Engineering magnetic domain wall energies in BiFeO3 via epitaxial strain: A route to assess skyrmionic stabilities in multiferroics from first principles
Antiferromagnetics; Domain wall energy; Energy; Epitaxial strain; Ferroelectric property; First principles; Magnetic domain walls; Magnetic interactions; Multiferroics; Perovskite oxides; Electronic, Optical and Magnetic Materials; Condensed Matter Physics
Abstract :
[en] Epitaxial strain has emerged as a powerful tool to tune magnetic and ferroelectric properties in functional materials such as in multiferroic perovskite oxides. Here, we use first-principles calculations to explore the evolution of magnetic interactions in the antiferromagnetic (AFM) multiferroic BiFeO3 (BFO), one of the most promising multiferroics for future technology. The epitaxial strain in BFO(001) oriented film is varied between É xx,yyâ [-2%,+2%]. We find that both strengths of the exchange interaction and Dzyaloshinskii-Moriya interaction decrease linearly from compressive to tensile strain whereas the uniaxial magnetocrystalline anisotropy follows a parabolic behavior which lifts the energy degeneracy of the (111) easy plane of bulk BFO. From the trends of the magnetic interactions we can explain the destruction of cycloidal order in compressive strain as observed in experiments due to the increasing anisotropy energy. For tensile strain, we predict that the ground state remains unchanged as a function of strain. By using the domain wall energy, we envision the region where isolated chiral magnetic textures might occur as a function of strain, i.e., where the collinear AFM and the spin spiral energies are equal. This transition between-1.5 and-0.5% of strain should allow topologically stable magnetic states such as antiferromagnetic skyrmions and/or merons to occur. Hence, our paper should trigger experimental and theoretical investigations in this range of strain.
Research Center/Unit :
Q-Mat
Disciplines :
Physics
Author, co-author :
Meyer, Sebastian ; Université de Liège - ULiège > Complex and Entangled Systems from Atoms to Materials (CESAM) ; Fonds de la Recherche Scientifique, Bruxelles, Belgium
Xu, Bin ; Jiangsu Key Laboratory of Frontier Material Physics and Devices, School of Physical Science and Technology, Soochow University, Suzhou, China ; Smart Ferroic Materials Center, Physics Department and Institute for Nanoscience and Engineering, University of Arkansas, Fayetteville, United States
Bellaiche, Laurent ; Smart Ferroic Materials Center, Physics Department and Institute for Nanoscience and Engineering, University of Arkansas, Fayetteville, United States
Dupé, Bertrand ; Université de Liège - ULiège > Département de physique > Physique des matériaux et nanostructures ; Fonds de la Recherche Scientifique, Bruxelles, Belgium
Language :
English
Title :
Engineering magnetic domain wall energies in BiFeO3 via epitaxial strain: A route to assess skyrmionic stabilities in multiferroics from first principles
Publication date :
May 2024
Journal title :
Physical Review. B
ISSN :
2469-9950
eISSN :
2469-9969
Publisher :
American Physical Society
Volume :
109
Issue :
18
Peer reviewed :
Peer Reviewed verified by ORBi
Tags :
CÉCI : Consortium des Équipements de Calcul Intensif
H2020 - 964931 - TSAR - Topological Solitons in Antiferroics
Funders :
