Abstract
It is shown that the energy of a ferromagnetic film deposited onto a paramagnetic or superconducting substrate acquires a contribution in the form of the Dzyaloshinskii–Moriya interaction. This contribution appears as a result of the magnetostatic interaction of the magnetization of the ferromagnetic film with the magnetization induced by it in a paramagnet or by the supercurrent in the superconductor and leads to the removal of the chiral degeneracy, nonreciprocity of spin waves, and the formation of chiral states such as magnetic skyrmions. Our estimates indicate the possibility of experimental observation of predicted effects.
Notes
The term being omitted is on the order of qh and, hence, cannot be ignored. However, we will henceforth show that the disregard of this term does not lead to significant errors.
REFERENCES
I. E. Dzialoshinskii, Sov. Phys. JETP 5, 1259 (1957).
T. Moriya, Phys. Rev. 120, 91 (1960).
S. Mühlbauer, B. Binz, F. Jonietz, et al., Science (Washington, DC, U. S.) 323, 915 (2009).
N. Romming, C. Hanneken, M. Menzel, et al., Science (Washington, DC, U. S.) 341, 636 (2013).
J.-H. Moon, S.-M. Seo, K.-J. Lee, et al., Phys. Rev. B 88, 184404 (2013).
K. Di, V. L. Zhang, H. S. Lim, et al., Appl. Phys. Lett. 106, 052403 (2015).
Y. Ishikawa, K. Tajima, D. Bloch, et al., Solid State Commun. 19, 525 (1976).
A. Crépieux and C. Lacroix, J. Magn. Magn. Mater. 182, 341 (1998).
H. Yang, A. Thiaville, S. Rohart, et al., Phys. Rev. Lett. 115, 267210 (2015).
H. Imamura, P. Bruno, and Y. Utsumi, Phys. Rev. B 69, 121303 (2004).
S.-X. Wang, H.-R. Chang, and J. Zhou, Phys. Rev. B 96, 115204 (2017).
N. Mikuszeit, S. Meckler, R. Wiesendanger, et al., Phys. Rev. B 84, 054404 (2011).
K. R. Mukhamatchin and A. A. Fraerman, JETP Lett. 93, 716 (2011).
I. M. Nefedov, A. A. Fraerman, and I. A. Shereshevskii, Phys. Solid State 58, 503 (2016).
K. R. Mukhamatchin and A. A. Fraerman, J. Exp. Theor. Phys. 131, 963 (2020).
M. A. Kuznetsov and A. A. Fraerman, Phys. Rev. B 105, 214401 (2022).
M. A. Kuznetsov, K. R. Mukhamatchin, and A. A. Fraerman, Phys. Rev. B 107, 184428 (2023).
R. E. Camley, Surf. Sci. Rep. 7, 103 (1987).
A. G. Gurevich and G. A. Melkov, Magnetization Oscillations and Waves (CRC, New York, 1996).
M. Jamali, J. H. Kwon, S.-M. Seo, et al., Sci. Rep. 3, 3160 (2013).
N. Sato, K. Sekiguchi, and Y. Nozaki, Appl. Phys. Express 6, 063001 (2013).
Y. Li, W. Zhang, V. Tyberkevych, et al., J. Appl. Phys. 128, 130902 (2020).
A. Barman, G. Gubbiotti, S. Ladak, et al., J. Phys.: Condens. Matter 33, 413001 (2021).
H. Yu, J. Xiao, and H. Schultheiss, Phys. Rep. 905, 1 (2021).
R. W. Damon and J. R. Eshbach, J. Phys. Chem. Solids 19, 308 (1961).
S. R. Seshadri, Proc. IEEE 58, 506 (1970).
R. E. de Wames and T. Wolfram, J. Appl. Phys. 41, 5243 (1970).
M. Mruczkiewicz and M. Krawczyk, J. Appl. Phys. 115, 113909 (2014).
R. L. Melcher, Phys. Rev. Lett. 30, 125 (1973).
L. Udvardi and L. Szunyogh, Phys. Rev. Lett. 102, 207204 (2009).
K. Zakeri, Y. Zhang, J. Prokop, et al., Phys. Rev. Lett. 104, 137203 (2010).
J.-H. Moon, S.-M. Seo, K.-J. Lee, et al., Phys. Rev. B 88, 184404 (2013).
