| CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES |
|
|
|
|
Second-Harmonic Response in Magnetic Nodal-Line Semimetal Fe$_3$GeTe$_2$ |
| V. D. Esin, A. A. Avakyants, A. V. Timonina, N. N. Kolesnikov, and E. V. Deviatov* |
| Institute of Solid State Physics of the Russian Academy of Sciences, Chernogolovka, Moscow District, 2 Academician Ossipyan Str. 142432, Russia |
|
| Cite this article: |
|
V. D. Esin, A. A. Avakyants, A. V. Timonina et al 2022 Chin. Phys. Lett. 39 097303 |
|
|
|
|
Abstract We experimentally investigate second-harmonic transverse voltage response to ac electrical current for a magnetic nodal-line semimetal Fe$_3$GeTe$_2$ (FGT). For zero magnetic field, the observed second-harmonic voltage behaves as a square of the longitudinal current, as it should be expected for nonlinear Hall effect. The magnetic field behavior is found to be sophisticated: while the first-harmonic response shows the known anomalous Hall hysteresis in FGT, the second-harmonic Hall voltage is characterized by the pronounced high-field hysteresis and flat ($B$-independent) region with curves touching at low fields. The high-field hysteresis strongly depends on the magnetic field sweep rate, so it reflects some slow relaxation process. For the lowest rates, it is also accomplished by multiple crossing points. Similar shape of the second-harmonic hysteresis is known for skyrmion spin textures in nonlinear optics. Since skyrmions have been demonstrated for FGT by direct visualization techniques, we can connect the observed high-field relaxation with deformation of the skyrmion lattice. Thus, the second-harmonic Hall voltage response can be regarded as a tool to detect spin textures in transport experiments.
|
|
|
Received: 28 June 2022
Published: 22 August 2022
|
|
| PACS: |
73.21.-b
|
(Electron states and collective excitations in multilayers, quantum wells, mesoscopic, and nanoscale systems)
|
| |
73.40.-c
|
(Electronic transport in interface structures)
|
| |
73.50.Fq
|
(High-field and nonlinear effects)
|
| |
75.70.Tj
|
(Spin-orbit effects)
|
|
|
|
|
|
| [1] | Armitage N P, Mele E J, and Vishwanath A 2018 Rev. Mod. Phys. 90 015001 |
| [2] | Fang C, Lu L, Liu J, and Fu L 2016 Nat. Phys. 12 936 |
| [3] | Bradlyn B, Cano J, Wang Z, Vergniory M G, Felser C, Cava R J, and Bernevig B A 2016 Science 353 aaf5037 |
| [4] | Tang P, Zhou Q, and Zhang S C 2017 Phys. Rev. Lett. 119 206402 |
| [5] | Jiang J, Tang F, Pan X C, Liu H M, Niu X H, Wang Y X, Xu D F, Yang H F, Xie B P, Song F Q, Dudin P, Kim T K, Hoesch M, Das P K, Vobornik I, Wan X G, and Feng D L 2015 Phys. Rev. Lett. 115 166601 |
