Amoroso, Danila ; Université de Liège - ULiège > Complex and Entangled Systems from Atoms to Materials (CESAM) ; Université de Liège - ULiège > Département de physique > Physique des matériaux et nanostructures ; Consiglio Nazionale delle Ricerche (CNR-SPIN) > CNR-SPIN
Picozzi, Silvia
Barone, Paolo
Stengel, Massimiliano
Language :
English
Title :
Curved Magnetism in CrI3
Publication date :
April 2022
Journal title :
Physical Review Letters
ISSN :
0031-9007
eISSN :
1079-7114
Publisher :
American Physical Society, New York, United States - New York
P. Zubko, G. Catalan, and A. K. Tagantsev, Annu. Rev. Mater. Res. 43, 387 (2013). ARMRCU 1531-7331 10.1146/annurev-matsci-071312-121634
R. Streubel, P. Fischer, F. Kronast, V. P. Kravchuk, D. D. Sheka, Y. Gaididei, O. G. Schmidt, and D. Makarov, J. Phys. D 49, 363001 (2016). JPAPBE 0022-3727 10.1088/0022-3727/49/36/363001
D. D. Sheka, Appl. Phys. Lett. 118, 230502 (2021). APPLAB 0003-6951 10.1063/5.0048891
H. Lu, C.-W. Bark, D. Esque de los Ojos, J. Alcala, C. B. Eom, G. Catalan, and A. Gruverman, Science 336, 59 (2012). SCIEAS 0036-8075 10.1126/science.1218693
U. K. Bhaskar, N. Banerjee, A. Abdollahi, Z. Wang, D. G. Schlom, G. Rijnders, and G. Catalan, Nat. Nanotechnol. 11, 263 (2016). NNAABX 1748-3387 10.1038/nnano.2015.260
L. Shu, S. Ke, L. Fei, W. Huang, Z. Wang, J. Gong, X. Jiang, L. Wang, F. Li, S. Lei, Z. Rao, Y. Zhou, R.-K. Zheng, X. Yao, Y. Wang, M. Stengel, and G. Catalan, Nat. Mater. 19, 605 (2020). NMAACR 1476-1122 10.1038/s41563-020-0659-y
A. Fasolino, J. H. Los, and M. I. Katsnelson, Nat. Mater. 6, 858 (2007). NMAACR 1476-1122 10.1038/nmat2011
O. M. Volkov, A. Kákay, F. Kronast, I. Mönch, M.-A. Mawass, J. Fassbender, and D. Makarov, Phys. Rev. Lett. 123, 077201 (2019). PRLTAO 0031-9007 10.1103/PhysRevLett.123.077201
R. Hertel, SPIN 03, 1340009 (2013). 10.1142/S2010324713400092
P. Gentile, M. Cuoco, and C. Ortix, SPIN 03, 1340002 (2013). 10.1142/S201032471340002X
P. Gentile, M. Cuoco, and C. Ortix, Phys. Rev. Lett. 115, 256801 (2015). PRLTAO 0031-9007 10.1103/PhysRevLett.115.256801
A. Pyatakov, A. Sergeev, F. Mikailzade, and A. Zvezdin, J. Magn. Magn. Mater. 383, 255 (2015), selected papers from the sixth Moscow International Symposium on Magnetism (MISM-2014). JMMMDC 0304-8853 10.1016/j.jmmm.2014.11.035
J. A. Otálora, M. Yan, H. Schultheiss, R. Hertel, and A. Kákay, Phys. Rev. Lett. 117, 227203 (2016). PRLTAO 0031-9007 10.1103/PhysRevLett.117.227203
O. V. Pylypovskyi, V. P. Kravchuk, D. D. Sheka, D. Makarov, O. G. Schmidt, and Y. Gaididei, Phys. Rev. Lett. 114, 197204 (2015). PRLTAO 0031-9007 10.1103/PhysRevLett.114.197204
Y. Gaididei, V. P. Kravchuk, and D. D. Sheka, Phys. Rev. Lett. 112, 257203 (2014). PRLTAO 0031-9007 10.1103/PhysRevLett.112.257203
D. D. Sheka, V. P. Kravchuk, and Y. Gaididei, J. Phys. A 48, 125202 (2015). JPAMB5 1751-8113 10.1088/1751-8113/48/12/125202
Y. Zhang, J. Liu, Y. Dong, S. Wu, J. Zhang, J. Wang, J. Lu, A. Rückriegel, H. Wang, R. Duine, H. Yu, Z. Luo, K. Shen, and J. Zhang, Phys. Rev. Lett. 127, 117204 (2021). PRLTAO 0031-9007 10.1103/PhysRevLett.127.117204