NSCF - National Natural Science Foundation of China [CN] Soochow University [TW] DARPA - Defense Advanced Research Projects Agency [US-VA] EU - European Union [BE] ARO - Army Research Office [US-WA] USDOD - United States Department of Defense [US-DC] F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]
Funding text :
B.D. and S.M. thank Prof. Philippe Ghosez, Louis Bastogne, Dr. Subhadeep Bandyopadhyay, Dr. He Xu, and Prof. Matthieu J. Verstraete for helpful discussions. This work is supported by the National Natural Science Foundation of China under Grant No. 12074277, the startup fund from Soochow University, and Priority Academic Program Development of Jiangsu Higher Education Institutions. S.M., B.D., and L.B. acknowledge DARPA Grant No. HR0011727183-D18AP00010 (TEE Program) and the European Union's Horizon 2020 research and innovation program under Grant No. 964931 (TSAR). L.B. also thanks the ARO for Grant No. W911NF-21-1-0113, the Grant MURI ETHOS W911NF-21-2-0162 from the Army Research Office (ARO), and the Vannevar Bush Faculty Fellowship (VBFF) Grant No. N00014-20-1-2834 from the Department of Defense. Computing time was provided by ARCHER and ARCHER2 based in the United Kingdom at National Supercomputing Service with support from the PRACE aisbl, the Consortium d'\u00C9quipements de Calcul Intensif (FRS-FNRS Belgium GA 2.5020.11), and the LUMI CECI/Belgium for awarding this project access to the LUMI supercomputer, owned by the EuroHPC Joint Undertaking, hosted by CSC (Finland) and the LUMI consortium through LUMI CECI/Belgium, ULiege-NANOMAT-SKYRM-1. S.M. is a Postdoctoral Researcher (CR) of the Fonds de la Recherche Scientifique - FNRS (F.R.S.-FNRS no. CR 1.B.324.24F). B.D. is a Research Associate (CQ) of the Fonds de la Recherche Scientifique (F.R.S.\u2013FNRS).
A. Bogdanov and D. A. Yablonskii, Zh. Eksp. Teor. Fiz. 95, 178 (1989)
A. Bogdanov and D. A. Yablonskii, [Sov. Phys. JETP 68, 101 (1989)].
A. Bogdanov and A. Hubert, J. Magn. Magn. Mater. 138, 255 (1994) 0304-8853 10.1016/0304-8853(94)90046-9.
S. Mühlbauer, B. Binz, F. Jonietz, C. Pfleiderer, A. Rosch, A. Neubauer, R. Georgii, and P. Boni, Science 323, 915 (2009) 0036-8075 10.1126/science.1166767.
X. Z. Yu, Y. Onose, N. Kanazawa, J. H. Park, J. H. Han, Y. Matsui, N. Nagaosa, and Y. Tokura, Nature (London) 465, 901 (2010) 0028-0836 10.1038/nature09124.
N. S. Kiselev, A. N. Bogdanov, R. Schäfer, and U. K. Rößler, J. Phys. D 44, 392001 (2011) 0022-3727 10.1088/0022-3727/44/39/392001.
A. Fert, V. Cros, and J. Sampaio, Nat. Nanotechnol. 8, 152 (2013) 1748-3387 10.1038/nnano.2013.29.
S. Parkin and S.-H. Yang, Nat. Nanotechnol. 10, 195 (2015) 1748-3387 10.1038/nnano.2015.41.
C. Back, V. Cros, H. Ebert, K. Everschor-Sitte, A. Fert, M. Garst, T. Ma, S. Mankovsky, T. L. Monchesky, M. Mostovoy, N. Nagaosa, S. S. P. Parkin, C. Pfleiderer, N. Reyren, A. Rosch, Y. Taguchi, Y. Tokura, K. von Bergmann, and J. Zang, J. Phys. D 53, 363001 (2020) 0022-3727 10.1088/1361-6463/ab8418.
T. Jungwirth, X. Marti, P. Wadley, and J. Wunderlich, Nat. Nanotechnol. 11, 231 (2016) 1748-3387 10.1038/nnano.2016.18.
X. Zhang, Y. Zhou, and M. Ezawa, Sci. Rep. 6, 24795 (2016) 2045-2322 10.1038/srep24795.
J. Barker and O. A. Tretiakov, Phys. Rev. Lett. 116, 147203 (2016) 0031-9007 10.1103/PhysRevLett.116.147203.
T. Jungwirth, J. Sinova, A. Manchon, X. Marti, J. Wunderlich, and C. Felser, Nat. Phys. 14, 200 (2018) 1745-2473 10.1038/s41567-018-0063-6.
N. Romming, C. Hanneken, M. Menzel, J. E. Bickel, B. Wolter, K. von Bergmann, A. Kubetzka, and R. Wiesendanger, Science 341, 636 (2013) 0036-8075 10.1126/science.1240573.
