y M, Qiu C G, Li M, Huang R, Jiao L Y, Lai K J, Yan B H, Gao P and Peng H L 2020 Nat. Electron. 3 473 [53] Wang F K, Yang S J, Wu J, Hu X Z, Li Y, Li H Q, Liu X T, Luo J H and Zhai T Y 2021 InfoMat 3 1251 [54] Ding X, Li M L, Chen P, Zhao Y, Zhao M, Leng H Q, Wang Y, Ali S, Raziq F, Wu X Q, Xiao H Y, Zu X T, Wang Q Y, Vinu A, Yi J B and Qiao L 2022 Matter 5 4274 [55] Wu M Q, Lou Z F, Dai C M, Wang T, Wang J, Zhu Z Y, Xu Z K, Sun T L, Li W B, Zheng X R and Lin X 2023 Adv. Mater. 35 2300450 [56] Wang W J, Meng Y, Zhang Y X, Zhang Z, Wang W, Lai Z X, Xie P S, Li D J, Chen D, Quan Q, Yin D, Liu C T, Yang Z B, Yip S and Ho J C 2023 Adv. Mater. 35 2210854 [57] Zhang W, Zhang L, Wong P K J, Yuan J, Vinai G, Torelli P, Van Der Laan G, Feng Y P and Wee A T S 2019 ACS Nano 13 8997 [58] Zhang B H, Hou Y S, Wang Z and Wu R Q 2021 Phys. Rev. B 103 054417 [59] Miwa S, Suzuki M, Tsujikawa M, Matsuda K, Nozaki T, Tanaka K, Tsukahara T, Nawaoka K, Goto M, Kotani Y, Ohkubo T, Bonell F, Tamura E, Hono K, Nakamura T, Shirai M, Yuasa S and Suzuki Y 2017 Nat. Commun. 8 15848 [60] Kresse G and Hafner J 1993 Phys. Rev. B 47 558 [61] Kresse G and Furthmüller J 1996 Phys. Rev. B 54 11169 [62] Kresse G and Furthmüller J 1996 Comput. Mater. Sci. 6 15 [63] Perdew J P, Burke K and Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 [64] Blöchl P E 1994 Phys. Rev. B 50 17953 [65] Grimme S, Antony J, Ehrlich S and Krieg H 2010 J. Chem. Phys. 132 154104 [66] Li J Q, Cheng C and Duan M Y 2023 Appl. Surf. Sci. 618 156541 [67] Yu J B and Sun Q 2018 Appl. Phys. Lett. 112 053901 [68] Yang H X, Liang J H and Cui Q R 2023 Nat. Rev. Phys. 5 43 [69] Boulle O, Vogel J, Yang H X, Pizzini S, Chaves D de S, Locatelli A, Klein O, Belmeguenai M, Roussigné Y, Stashkevich A, Chérif S M, Aballe L, Foerster M, Chshiev M, Auffret S, Miron I M and Gaudin G 2016 Nat. Nanotechnol. 11 449 [70] Dupé B, Hoffmann M, Paillard C and Heinze S 2014 Nat. Commun. 5 4030 [71] Cui Q R, Zhu Y M, Ga Y L, Liang J H, Li P, Yu D X, Cui P and Yang H X 2022 Nano Lett. 22 2334 [72] Rohart S and Thiaville A 2013 Phys. Rev. B 88 184422 [73] Jia H Y, Zimmermann B and Blügel S 2018 Phys. Rev. B 98 144427 [74] Muckel F, Von Malottki S, Holl C, Pestka B, Pratzer M, Bessarab P F, Heinze S and Morgenstern M 2021 Nat. Phys. 17 395 [75] Müller G P, Hoffmann M, Dißelkamp C, Schürhoff D, Mavros S, Sallermann M, Kiselev N S, Jónsson H and Blügel S 2019 Phys. Rev. B 99 224414 [76] Lin S Z, Saxena A and Batista C D 2015 Phys. Rev. B 91 224407 [77] Cui Q R, Zhu Y M, Jiang J W, Liang J H, Yu D X, Cui P and Yang H X 2021 Phys. Rev. Res. 3 043011 [78] Jiang J W, Liu X, Li R and Mi W B 2021 Appl. Phys. Lett. 119 072401 [79] Li P, Cui Q R, Ga Y L, Liang J H and Yang H X 2022 Phys. Rev. B 106 024419 [80] Hervé M, Dupé B, Lopes R, Böttcher M, Martins M D, Balashov T, Gerhard L, Sinova J and Wulfhekel W 2018 Nat. Commun. 9 1015 [81] Mühlbauer S, Binz B, Jonietz F, Pfleiderer C, Rosch A, Neubauer A, Georgii R and Böni P 2009 Science 323 915 [82] Chen S H, Lourembam J, Ho P, Toh A K J, Huang J F, Chen X Y, Tan H K, Yap S L K, Lim R J J, Tan H R, Suraj T S, Sim M I, Toh Y T, Lim I, Lim N C B, Zhou J, Chung H J, Lim S T and Soumyanarayanan A 2024 Nature 627 522 [83] Seki S, Yu X Z, Ishiwata S and Tokura Y 2012 Science 336 198 [84] Moreau-Luchaire C, Moutafis C, Reyren N, Sampaio J, Vaz C A F, Van Horne N, Bouzehouane K, Garcia K, Deranlot C, Warnicke P, Wohlhüter P, George J-M, Weigand M, Raabe J, Cros V and Fert A 2016 Nat. Nanotechnol. 11 444 [85] Du W, Dou K, He Z, Dai Y, Huang B and Ma Y 2022 Nano Lett. 22 3440 |