A. Fernández-Pacheco, R. Streubel, O. Fruchart, R. Hertel, P. Fischer, and R. P. Cowburn, Nat. Commun. 8, 15756 (2017). NCAOBW 2041-1723 10.1038/ncomms15756
C. Donnelly, M. Guizar-Sicairos, V. Scagnoli, S. Gliga, M. Holler, J. Raabe, and L. J. Heyderman, Nature (London) 547, 328 (2017). NATUAS 0028-0836 10.1038/nature23006
M. Heide, G. Bihlmayer, and S. Blügel, Physica (Amsterdam) 404B, 2678 (2009). PHYBE3 0921-4526 10.1016/j.physb.2009.06.070
C. Xu, J. Feng, H. Xiang, and L. Bellaiche, npj Comput. Mater. 4, 57 (2018). 2057-3960 10.1038/s41524-018-0115-6
D. Amoroso, P. Barone, and S. Picozzi, Nat. Commun. 11, 5784 (2020). NCAOBW 2041-1723 10.1038/s41467-020-19535-w
S. Tiwari, M. L. Van de Put, B. Sorée, and W. G. Vandenberghe, npj 2D Mater. Appl. 5, 54 (2021). 10.1038/s41699-021-00233-0
B. Huang, G. Clark, E. Navarro-Moratalla, D. R. Klein, R. Cheng, K. L. Seyler, D. Zhong, E. Schmidgall, M. A. McGuire, D. H. Cobden, W. Yao, D. Xiao, P. Jarillo-Herrero, and X. Xu, Nature (London) 546, 270 (2017). NATUAS 0028-0836 10.1038/nature22391
C. Gong, L. Li, Z. Li, H. Ji, A. Stern, Y. Xia, T. Cao, W. Bao, C. Wang, Y. Wang, Z. Q. Qiu, R. J. Cava, S. G. Louie, J. Xia, and X. Zhang, Nature (London) 546, 265 (2017). NATUAS 0028-0836 10.1038/nature22060
M. A. McGuire, Crystals 7, 121 (2017). CRYSBC 2073-4352 10.3390/cryst7050121
K. S. Burch, D. Mandrus, and J.-G. Park, Nature (London) 563, 47 (2018). NATUAS 0028-0836 10.1038/s41586-018-0631-z
T. Song, X. Cai, M. W.-Y. Tu, X. Zhang, B. Huang, N. P. Wilson, K. L. Seyler, L. Zhu, T. Taniguchi, K. Watanabe, M. A. McGuire, D. H. Cobden, D. Xiao, W. Yao, and X. Xu, Science 360, 1214 (2018). SCIEAS 0036-8075 10.1126/science.aar4851
M.-G. Han, J. A. Garlow, Y. Liu, H. Zhang, J. Li, D. DiMarzio, M. W. Knight, C. Petrovic, D. Jariwala, and Y. Zhu, Nano Lett. 19, 7859 (2019). NALEFD 1530-6984 10.1021/acs.nanolett.9b02849
X. Yao, Y. Wang, and S. Dong, Int. J. Mod. Phys. B 35, 2130004 (2021). IJPBEV 0217-9792 10.1142/S0217979221300048
A. V. Kuklin, M. A. Visotin, W. Baek, and P. V. Avramov, Physica (Amsterdam) 123E, 114205 (2020). PELNFM 1386-9477 10.1016/j.physe.2020.114205
W. Shi, Y. Guo, Z. Zhang, and W. Guo, J. Phys. Chem. C 123, 24988 (2019). JPCCCK 1932-7447 10.1021/acs.jpcc.9b08445
J. L. Lado and J. Fernández-Rossier, 2D Mater. 4, 035002 (2017). DMATB7 2053-1583 10.1088/2053-1583/aa75ed
P. E. Blöchl, Phys. Rev. B 50, 17953 (1994). PRBMDO 0163-1829 10.1103/PhysRevB.50.17953
G. Kresse and D. Joubert, Phys. Rev. B 59, 1758 (1999). PRBMDO 0163-1829 10.1103/PhysRevB.59.1758
G. Kresse and J. Furthmüller, Comput. Mater. Sci. 6, 15 (1996). CMMSEM 0927-0256 10.1016/0927-0256(96)00008-0
G. Kresse and J. Hafner, Phys. Rev. B 49, 14251 (1994). PRBMDO 0163-1829 10.1103/PhysRevB.49.14251
G. Kresse and J. Hafner, Phys. Rev. B 47, 558 (1993). PRBMDO 0163-1829 10.1103/PhysRevB.47.558
S. L. Dudarev, G. A. Botton, S. Y. Savrasov, C. J. Humphreys, and A. P. Sutton, Phys. Rev. B 57, 1505 (1998). PRBMDO 0163-1829 10.1103/PhysRevB.57.1505
The value of (Equation presented) and other computational settings are chosen in accordance with Ref. [21].