C. Moreau-Luchaire, C. Moutafis, N. Reyren, J. Sampaio, C. A. F. Vaz, N. Van Horne, K. Bouzehouane, K. Garcia, C. Deranlot, P. Warnicke, P. Wohlhüter, J.-M. George, M. Weigand, J. Raabe, V. Cros, and A. Fert, Nat. Nanotechnol. 11, 444 (2016) 1748-3387 10.1038/nnano.2015.313.
A. Soumyanarayanan, M. Raju, A. L. Gonzalez Oyarce, A. K. C. Tan, M.-Y. Im, A. P. Petrović, P. Ho, K. H. Khoo, M. Tran, C. K. Gan, F. Ernult, and C. Panagopoulos, Nat. Mater. 16, 898 (2017) 1476-1122 10.1038/nmat4934.
O. Boulle, J. Vogel, H. Yang, S. Pizzini, D. de Souza Chaves, A. Locatelli, T. O. Menteş, A. Sala, L. D. Buda-Prejbeanu, O. Klein, M. Belmeguenai, Y. Roussigné, A. Stashkevich, S. M. Chérif, L. Aballe, M. Foerster, M. Chshiev, S. Auffret, I. M. Miron, and G. Gaudin, Nat. Nanotechnol. 11, 449 (2016) 1748-3387 10.1038/nnano.2015.315.
M. Hervé, B. Dupé, R. Lopes, M. Böttcher, M. D. Martins, T. Balashov, L. Gerhard, J. Sinova, and W. Wulfhekel, Nat. Commun. 9, 1015 (2018) 2041-1723 10.1038/s41467-018-03240-w.
S. D. Pollard, J. A. Garlow, J. Yu, Z. Wang, Y. Zhu, and H. Yang, Nat. Commun. 8, 14761 (2017) 2041-1723 10.1038/ncomms14761.
A. J. Hatt, N. A. Spaldin, and C. Ederer, Phys. Rev. B 81, 054109 (2010) 1098-0121 10.1103/PhysRevB.81.054109.
B. Dupé, S. Prosandeev, G. Geneste, B. Dkhil, and L. Bellaiche, Phys. Rev. Lett. 106, 237601 (2011) 0031-9007 10.1103/PhysRevLett.106.237601.
D. Sando, A. Agbelele, D. Rahmedov, J. Liu, P. Rovillain, C. Toulouse, I. C. Infante, A. P. Pyatakov, S. Fusil, E. Jacquet, C. Carrétéro, C. Deranlot, S. Lisenkov, D. Wang, J.-M. L. Breton, M. Cazayous, A. Sacuto, J. Juraszek, A. K. Zvezdin, L. Bellaiche, Nat. Mater. 12, 641 (2013) 1476-1122 10.1038/nmat3629.
J. M. Hu, T. Yang, and L. Q. Chen, npj Comput. Mater. 4, 62 (2018) 2057-3960 10.1038/s41524-018-0119-2.
J. Wang, Y. Shi, and M. Kamlah, Phys. Rev. B 97, 024429 (2018) 2469-9950 10.1103/PhysRevB.97.024429.
S. Budhathoki, A. Sapkota, K. M. Law, S. Ranjit, B. Nepal, B. D. Hoskins, A. S. Thind, A. Y. Borisevich, M. E. Jamer, T. J. Anderson, A. D. Koehler, K. D. Hobart, G. M. Stephen, D. Heiman, T. Mewes, R. Mishra, J. C. Gallagher, and A. J. Hauser, Phys. Rev. B 101, 220405 (R) (2020) 2469-9950 10.1103/PhysRevB.101.220405.
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) 0031-9007 10.1103/PhysRevLett.127.117204.
V. Govinden, P. Tong, X. Guo, Q. Zhang, S. Mantri, M. M. Seyfouri, S. Prokhorenko, Y. Nahas, Y. Wu, L. Bellaiche, T. Sun, H. Tian, Z. Hong, N. Valanoor, and D. Sando, Nat. Commun. 14, 4178 (2023) 2041-1723 10.1038/s41467-023-39841-3.