| [6] | Rhodes D, Das S, Zhang Q R, Zeng B, Pradhan N R, Kikugawa N, Manousakis E, and Balicas L 2015 Phys. Rev. B 92 125152 |
| [7] | Wang Y, Wang K, Robey J R, Paglione J, and Fuhrer M S 2016 Phys. Rev. B 93 121108 |
| [8] | Xu S Y, Liu C, Kushwaha S K, Sankar R, Krizan J W, Belopolski I, Neupane M, Bian G, Alidoust N, Chang T R, Jeng H T, Huang C Y, Tsai W F, Lin H, Shibayev P P, Chou F C, Cava R J, and Hasan M Z 2014 Science 347 294 |
| [9] | Kim K, Seo J, Lee E, Ko K T, Kim B S, Jang B G, Ok J M, Lee J, Jo Y J, Kang W, Shim J H, Kim C, Yeom H W, Min B I, Yang B J, and Kim J S 2018 Nat. Mater. 17 794 |
| [10] | Deng Y, Yu Y, Song Y, Zhang J, Wang N Z, Sun Z, Yi Y, Wu Y Z, Wu S, Zhu J, Wang J, Chen X H, and Zhang Y 2018 Nature 563 94 |
| [11] | Guo J J, Xia Q L, Wang X G, Nie Y Z, Xiong R, and Guo G H 2021 J. Magn. Magn. Mater. 527 167719 |
| [12] | Tan C, Lee J, Jung S G, Park T, Albarakati S, Partridge J, Field M R, McCulloch D G, Wang L, and Lee C 2018 Nat. Commun. 9 1554 |
| [13] | Zhuang H L, Kent P R C, and Henning R G 2016 Phys. Rev. B 93 134407 |
| [14] | Cai L, Yu C, Liu L, Xia W, Zhou H A, Zhao L, Dong Y, Xu T, Wang Z, Guo Y, Zhao Y, Zhang J, Yang L, Yang L, and Jiang W 2020 Appl. Phys. Lett. 117 192401 |
| [15] | Chen B, Yang J H, Wang H D, Imai M, Ohta H, Michioka C, Yoshimura K, and Fang M H 2013 J. Phys. Soc. Jpn. 82 124711 |
| [16] | Wang Y, Xian C, Wang J, Liu B, Ling L, Zhang L, Cao L, Qu Z, and Xiong Y 2017 Phys. Rev. B 96 134428 |
| [17] | Xu J, Phelan W A, and Chien C L 2019 Nano Lett. 19 8250 |
| [18] | You Y, Gong Y, Li H, Li Z, Zhu M, Tang J, Liu E, Yao Y, Xu G, Xu F, and Wang W 2019 Phys. Rev. B 100 134441 |
| [19] | Song T, Cai X, Tu M W Y, Zhang X, Huang B, Wilson N P, Seyler K L, Zhu L, Taniguchi T, Watanabe K, McGuire M A, Cobden D H, Xiao D, Yao W, and Xu X 2018 Science 360 1214 |
| [20] | Zhang Y, Lu H, Zhu X, Tan S, Feng W, Liu Q, Zhang W, Chen Q, Liu Y, Luo X, Xie D, Luo L, Zhang Z, and Lai X 2018 Sci. Adv. 4 eaao6791 |
| [21] | Yang M, Li Q, Chopdekar R V, Dhall R, Turner J, Carlström J D, Ophus C, Klewe C, Shafer P, N'Diaye A T, Choi J W, Chen G, Wu Y Z, Hwang C, Wang F, and Qiu Z Q 2020 Sci. Adv. 6 eabb5157 |
| [22] | Ding B, Li Z, Xu G, Li H, Hou Z, Liu E, Xi X, Xu F, Yao Y, and Wang W 2020 Nano Lett. 20 868 |
| [23] | Nguyen G D, Lee J, Berlijn T, Zou Q, Hus S M, Park J, Gai Z, Lee C, and Li A P 2018 Phys. Rev. B 97 014425 |
| [24] | Li Q, Yang M, Gong C, Chopdekar R V, N'Diaye A T, Turner J, Chen G, Scholl A, Shafer P, Arenholz E, Schmid A K, Wang S, Liu K, Gao N, Admasu A S, Cheong S W, Hwang C, Li J, Wang F, Zhang X, and Qiu Z 2018 Nano Lett. 18 5974 |
