Abstract
Spin waves - electron carrier interaction in a magnetic medium is described from the Landau-Lifshitz-Gilbert-Bazaliy (LLGB) approximation, by adapting the diffusion propagator formalism on both infinitely extended and confined systems. The static and thermal correction due to the transverse fluctuations on the magnetic susceptibility are obtained in terms of the carrier density current Je and the externally applied field H0Z, providing a critical relationship giving by Je ~ H1/2, which is valid for 1D systems. The spin density distribution response as a function of Je, as well as its correlation with the spin current (JS) in steady state, are discussed for different values of the applied field and boundary magnetization phase difference. Average lifetime phase diagram for thermally stimulated spin waves is also calculated The Gilbert factor rôle on the thermal stability for the spin waves states is also quantitatively analyzed in this scenarioSpin waves - electron carrier interaction in a magnetic medium is described from the Landau-Lifshitz-Gilbert-Bazaliy (LLGB) approximation, by adapting the diffusion propagator formalism on both infinitely extended and confined systems. The static and thermal correction due to the transverse fluctuations on the magnetic susceptibility are obtained in terms of the carrier density current Je and the externally applied field H0Z, providing a critical relationship giving by Je ~ H1/2, which is valid for 1D systems. The spin density distribution response as a function of Je, as well as its correlation with the spin current (JS) in steady state, are discussed for different values of the applied field and boundary magnetization phase difference. Average lifetime phase diagram for thermally stimulated spin waves is also calculated. The Gilbert factor rôle on the thermal stability for the spin waves states is also quantitatively analyzed in this scenario. © 2016. Acad. Colomb. Cienc. Ex. Fis. Nat. All rights reserved.References
Anderson P. W. (1961). Localized Magnetic States in Metals, Phys. Rev. 124: 41. doi: 10.1103/PhysRev.124.41
Akhiezer I. A., Bar’yakhtar V. G. and Peletminskii S. V. (1961). On the theory of low-temperature, high-frequency magnetic susceptibility of a ferrodielectric, Soviet Physics JETP 13: 249.
Bazaliy Ya, B. Jones B. A. and Zhang S. -C. (1998). Modification of the Landau-Lifshitz equation in the presence of a spin-polarized current in colossal- and giant-magnetoresistive materials, Phys Rev. B 57, R3213. doi:10.1103/ Phys Rev. B 57, R3213.
Berger L. (1996). Emission of spin waves by a magnetic multilayer traversed by a current, Phys. Rev. B 54, 9353. doi:10.1103/PhysRevB.54.9353.
Chupis I. E. (1964). Theory of Relaxation processes in a uniaxial antiferrodielectric, Soviet Physics JETP 19, 212. doi:http://www.jetp.ac.ru/cgi-bin/dn/e_019_01_0212.pdf
Cottam M. and Tilley M. R. (1989). Introduction to Surface and Superlattice Excitations, Cambridge University Press, (1989).
Demidov V. E., Urazhdin S. and Demokritov S. O. (2010).Direct observation and mapping of spin waves emitted by spin-torque nanooscillators, Nature 9, 984. doi:0.1038/nmat2882.
Eshbach J. R. and Damon R. W. (1960). Surface Magnetostatic Modes and Surface Spin Waves, Phys. Rev. 118, 1208. doi:10.1103/PhysRev.118.1208
Fetter A. and Walecka J. D. (2002). Quantum Theory of Many Particle Systems, Dover Publications.
Función Lin (z), http://functions.wolfram.com/10.08.02.0001.01
Gilbert T. L. (2004). Classics in Magnetics: A Phenomenological Theory of Damping in Ferromagnetic Materials, IEEE Transactions on Magnetics, Vol. 40, 6, 3443. doi:10.1109/TMAG.2004.836740.
Gómez J., Pérez F., Jusserand B., Karczewzski K. and Wojtowicz T. (2011). Propagation length of spin waves in a conducting system, Journal of Physics: Conference Series 334 012055. doi:10.1088/1742-6596/334/1/012055
Guenther R. B. and Lee J. W. (1988). Partial Differential Equations of Mathematical Physics and Integral Equations, Dover Publications.
Hertz J. and Edwards D. M. (1973). Electron-magnon interactions in itinerant ferromagnetism: Formal theory, J. Phys. F: Metal Phys., 3 2174. doi:10.1088/0305-4608/3/12/018
Kitamura Y., Shikoh E., Ando Y., Shinjo T., Shiraishi M. (2013). Vertical spin transport in Al with Pd/Al/Ni80Fe20 trilayer films at room temperature by spin pumping, M. Sci. Rep. 3, 1739; doi:10.1038/srep01739
Kondo J. (1964). Resistance Minimum in Dilute Magnetic Alloys, Prog. Theor. Phys. 2 (1): 37-49. doi: 10.1143/PTP.32.37
Lavrik A. F. Complex integration, method of. A.F. Lavrik (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org
Li Z., He J. and Zhang S. (2006). Effects of spin current on ferromagnets, Journal of Applied Physics 99 08Q702. doi:10.1063/1.2166590
Maekawa S., Adachi H., Uchida K., Ieda J. and Saitoh E. (2013). Spin Current: Experimental and Theoretical Aspects, Journal of the Physical Society of Japan 82 102002. doi:10.7566/JPSJ.82.102002.