B. W. Qiang, N. Togashi, S. Momose, T. Wada, T. Hajiri, M. Kuwahara, and H. Asano, Appl. Phys. Lett. 117, 142401 (2020) 0003-6951 10.1063/5.0024071.
P. Hemme, J.-C. Philippe, A. Medeiros, A. Alekhin, S. Houver, Y. Gallais, A. Sacuto, A. Forget, D. Colson, S. Mantri, B. Xu, L. Bellaiche, and M. Cazayous, Phys. Rev. Lett. 131, 116801 (2023) 0031-9007 10.1103/PhysRevLett.131.116801.
P. Dufour, A. Abdelsamie, J. Fischer, A. Finco, A. Haykal, M. F. Sarott, S. Varotto, C. Carrétéro, S. Collin, F. Godel, N. Jaouen, M. Viret, M. Trassin, K. Bouzehouane, V. Jacques, J.-Y. Chauleau, S. Fusil, and V. Garcia, Nano Lett. 23, 9073 (2023) 1530-6984 10.1021/acs.nanolett.3c02875.
Y. E. Roginskaya, Y. Y. Tomashpol'SkiÇ , Y. N. Venevtsev, V. M. Petrov, and G. S. Zhdanov, Sov. Phys. JETP 23, 47 (1966).
J. B. Neaton, C. Ederer, U. V. Waghmare, N. A. Spaldin, and K. M. Rabe, Phys. Rev. B 71, 014113 (2005) 1098-0121 10.1103/PhysRevB.71.014113.
P. Ravindran, R. Vidya, A. Kjekshus, H. Fjellvåg, and O. Eriksson, Phys. Rev. B 74, 224412 (2006) 1098-0121 10.1103/PhysRevB.74.224412.
I. A. Kornev, S. Lisenkov, R. Haumont, B. Dkhil, and L. Bellaiche, Phys. Rev. Lett. 99, 227602 (2007) 0031-9007 10.1103/PhysRevLett.99.227602.
R. Haumont, I. A. Kornev, S. Lisenkov, L. Bellaiche, J. Kreisel, and B. Dkhil, Phys. Rev. B 78, 134108 (2008) 1098-0121 10.1103/PhysRevB.78.134108.
I. Sosnowska, T. P. Neumaier, and E. Steichele, J. Phys. C 15, 4835 (1982) 0022-3719 10.1088/0022-3719/15/23/020.
I. Sosnowska, R. Przeniosło, P. Fischer, and V. Murashov, J. Magn. Magn. Mater. 160, 384 (1996) 0304-8853 10.1016/0304-8853(96)00240-5.
F. Bai, J. Wang, M. Wuttig, J. Li, N. Wang, A. P. Pyatakov, A. K. Zvezdin, L. E. Cross, and D. Viehland, Appl. Phys. Lett. 86, 032511 (2005) 0003-6951 10.1063/1.1851612.
H. Béa, M. Bibes, S. Petit, J. Kreisel, and A. Barthélémy, Philos. Mag. Lett. 87, 165 (2007) 0950-0839 10.1080/09500830701235802.
T. Zhao, A. Scholl, F. Zavaliche, K. Lee, M. Barry, A. Doran, M. P. Cruz, Y. H. Chu, C. Ederer, N. A. Spaldin, R. R. Das, D. M. Kim, S. H. Baek, C. B. Eom, and R. Ramesh, Nat. Mater. 5, 823 (2006) 1476-1122 10.1038/nmat1731.
W. Ratcliff II, D. Kan, W. Chen, S. Watson, S. Chi, R. Erwin, G. J. McIntyre, S. C. Capelli, and I. Takeuchi, Adv. Funct. Mater. 21, 1567 (2011) 1616-301X 10.1002/adfm.201002125.
www.abinit.org.