| [25] | Lachman E, Murphy R A, Maksimovic N, Kealhofer R, Haley S, McDonald R D, Long J R, and Analytis J G 2020 Nat. Commun. 11 560 |
| [26] | Hayashi M, Kim J, Yamanouchi M, and Ohno H 2014 Phys. Rev. B 89 144425 |
| [27] | Vlietstra N, Shan J, Van Wees B, Isasa M, Casanova F, and Youssef J B 2014 Phys. Rev. B 90 174436 |
| [28] | Avci C O, Garello K, Gabureac M, Ghosh A, Fuhrer A, Alvarado S F, and Gambardella P 2014 Phys. Rev. B 90 224427 |
| [29] | MacNeill D, Stiehl G M, Guimaraes M H, Reynolds N D, Buhrman R A, and Ralph D C 2017 Phys. Rev. B 96 054450 |
| [30] | Chen Y, Roy D, Cogulu E, Chang H, Wu M, and Kent A D 2018 Appl. Phys. Lett. 113 202403 |
| [31] | Schippers C F, Swagten H J, and Guimarães M H 2020 Phys. Rev. Mater. 4 084007 |
| [32] | Feringa F, Bauer G E W, and van Wees B J 2022 arXiv:2201.13241 [cond-mat.mes-hall] |
| [33] | Fiebig M, Pavlov V V, and Pisarev R V 2005 J. Opt. Soc. Am. B 22 96 |
| [34] | Murzina T V, Lazareva K A, Shalygina E E, Kolmychek I A, Karashtin E A, Gusev N S, and Fraerman A A 2018 arXiv:1812.03922 [cond-mat.mes-hall] |
| [35] | Krutyanskiy V L, Kolmychek I A, Gribkov B A, Karashtin E A, Skorohodov E V, and Murzina T V 2013 Phys. Rev. B 88 094424 |
| [36] | Juge R, Sisodia N, Larrañaga J U, Zhang Q, Pham V T, Rana K G, Sarpi B, Mille N, Stanescu S, Belkhou R, Mawass M A, Marinkovic N N, Kronast F, Weigand M, Gräfe J, Wintz S, Finizio S, Raabe J, Aballe L, Foerster M, Belmeguenai M, Prejbeanu B L, Shaw J M, Nembach H T, Ranno L, Gaudin G, and Boulle O 2021 arXiv:2111.11878 [cond-mat.mtrl-sci] |
| [37] | Sodemann I and Fu L 2015 Phys. Rev. Lett. 115 216806 |
| [38] | Deyo E, Golub L E, Ivchenko E L, and Spivak B 2009 arXiv:0904.1917 [cond-mat.mes-hall] |
| [39] | Golub L E, Ivchenko E L, and Spivak B Z 2017 JETP Lett. 105 782 |
| [40] | Moore J E and Orenstein J 2010 Phys. Rev. Lett. 105 026805 |
| [41] | Low T, Jiang Y, and Guinea F 2015 Phys. Rev. B 92 235447 |
| [42] | Zhang Y, van den Brink J, Felser C, and Yan B 2018 2D Mater. 5 044001 |
| [43] | Du Z Z, Wang C M, Lu H Z, and Xie X C 2018 Phys. Rev. Lett. 121 266601 |
| [44] | Du Z Z, Wang C M, Li S, Lu H Z, and Xie X C 2019 Nat. Commun. 10 3047 |
| [45] | Xiao C, Du Z Z, and Niu Q 2019 Phys. Rev. B 100 165422 |
| [46] | Nandy S and Sodemann I 2019 Phys. Rev. B 100 195117 |
| [47] | Wang H and Qian X F 2019 npj Comput. Mater. 5 119 |
| [48] | Zhou B T, Zhang C P, and Law K T 2020 Phys. Rev. Appl. 13 024053 |
| [49] | Rostami H and Jurićić V 2020 Phys. Rev. Res. 2 013069 |
| [50] | Shao D F, Zhang S H, Gurung G, Yang W, and Tsymbal E Y 2020 Phys. Rev. Lett. 124 067203 |