F. Garcia-Sanchez, P. Borys, J.-V. Kim, et al., Phys. Rev. B 89, 224408 (2014).
A. A. Stashkevich, M. Belmeguenai, Y. Roussigné, et al., Phys. Rev. B 91, 214409 (2015).
M. Belmeguenai, J.-P. Adam, Y. Roussigné, et al., Phys. Rev. B 91, 180405(R) (2015).
V. L. Zhang, K. Di, H. S. Lim, et al., Appl. Phys. Lett. 107, 022402 (2015).
J. M. Lee, C. Jang, B.-C. Min, et al., Nano Lett. 16, 62 (2016).
T. Brächer, O. Boulle, and G. Gaudin, Phys. Rev. B 95, 064429 (2017).
K. Szulc, P. Graczyk, M. Mruczkiewicz, et al., Phys. Rev. Appl. 14, 034063 (2020).
F. J. dos Santos, M. dos Santos Dias, and S. Lounis, Phys. Rev. B 102, 104401 (2020).
H. Wang, J. Chen, T. Liu, et al., Phys. Rev. Lett. 124, 027203 (2020).
A. F. Franco and P. Landeros, Phys. Rev. B 102, 184424 (2020).
I. A. Golovchanskiy, N. N. Abramov, V. S. Stolyarov, et al., J. Appl. Phys. 124, 233903 (2018).
I. A. Golovchanskiy, N. N. Abramov, and V. S. Stolyarov, J. Appl. Phys. 127, 093903 (2020).
R. E. Camley and A. A. Maradudin, Solid State Commun. 41, 585 (1982).
P. X. Zhang and W. Zinn, Phys. Rev. B 35, 5219 (1987).
J. Barnaś and P. Grünberg, J. Magn. Magn. Mater. 82, 186 (1989).
F. C. Nörtemann, R. L. Stamps, and R. E. Camley, Phys. Rev. B 47, 11910 (1993).
A. V. Vashkovskii and E. G. Lokk, J. Commun. Technol. Electron. 51, 568 (2006).
R. A. Gallardo, T. Schneider, A. K. Chaurasiya, et al., Phys. Rev. Appl. 12, 034012 (2019).
M. Ishibashi, Y. Shiota, T. Li, et al., Sci. Adv. 6, eaaz6931 (2020).
W. Song, X. Wang, W. Wang, et al., Phys. Status Solidi RRL 14, 2000118 (2020).
M. Grassi, M. Geilen, D. Louis, et al., Phys. Rev. Appl. 14, 024047 (2020).
J. Han, Y. Fan, B. C. McGoldrick, et al., Nano Lett. 21, 7037 (2021).
S. Rohart and A. Thiaville, Phys. Rev. B 88, 184422 (2013).
A. N. Bogdanov and D. A. Yablonskii, Sov. Phys. JETP 68, 101 (1989).
A. Bogdanov and A. Hubert, Phys. Status Solidi B 186, 527 (1994).
A. Bogdanov and A. Hubert, J. Magn. Magn. Mater. 138, 255 (1994).
S. Y. Dan’kov, A. M. Tishin, V. K. Pecharsky, et al., Phys. Rev. B 57, 3478 (1998).
M. Baćani, M. A. Marioni, J. Schwenk, et al., Sci. Rep. 9, 3114 (2019).
A. Samardak, A. Kolesnikov, and M. Stebliy, Appl. Phys. Lett. 112, 192406 (2018).
A. G. Temiryazev, M. P. Temiryazeva, A. V. Zdoroveyshchev, et al., Phys. Solid State 60, 2200 (2018).
L.-C. Peng, Y. Zhang, S.-L. Zuo, et al., Chin. Phys. B 27, 066802 (2018).
ACKNOWLEDGMENTS
The authors are grateful to M.V. Sapozhnikov, A.S. Mel’nikov, N. I. Polushkin, and I.S. Burmistrov for fruitful discussions.
Funding
This study was supported by the Russian Science Foundation (project no. 21-72-10176)
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Translated by N. Wadhwa
This article is prepared for the memorial issue of the journal dedicated to the 95th birthday of L.A. Prozorova.
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Kuznetsov, M.A., Fraerman, A.A. Magnetostatic Mechanism of Chiral Symmetry Breaking in Multilayer Magnetic Structures. J. Exp. Theor. Phys. 137, 442–452 (2023). https://doi.org/10.1134/S1063776123100187
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DOI: https://doi.org/10.1134/S1063776123100187