X. Gonze, B. Amadon, G. Antonius, F. Arnardi, L. Baguet, J.-M. Beuken, J. Bieder, F. Bottin, J. Bouchet, E. Bousquet, N. Brouwer, F. Bruneval, G. Brunin, T. Cavignac, J.-B. Charraud, W. Chen, M. Côté, S. Cottenier, J. Denier, G. Geneste, Comput. Phys. Commun. 248, 107042 (2020) 0010-4655 10.1016/j.cpc.2019.107042.
P. E. Blöchl, Phys. Rev. B 50, 17953 (1994) 0163-1829 10.1103/PhysRevB.50.17953.
C. Paillard, B. Xu, B. Dkhil, G. Geneste, and L. Bellaiche, Phys. Rev. Lett. 116, 247401 (2016) 0031-9007 10.1103/PhysRevLett.116.247401.
B. Xu, S. Meyer, M. J. Verstraete, L. Bellaiche, and B. Dupé, Phys. Rev. B 103, 214423 (2021) 2469-9950 10.1103/PhysRevB.103.214423.
S. Meyer, B. Xu, M. J. Verstraete, L. Bellaiche, and B. Dupé, Phys. Rev. B 108, 024403 (2023) 2469-9950 10.1103/PhysRevB.108.024403.
H. Krakauer, M. Posternak, and A. J. Freeman, Phys. Rev. B 19, 1706 (1979) 0163-1829 10.1103/PhysRevB.19.1706.
E. Wimmer, H. Krakauer, M. Weinert, and A. J. Freeman, Phys. Rev. B 24, 864 (1981) 0163-1829 10.1103/PhysRevB.24.864.
M. Weinert, E. Wimmer, and A. J. Freeman, Phys. Rev. B 26, 4571 (1982) 0163-1829 10.1103/PhysRevB.26.4571.
www.flapw.de.
S. H. Vosko, L. Wilk, and M. Nusair, Can. J. Phys. 58, 1200 (1980) 0008-4204 10.1139/p80-159.
L. M. Sandratskii, J. Phys.: Condens. Matter 3, 8565 (1991) 0953-8984 10.1088/0953-8984/3/44/004.
A. Mackintosh and O. Andersen, in Electrons at the Fermi Surface, edited by M. Springford (Cambridge University, London, 1980), p. 149.
A. Oswald, R. Zeller, P. J. Braspenning, and P. H. Dederichs, J. Phys. F 15, 193 (1985) 0305-4608 10.1088/0305-4608/15/1/021.
M. Heide, G. Bihlmayer, and S. Blügel, Phys. B: Condens. Matter 404, 2678 (2009) 0921-4526 10.1016/j.physb.2009.06.070.
S. Meyer, B. Dupé, P. Ferriani, and S. Heinze, Phys. Rev. B 96, 094408 (2017) 2469-9950 10.1103/PhysRevB.96.094408.
I. Dzyaloshinsky, J. Phys. Chem. Solids 4, 241 (1958) 0022-3697 10.1016/0022-3697(58)90076-3.
T. Moriya, Phys. Rev. 120, 91 (1960) 0031-899X 10.1103/PhysRev.120.91.
H. Katsura, N. Nagaosa, and A. V. Balatsky, Phys. Rev. Lett. 95, 057205 (2005) 0031-9007 10.1103/PhysRevLett.95.057205.
D. Rahmedov, D. Wang, J. Íñiguez, and L. Bellaiche, Phys. Rev. Lett. 109, 037207 (2012) 0031-9007 10.1103/PhysRevLett.109.037207.
Note that we have shown in Ref. [46] that the spin current DMI is mainly driven by the Fe-Bi displacement rather than the oxygen octahedra tilts. The oxygen octahedra are more important for the DMI that is related to the weak ferromagnetic order of the antiferromagnetic (and not cycloidal) state which we do not address within our paper.
M. R. Walden, C. V. Ciobanu, and G. L. Brennecka, J. Appl. Phys. 130, 104102 (2021) 0021-8979 10.1063/5.0054979.
Note that in Ref. [62], the authors distinguish between in-plane and out-of-plane components of the exchange, whereas we use a pseudocubic approximation.
