Abstract
Magnetic domain walls are fundamental objects arising in ferromagnetic materials, largely investigated both through micromagnetic simulations and experiments. While current- and field-based techniques for inducing domain wall propagation have been widely studied for fundamental understanding and application-oriented purposes, the possibility to manipulate domain walls using mechanical stress in magnetoelastic materials has only recently drawn interest. Here, a complete analytical model describing stress-induced transverse domain wall movement in ferromagnetic nanostripe with variable cross-section is presented. This approach yields a nonlinear integro-differential equation describing the magnetization field. Its numerical implementation, based on the nonlinear relaxation method, demonstrates the possibility to precisely control the position of a domain wall through mechanical action.
Similar content being viewed by others
References
D.A. Allwood, G. Xiong, C. Faulkner, D. Atkinson, D. Petit, R.P. Cowburn, Science, 309, 1688 (2005)
S.S. Parkin, M. Hayashi, L. Thomas, Science 320, 190 (2008)
T. Ono, H. Miyajima, K. Shigeto, K. Mibu, N. Hosoito, T. Shinjo, Science 284, 468 (1999)
D. Atkinson, D.A. Allwood, G. Xiong, M.D. Cooke, C.C. Faulkner, R.P. Cowburn, Nat. Mater. 2, 85 (2003)
G.S.D. Beach, C. Nistor, C. Knutson, M. Tsoi, J.L. Erskine, Nat. Mater. 4, 741 (2005)
M. Hayashi, L. Thomas, C. Rettner, R. Moriya, Y.B. Bazaliy, S.S.P. Parkin, Phys. Rev. Lett. 98, 037204 (2007)
D. Ravelosona, S. Mangin, J.A. Katine, E.E. Fullerton, B.D. Terris, Appl. Phys. Lett. 90, 072508 (2007)
A.V. Khvalkovskiy, V. Cros, D. Apalkov, V. Nikitin, M. Krounbi, K.A. Zvezdin, A. Anane, J. Grollier, A. Fert, Phys. Rev. B 87, 020402 (2013)
P.N. Skirdkov, K.A. Zvezdin, A.D. Belanovsky, J. Grollier, V. Cros, C.A. Ross, A.K. Zvezdin, Appl. Phys. Lett. 104, 242401 (2014)
J. Dean, M.T. Bryan, T. Schrefl, D.A. Allwood, J. Appl. Phys. 109, 023915 (2011)
M.T. Bryan, J. Dean, D.A. Allwood, Phys. Rev. B 85, 144411 (2012)
N. Lei, T. Devolder, G. Agnus, P. Aubert, L. Daniel, J.-V. Kim, W. Zhao, T. Trypiniotis, R.P. Cowburn, C. Chappert, D. Ravelosona, P. Lecoeur, Nat. Commun. 4, 1378 (2013)
B. Van de Wiele, L. Laurson, K.J.A. Franke, S. van Dijken, Appl. Phys. Lett. 104, 012401 (2014)
K.J.A. Franke, B. Van de Wiele, Y. Shirahata, S.J. Hämäläinen, T. Taniyama, S. van Dijken, Phys. Rev. X 5, 011010 (2015)
R. Tolley, T. Liu, Y. Xu, S. Le Gall, M. Gottwald, T. Hauet, M. Hehn, F. Montaigne, E.E. Fullerton, S. Mangin, Appl. Phys. Lett. 106, 242403 (2015)
E. De Ranieri, P.E. Roy, D. Fang, E.K. Vehsthedt, A.C. Irvine, D. Heiss, A. Casiraghi, R.P. Campion, B.L. Gallagher, T. Jungwirth, J. Wunderlich, Nat. Mater. 12, 808 (2013)
G. Catalan, J. Seidel, R. Ramesh, J.F. Scott, Rev. Mod. Phys. 84, 119 (2012)
M. Sharad, C. Augustine, G. Panagopoulos, K. Roy, IEEE Trans. Nanotechnol. 11, 843 (2012)
B. Behin-Aein, D. Datta, S. Salahuddin, S. Datta, Nat. Nanotechnol. 5, 266 (2010)
S. Parkin, S.-H. Yang, Nat. Nanotechnol. 10, 195 (2015)
N. Locatelli, V. Cros, J. Grollier, Nat. Mater. 13, 11 (2014)
H. Sohn, M.E. Nowakowski, C.Y. Liang, J.L. Hockel, K. Wetzlar, S. Keller, B.M. McLellan, M.A. Marcus, A. Doran, A. Young, M. Kläui, G.P. Carman, J. Bokor, R.N. Candler, ACS Nano 9, 4814 (2015)
M. Kruzík, A. Prohl, SIAM Rev. 48, 439 (2006)
T. Mathurin, S. Giordano, Y. Dusch, N. Tiercelin, P. Pernod, V. Preobrazhensky, Appl. Phys. Lett. 108, 082401 (2016)
C.W. Nan, M.I. Bichurin, S. Dong, D. Viehland, G. Srinivasan, J. Appl. Phys. 103, 031101 (2008)
S. Giordano, M. Goueygou, N. Tiercelin, A. Talbi, P. Pernod, V. Preobrazhensky, Int. J. Eng. Sci. 78, 134 (2014)
S.-T. Gu, Q.-C. He, Philos. Mag. 95, 2793, (2015)
S. Giordano, Mech. Res. Comm. 55, 18 (2014)
N. Tiercelin, Y. Dusch, V. Preobrazhensky, P. Pernod, J. Appl. Phys. 109, 07D726 (2011)
