Skip to content
BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access September 23, 2015

Spin waves in a ferromagnetic nanotube of an elliptic cross-section in the presence of a spin-polarized current

Yuri I. Gorobets and Volodymyr V. Kulish
From the journal Open Physics


In the paper, spin waves in a ferromagnetic nanotube of an elliptic cross-section in the presence of a spinpolarized electric current are investigated. The linearized Landau-Lifshitz equation in themagnetostatic approximation is used, with the exchange interaction, the dipoledipolemagnetic interaction, the anisotropy effects and the dissipation effects taken into account; the influence of the spin-polarized current is considered by the Slonczewski- Berger term. After elimination of the magnetization density perturbation, an equation for the magnetic potential for the above-described spin excitations is obtained. From this equation, a dispersion relation for spin waves in the nanosystem described previously is obtained. Analysis of the dispersion relation shows that the presence of the spinpolarized current can strengthen or weaken the dissipation, creating an “effective dissipation”; the effect is analogous to the “effective dissipation” in a two-layer ferromagnetic film in the presence of a spin-polarized current. Depending on the direction and the density of the current the spinwave can decay faster or slower than in the absence of the current, transform into a self-sustained wave or grow in amplitude, thus leading to a spin wave generation.


[1] V. V. Kruglyak, S. O. Demokritov, D. Grundler, J. Phys. D: Appl. Phys. 43, 264001 (2010) 10.1088/0022-3727/43/26/264001Search in Google Scholar

[2] S. D. Bader, S. S. P. Parkin, Annual Review of Condensed Matter Physics 1, 71 (2010) 10.1146/annurev-conmatphys-070909-104123Search in Google Scholar

[3] T. Schneider, A. A. Serga, B. Leven, B. Hillebrands, R. L. Stamps, M. P. Kostylev, Appl. Phys. Lett. 92, 022505 (2008) 10.1063/1.2834714Search in Google Scholar

[4] M. R. Freeman, B. C. Choi, Science 294, 1484 (2001) 10.1126/science.1065300Search in Google Scholar PubMed

[5] S. Neusser, D. Grundler, Adv. Mat. 21, 2927 (2009) 10.1002/adma.200900809Search in Google Scholar

[6] R. E. De Wames, T. Wolfram, Appl. Phys. Lett. 16, 305 (1970) 10.1063/1.1653205Search in Google Scholar

[7] R. Arias, D. L. Mills, Phys. Rev. B 63, 134439 (2001) 10.1103/PhysRevB.63.134439Search in Google Scholar

[8] R. Arias, D. L. Mills, Phys. Rev. B 67, 094423 (2003) 10.1103/PhysRevB.67.094423Search in Google Scholar

[9] R. Arias, D. L. Mills, Phys. Rev. B 72, 104418 (2005) 10.1103/PhysRevB.72.104418Search in Google Scholar

[10] I. V. Zavislyak, G. P. Golovach, M. A. Popov, V. F. Romanyuk, Journal of Communications Technology and Electronics 51, 203 (2006) 10.1134/S1064226906020112Search in Google Scholar

[11] T. K. Das, M. G. Cottam, J. Appl. Phys. 109, 07D323 (2011) 10.1063/1.3554208Search in Google Scholar

[12] A. Kozhanov, M. Popov, I. Zavislyak, D. Ouellette, D. W. Lee, S. X. Wang, M. Rodwell, S. J. Allen, J. Appl. Phys. 111, 013905 (2012) 10.1063/1.3672835Search in Google Scholar

[13] H. Leblond, V. Veerakumar, Phys. Rev. B 70, 134413 (2004) 10.1103/PhysRevB.70.134413Search in Google Scholar

[14] A. L. González, P. Landeros, Á. S. Núñez, J. Magn. Magn. Mater 322, 530 (2010) 10.1016/j.jmmm.2009.10.010Search in Google Scholar

[15] J. A. Otálora, J. A. López-López, A. S. Núñez, P. Landeros, J. Phys.: Condens. Matter 24, 436007 (2012) 10.1088/0953-8984/24/43/436007Search in Google Scholar PubMed

[16] Y. Ye, B. Geng, Critical Reviews in Solid State and Materials Sciences 37, 75 (2012) 10.1080/10408436.2011.613491Search in Google Scholar

[17] A. K. Salem, P. C. Searson, K.W. Leong, Nat.Mater. 2, 668 (2003) 10.1038/nmat974Search in Google Scholar PubMed