S. Meyer, Complex spin structures in frustrated ultrathin films, Ph.D.Thesis, Christian-Albrechts University of Kiel, 2 020, https://nbn-resolving.org/urn:nbn:de:gbv:8-mods-2020-00349-2.
S. Meyer, M. Perini, S. von Malottki, A. Kubetzka, R. Wiesendanger, K. von Bergmann, and S. Heinze, Nat. Commun. 10, 3823 (2019) 2041-1723 10.1038/s41467-019-11831-4.
Z. Chen, Z. Chen, C.-Y. Kuo, Y. Tang, L. R. Dedon, Q. Li, L. Zhang, C. Klewe, Y.-L. Huang, B. Prasad, A. Farhan, M. Yang, J. D. Clarkson, S. Das, S. Manipatruni, A. Tanaka, P. Shafer, E. Arenholz, A. Scholl, Y.-H. Chu, Nat. Commun. 9, 3764 (2018) 2041-1723 10.1038/s41467-018-06190-5.
I. C. Infante, S. Lisenkov, B. Dupé, M. Bibes, S. Fusil, E. Jacquet, G. Geneste, S. Petit, A. Courtial, J. Juraszek, L. Bellaiche, A. Barthélémy, and B. Dkhil, Phys. Rev. Lett. 105, 057601 (2010) 0031-9007 10.1103/PhysRevLett.105.057601.
D. Sando, A. Agbelele, C. Daumont, D. Rahmedov, W. Ren, I. C. Infante, S. Lisenkov, S. Prosandeev, S. Fusil, E. Jacquet, C. Carrétéro, S. Petit, M. Cazayous, J. Juraszek, J.-M. L. Breton, L. Bellaiche, B. Dkhil, A. Barthélémy, and M. Bibes, Phil. Trans. R. Soc. A 372, 20120438 (2014) 1364-503X 10.1098/rsta.2012.0438.
X. Ke, P. P. Zhang, S. H. Baek, J. Zarestky, W. Tian, and C. B. Eom, Phys. Rev. B 82, 134448 (2010) 1098-0121 10.1103/PhysRevB.82.134448.
A. Haykal, J. Fischer, W. Akhtar, J.-Y. Chauleau, D. Sando, A. Finco, F. Godel, Y. A. Birkhölzer, C. Carrétéro, N. Jaouen, M. Bibes, M. Viret, S. Fusil, V. Jacques, and V. Garcia, Nat. Commun. 11, 1704 (2020) 2041-1723 10.1038/s41467-020-15501-8.
D. J. Craik, Magnetism: Principles and Applications (Wiley, 1995).
E. D. T. de Lacheisserie, D. Gignoux, and M. Schlenker, Magnetism (Springer, New York, 2005), Vol. 1.
S. Rohart and A. Thiaville, Phys. Rev. B 88, 184422 (2013) 1098-0121 10.1103/PhysRevB.88.184422.
Note that compared to this paper, in Ref. [77], the authors assume a [111] directed anisotropy which exceeds the bulk value by a factor of 3 to stabilize magnetic Skyrmions in BFO. Here, we have calculated the anisotropy based on DFT and only find an easy axis within the (111) plane.
Note that contrary to the spin spiral pitch (Equation presented), the DW width (Equation presented) is independent of the DMI, hence for spin spirals with a certain pitch length the quantitative description differs as well as its energy. However, due to the simplicity of Eq. (6), the trends for the magnetic ground-state energies can be recognized directly and give qualitatively the same results as spin spiral energies.
Note that we expect a small energy offset due to systematic errors coming from the DFT (the functional, the Hubbard correction, the geometry, etc.). The offset on the energies is impossible to quantify, but should be consistent throughout all our calculations.
Z. Li, T. Chirac, J. Tranchida, V. Garcia, S. Fusil, V. Jacques, J.-Y. Chauleau, and M. Viret, Phys. Rev. Res. 5, 043109 (2023) 2643-1564 10.1103/PhysRevResearch.5.043109.