N. Tiercelin, Y. Dusch, A. Klimov, S. Giordano, V. Preobrazhensky, P. Pernod, Appl. Phys. Lett. 99, 192507 (2011)
Y. Dusch, N. Tiercelin, A. Klimov, S. Giordano, V. Preobrazhensky, P. Pernod, J. Appl. Phys. 113, 17C719 (2013)
Y. Dusch, V. Rudenko, N. Tiercelin, S. Giordano, V. Preobrazhensky, P. Pernod, Nanomater. Nanostruct. 2, 44 (2012)
A.K. Biswas, S. Bandyopadhyay, J. Atulasimha, Appl. Phys. Lett. 104, 232403 (2014)
S. Giordano, Y. Dusch, N. Tiercelin, P. Pernod, V. Preobrazhensky, Phys. Rev. B 85, 155321 (2012)
S. Giordano, Y. Dusch, N. Tiercelin, P. Pernod, V. Preobrazhensky, J. Phys. D 46, 325002 (2013)
N. Tiercelin, Y. Dusch, S. Giordano, A. Klimov, V. Preobrazhensky, P. Pernod, Strain Mediated Magnetoelectric Memory, in Nanomagnetic and Spintronic Devices for Energy-Efficient Memory and Computing, edited by S. Bandyopadhyay, J. Atulasimha (John Wiley & Sons Ltd., 2016)
K. Roy, S. Bandyopadhyay, J. Atulasimha, J. Appl. Phys. 112, 023914 (2012)
H. Ahmad, J. Atulasimha, S. Bandyopadhyay, Sci. Rep. 5, 18264 (2015)
L.D. Landau, E.M. Lifshitz, Electrodynamics of Continuous Media (Pergamon Press, London, 1984)
W.F. Brown, Micromagnetics (Interscience Publisher, New York, 1963)
W.F. Brown, Magnetoelastic Interactions (Springer-Verlag, Berlin, 1966)
J.A. Stratton, Electromagnetic theory (Mc Graw Hill, New York, 1941)
C. Miehe, G. Ethiraj, Comput. Methods Appl. Mech. Eng. 245, 331 (2012)
G. Bertotti, I. Mayergoyz, C. Serpico, Nonlinear Magnetization Dynamic in Nanosystems (Elsevier, Oxford, 2000)
N.L. Schryer, L.R. Walker, J. Appl. Phys. 45, 5406 (1974)
Y. Dusch, N. Tiercelin, A. Klimov, V. Rudenko, Y. Ignatov, S. Hage-Ali, P. Pernod, V. Preobrazhensky, J. Appl. Phys. 109, 07A720 (2011)
P. Gaunt, Philos. Mag. 48, 261 (1983)
T. Rojac, M. Kosec, B. Budic, N. Setter, D. Damjanovic, J. Appl. Phys. 108, 074107 (2010)
D.I. Paul, J. Appl. Phys. 53, 1649 (1982)
J.P. Attané, Y. Samson, A. Marty, D. Halley, C. Beigné, Appl. Phys. Lett. 79, 794 (2001)
M. Kläui, C.A.F. Vaz, J. Rothman, J.A.C. Bland, W. Wernsdorfer, G. Faini, E. Cambril, Phys. Rev. Lett. 90, 097202 (2003)
D. Petit, A.-V. Jausovec, D. Read, R.P. Cowburn, J. Appl. Phys. 103, 114307 (2008)
M. Kläui, H. Ehrke, U. Rüdiger, T. Kasama, R.E. Dunin-Borkowski, D. Backes, L.J. Heyderman, C.A.F. Vaz, J.A.C. Bland, G. Faini, E. Cambril, W. Wernsdorfer, Appl. Phys. Lett. 87, 102509 (2005)
A.N. Kolmogorov, S.V. Fomin, Elements of the Theory of Functions and Functional Analysis (Dover, New York, 1999)
D.B. Gopman, J.W. Lau, K.P. Mohanchandra, K. Wetzlar, G.P. Carman, Phys. Rev. B 93, 064425 (2016)
Y.Y. Huang, Y.M. Jin, Appl. Phys. Lett. 93, 142504 (2008)
H.B. Keller, Numerical Solution of Two Point Boundary Value Problems (SIAM, Philadelphia, 1976)
P. Xu, K. Xia, C. Gu, L. Tang, H. Yang, J. Li, Nat. Nanotechnol. 3, 97 (2008)
L. Landau, E. Lifshitz, Phys. Zeitsch. der Sow. 8, 153 (1935)
T.L. Gilbert, Phys. Rev. 100, 1243 (1955) (abstract only)
T.L. Gilbert, IEEE Trans. Mag. 40, 3443 (2004)
S. Giordano, Y. Dusch, N. Tiercelin, P. Pernod, V. Preobrazhensky, Eur. Phys. J. B 86, 249 (2013)
R. Ravaud, G. Lemarquand, Prog. Electromagn. Res. B 98, 207 (2009)
I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series and Products (Academic Press, San Diego, 1965)
M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions (Dover Publication, New York, 1970)
F.W.J. Olver, D.W. Lozier, R.F. Boisvert, C.W. Clark, NIST Handbook of Mathematical Functions (National Institute of Standards and Technology and Cambridge University Press, New York, 2010)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mathurin, T., Giordano, S., Dusch, Y. et al. Mechanically driven domain wall movement in magnetoelastic nanomagnets. Eur. Phys. J. B 89, 169 (2016). https://doi.org/10.1140/epjb/e2016-70226-0
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjb/e2016-70226-0