| [51] | Singh S, Kim J, Rabe K M, and Vanderbilt D 2020 Phys. Rev. Lett. 125 046402 |
| [52] | Tu M W Y, Li C, Yu H, and Yao W 2020 2D Mater. 7 045004 |
| [53] | Du Z Z, Wang C M, Sun H P, Lu H Z, and Xie X C 2020 arXiv:2004.09742 [cond-mat.mes-hall] |
| [54] | Ma Q, Xu S Y, Shen H, MacNeill D, Fatemi V, Chang T R, Valdivia A M M, Wu S, Du Z, Hsu C H, Fang S, Gibson Q D, Watanabe K, Taniguchi T, Cava R J, Kaxiras E, Lu H Z, Lin H, Fu L, Gedik N, and Herrero P J 2019 Nature 565 337 |
| [55] | Kang K, Li T, Sohn E, Shan J, and Mak K F 2019 Nat. Mater. 18 324 |
| [56] | Shvetsov O O, Esin V D, Timonina A V, Kolesnikov N N, and Deviatov E V 2019 JETP Lett. 109 715 |
| [57] | Tiwari A, Chen F, Zhong S, Drueke E, Koo J, Kaczmarek A, Xiao C, Gao J, Luo X, Niu Q, Sun Y, Yan B, Zhao L, and Tsen A W 2021 Nat. Commun. 12 2049 |
| [58] | Deiseroth H J, Aleksandrov K, Reiner C, Kienle L, Kremer R K, and Inorg E J 2006 Eur. J. Inorg. Chem. 2006 1561 |
| [59] | Shvetsov O O, Barash Y S, Timonina A V, Kolesnikov N N, and Deviatov E V 2022 JETP Lett. 115 267 |
| [60] | Shvetsov O O, Esin V D, Timonina A V, Kolesnikov N N, and Deviatov E V 2019 Phys. Rev. B 99 125305 |
| [61] | Shvetsov O O, Esin V D, Timonina A V, Kolesnikov N N, and Deviatov E V 2019 Europhys. Lett. 127 57002 |
| [62] | Orlova N N, Ryshkov N S, Zagitova A A, Kulakov V I, Timonina A V, Borisenko D N, Kolesnikov N N, and Deviatov E V 2020 Phys. Rev. B 101 235316 |
| [63] | Esin V D, Borisenko D N, Timonina A V, Kolesnikov N N, and Deviatov E V 2020 Phys. Rev. B 101 155309 |
| [64] | Mandal D, Das K, and Agarwal A 2022 arXiv:2201.02505 [cond-mat.mes-hall] |
| [65] | Zyuzin A A and Zyuzin A Y 2017 Phys. Rev. B 95 085127 |
| [66] | He P, Zhang S S L, Zhu D, Shi S, Heinonen O G, Vignale G, and Yang H 2019 Phys. Rev. Lett. 123 016801 |
| [67] | Esin V D, Timonina A V, Kolesnikov N N, and Deviatov E V 2020 JETP Lett. 111 685 |
| [68] | Isobe H, Xu S Y, and Fu L 2020 Sci. Adv. 6 eaay2497 |
| [69] | Grigorieva I V, Escoffier W, Richardson J, Vinnikov L Y, Dubonos S, and Oboznov V 2006 Phys. Rev. Lett. 96 077005 |
| [70] | Eskildsen M R, Vinnikov L Y, Blasius T D, Veshchunov I S, Artemova T M, Densmore J M, Dewhurst C D, Ni N, Kreyssig A, Bud'ko S L, Canfield P C, and Goldman A I 2009 Phys. Rev. B 79 100501(R) |
| [71] | Avakyants A A, Orlova N N, Timonina A V, Kolesnikov N N, and Deviatov E V 2022 arXiv:2206.03357 [cond-mat.mes-hall] |
| [72] | Dzyaloshinskii I 1958 J. Phys. Chem. Solids 4 241 |
| [73] | Li R H, Heinonen O G, Burkov A A, and Zhang S S L 2021 Phys. Rev. B 103 045105 |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