[18] C. C. Berry, A. S. G. Curtis, J. Phys. D: Appl. Phys. 36, R198 (2003) 10.1088/0022-3727/36/13/203Search in Google Scholar

[19] G. Xiao-Kun, C. Bing-Yang, Chinese Phys. 16, 3777 (2007) 10.1088/1009-1963/16/12/037Search in Google Scholar

[20] D. M. N. Hasan, M. N. Hossain, K. M. Mohsin, M. S. Alam, In: TENCON-2010 Computer, Circuit and Systems, Antennas and Propagation - 2010 IEEE Region 10 Conference, Nov. 21-24, 2010, Fukuoka, Japan (IEEE, Japan, 2010) 1915 Search in Google Scholar

[21] S. Dag, S. Ciraci, Phys. Rev. B. 71, 165414 (2005) 10.1103/PhysRevB.71.165414Search in Google Scholar

[22] R. L. D. Whitby,W. K. Hsu, Y. Q. Zhu, H.W. Kroto, D. R. M.Walton, Phil. Trans. R. Soc. Lond. A. 362, 2127 (2004) 10.1098/rsta.2004.1432Search in Google Scholar

[23] V. Holovatsky, V. Gutsul, Cond. Matt. Phys. 10, 61 (2007) 10.5488/CMP.10.1.61Search in Google Scholar

[24] Y. Ye, B. Geng, Crit. Rev. Solid State Mater. Sci. 37, 75 (2012) 10.1080/10408436.2011.613491Search in Google Scholar

[25] M. A. Popov, I. V. Zavislyak, Ukr. J. Phys. 53, 702 (2008) 10.1134/S1063784208040130Search in Google Scholar

[26] C.Wu, Ph.D. thesis, City University of New York (New York, USA, 2008) Search in Google Scholar

[27] A. Slavin, V. Tiberkevich, IEEE Transactions on Magnetics 44, 1916 (2008) 10.1109/TMAG.2008.924537Search in Google Scholar

[28] J. C. Slonczewski, J. Magn. Magn. Mater. 159, L1 (1996) 10.1016/0304-8853(96)00062-5Search in Google Scholar

[29] L. Berger, Phys. Rev. B 54, 9353 (1996) 10.1103/PhysRevB.54.9353Search in Google Scholar

[30] A. I. Akhiezer, V. G. Barýakhtar, S. V. Peletminskiy, Spin waves, 1st edition (North-Holland, Amsterdam, 1968) Search in Google Scholar

[31] Yu. I. Gorobets, V. V. Kulish, Ukr. Journ. Phys. 59, 541 (2014) 10.15407/ujpe59.05.0541Search in Google Scholar

[32] A. Slavin, V. Tiberkevich, IEEE Transactions on Magnetics 45, 1875 (2009) 10.1109/TMAG.2008.2009935Search in Google Scholar

[33] H. Y. Liu, Z. K. Wang, H. S. Lim, S. C. Ng, M. H. Kuok, D. J. Lockwood, M. G. Cottam, K. Nielsch, U. Gösele, J. Appl. Phys. 98, 046103 (2005) 10.1063/1.2009072Search in Google Scholar

[34] C. Mathieu, J. Jorzick, A. Frank, S. O. Demokritov, A. N. Slavin, B. Hillebrands, Phys. Rev. Lett. 81, 3968 (1998) 10.1103/PhysRevLett.81.3968Search in Google Scholar

[35] N. A. Usov, S. E. Peschany,Magn. Magn.Mater 118, L290 (1993) 10.1016/0304-8853(93)90428-5Search in Google Scholar

[36] Y. Tserkovnyak, A. Brataas, G. E. W. Bauer, Phys. Rev. Lett. 88, 117601 (2002) 10.1103/PhysRevLett.88.117601Search in Google Scholar PubMed

[37] S. J. Gamble, M. H. Burkhardt, A. Kashuba, R. Allenspach, S. S. P. Parkin, H. C. Siegmann, J. Stöhr, Phys. Rev. Lett. 102, 217201 (2009) 10.1103/PhysRevLett.102.217201Search in Google Scholar PubMed

[38] W. H. Rippard, M. R. Pufall, S. Kaka, S. E. Russek, T. J. Silva, Phys. Rev. Lett. 92, 027201 (2004) 10.1103/PhysRevLett.92.027201Search in Google Scholar PubMed

Received: 2014-12-26
Accepted: 2015-7-13
Published Online: 2015-9-23

©2015 Yuri I. Gorobets and Volodymyr V. Kulish

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Scroll Up Arrow