Using (Equation presented)-points changes the magnetic anisotropy of the monolayer by less than 3%.
M. Dresselhaus, G. Dresselhaus, and R. Saito, Carbon 33, 883 (1995). CRBNAH 0008-6223 10.1016/0008-6223(95)00017-8
D. Hobbs, G. Kresse, and J. Hafner, Phys. Rev. B 62, 11556 (2000). PRBMDO 0163-1829 10.1103/PhysRevB.62.11556
P.-W. Ma and S. L. Dudarev, Phys. Rev. B 91, 054420 (2015). PRBMDO 1098-0121 10.1103/PhysRevB.91.054420
See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevLett.128.177202 for a detailed discussion about the fitting procedure for (Equation presented) and (Equation presented), calculations without constraints on the spin directions and confirmations that the energy differences studied are independent of the constraint value, comparison to other continuum models, and discussion of stationary states of the continuum energy and related magnetic domain walls. Additionally contains Refs. [47-49].
O. Besbes, S. Nikolaev, N. Meskini, and I. Solovyev, Phys. Rev. B 99, 104432 (2019). PRBMDO 2469-9950 10.1103/PhysRevB.99.104432
I. V. Kashin, V. V. Mazurenko, M. I. Katsnelson, and A. N. Rudenko, 2D Mater. 7, 025036 (2020). DMATB7 2053-1583 10.1088/2053-1583/ab72d8
S. Grytsiuk, M. Hoffmann, J.-P. Hanke, P. Mavropoulos, Y. Mokrousov, G. Bihlmayer, and S. Blügel, Phys. Rev. B 100, 214406 (2019). PRBMDO 2469-9950 10.1103/PhysRevB.100.214406
S. Kumar and P. Suryanarayana, Nanotechnology 31, 43LT01 (2020). NNOTER 0957-4484 10.1088/1361-6528/aba2a2
Note that (Equation presented), in addition to the single-ion anisotropy, also accounts for anisotropic symmetric exchange, whose importance in (Equation presented) was recently pointed out. [21].
We consider (Equation presented) as a constant function of the axial (Equation presented) coordinate.
Considering an area of (Equation presented).
S. I. Vishkayi, Z. Torbatian, A. Qaiumzadeh, and R. Asgari, Phys. Rev. Mater. 4, 094004 (2020). PRMHAR 2475-9953 10.1103/PhysRevMaterials.4.094004
Y. O. Kvashnin, A. Bergman, A. I. Lichtenstein, and M. I. Katsnelson, Phys. Rev. B 102, 115162 (2020). PRBMDO 2469-9950 10.1103/PhysRevB.102.115162
The value of (Equation presented) in brackets was obtained from spin cycloid energies of the flat monolayer, showing a moderate numerical discrepancy to the value fitted including the curved systems.
A. S. Banerjee and P. Suryanarayana, J. Mech. Phys. Solids 96, 605 (2016). JMPSA8 0022-5096 10.1016/j.jmps.2016.08.007
M. Stengel and D. Vanderbilt, First-principles theory of flexoelectricity, in Flexoelectricity in Solids (World Scientific Publishing Co., Singapore, 2016), Chap. Chapter 2, pp. 31-110.