Madami M., Bonetti S., Consolo G., Tacchi S., Carlotti G, Gubbiotti G., Mancoff F. B., Yar M. A. and Akerman J. (2011). Direct observation of a propagating spin wave induced by spin-transfer torque, Nature Nanotechnology 6: 635. doi: 10.1038/nnano.2011.140
Phillips T. G. and Rosenberg H. M. (1966). Spin Waves in Ferromagnets, Rep. Prog. Phys. 29 285. doi: 10.1088/0034-4885/29/1/307
Saitoh, E., Ueda, M., Miyajima, H. and Tatara, G. (2006). Conversion of spin current into charge current at room temperature: Inverse spin-Hall effect. Appl. Phys. Lett. 88, 182509. doi: 10.1063/1.2199473
Sears M. R. and Saslow W. M. (2012). Spin accumulation at ferromagnet/nonmagnetic material interfaces, Phys. Rev. B 85, 014404. doi: 10.1103/PhysRevB.85.014404
Tan S. G. et al., (2015). Gauge Physics of Spin Hall Effect, Sci. Rep. 5, 18409. doi: 10.1038/srep18409
Tang Z, Shikoh E., Ago H., Kawahara K., Ando Y., Shinjo T., and Shiraishi M. (2013). Phys. Rev. B 87, 140401 (R). doi:10.1103/PhysRevB.87.140401
Tsoi M., Jansen A. G. M., Bass J., Chiang W. -C, Tsoi V. and Wyder P. (2000).Generation and detection of phasecoherent current-driven magnons in magnetic multilayers, Nature 406, 46. doi:10.1038/35017512
Yamaguchi A. (2004). Real-Space Observation of Current-Driven Domain Wall Motion in Submicron Magnetic Wires Phys. Rev. Lett. 92, 077205. doi: 10.1103/PhysRevLett.92.077205
Zhang S. and Li Z. (2010). Roles of Nonequilibrium Conduction Electrons on the Magnetization Dynamics of Ferromagnets, Physical Review Letters 93, 127204. doi: 10.1103/PhysRevLett.93.127204
Zhang S. and Zhang S. S. -L. (2009). Generalization of the LandauLifshitz-Gilbert Equation for Conducting Ferromagnets, Physical Review Letters 102, 086601. doi: 10.1103/PhysRevLett.102.086601
Žuti´c I., Fabian J., Das Sarma S. (2004). Spintronics: Fundamentals and Applications, Review of Modern Physics 76: 323-414, arXiv:cond-mat/0405528v1.
Declaration of originality and transfer author's rights
The authors declare:
- The published data and reference materials have been duly identified with their respective credits and have been included in the bibliographic notes and citations that have been so identified and that should it be required, I have all releases and permissions from any copyrighted material.
- All material presented is free from any copyright and that I accept full legal responsibility for any legal claims relating to copyrighted intellectual property, fully exonerating from responsibility the Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales.
- This work is unpublished and will not be sent to any other journal while waiting for the editorial decision of this journal. I declare that there is no conflict of interest in this manuscript.
- In case of publication of this article, all author´s rights are transferred to the Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales, and so cannot be reproduced in any form without the express permission of it.
- By means of this document, if the article is accepted for publication by the Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales, the Revista assumes the right to edit and publish the articles in national and international indices or data bases for academic and scientific use in paper, electronic, CD-ROM, internet form either of the complete text or any other known form known or to be known and non-commercial, respecting the rights of the authors.
Transfer of author rights
In case the article is approved for publication, the main author in representation of himself and his co-authors or the main author and his co-authors must cede the author rights of the corresponding article to the Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales, except in the following cases:
The authors and co-authors will retain the right to revise, adapt, prepare derived works, oral presentations, and distribution to some colleagues of reprints of their own published work, if the corresponding credit is given to the Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales. It is also permissible to publish the title of the work, summary, tables, and figures of the work in the corresponding web sites of the authors or their employers, also giving credit to the Revista.
If the work has been realized under contract, the author’s employer has the right to revise, adapt, prepare derivative works, reproduce, or distribute in hard copy the published work, in a secure manner and for the exclusive use of his employees.
If the Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales were approached for permission by a third party for using, printing, or publishing specifically articles already published, the Revista must obtain the express permission of the author and co-authors of the work or of the employer except for use in classrooms, libraries, or reprinted in a collective work. The Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales reserves the possible use in its front cover of figures submitted with the manuscripts.
No other right, other than the author’s right, can be claimed by the Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales.