Abstract
Vortices are objects that are important to describe several physical phenomena. There are many examples of such objects in nature as in a large variety of physical situations like in fluid dynamics, superconductivity, magnetism, and biology. Historically, the interest in magnetic vortex-like excitations begun in the 1960s. That interest was mainly associated with an unusual phase-transition phenomenon in two-dimensional magnetic systems. More recently, direct experimental evidence for the existence of magnetic vortex states in nano-disks was found. The interest in such model was renewed due to the possibility of the use of magnetic nano-disks as bit elements in nano-scale memory devices. The goal of this study is to review some key points for the understanding of the vortex behavior and the progress that have been done in the study of vortices in low-dimensional magnetic systems.
Similar content being viewed by others
References
L. Jacquin, D. Fabre, D. Sipp, V. Theofilis, H. Vollmers, Aerosp. Sci. Technol. 7, 577 (2003)
A.A. Abrikosov, Rev. Mod. Phys. 76, 975 (2004)
P. Minnhagen, Rev. Mod. Phys. 59, 1001 (1987)
H.W. Schumacher, C. Chappert, R.C. Sousa, P.P. Freitas, J. Miltat, Phys. Rev. Lett. 90, 017204 (2003)
V.L. Berezinskii, Sov. Phys. JETP-USSR 32, 493 (1971)
J.M. Kosterlitz, D.J. Thouless, J. Phys. C 6, 1181 (1973)
J.A. Krumhansl, J.R. Schrieffer, Phys. Rev. B 11, 3535 (1971)
J.F. Currie, Phys. Rev. A 16, 1692 (1977)
H.J. Mikeska, J. Phys. C 11, L29 (1978)
R.W. Gerling, Comput. Phys. Rep. 7, 73 (1987)
B.V. Costa, M.E. Gouvea, A.S.T. Pires, Phys. Rev. B 47, 5059 (1993)
N.D. Mermin, H. Wagner, Phys. Rev. Lett. 17, 1133 (1976)
N.D. Mermin, Rev. Mod. Phys. 51, 591 (1979)
A. Patrascioiu, E. Seiler, Phys. Rev. Lett. 60, 878 (1988)
Z. Hadzibabic, P. Kruger, M. Cheneau, B. Battelier, J. Dalibard, Nature 441, 1118 (2006)
T. Shinjo, T. Okuno, R. Hassdorf, K. Shigeto, T. Ono, Science 289, 930 (2000)
A. Wachowiak, J. Wiebe, M. Bode, O. Pietzsch, M. Morgenstern, R. Wiesendanger, Science 298, 577 (2002)
M. Schneider, H. Hoffmann, J. Zweck, J. Magn. Magn. Mater. 257, 1 (2003)
R.P. Cowburn, D.K. Koltsov, A.O. Adyeye, M.E. Welland, Phys. Rev. Lett. 83, 1042 (1999)
A.O. Pak, K.J. Kirk, R.D. Gomez, T.V. Luu, J.N. Chapman, J. Appl. Phys. 85, 6163 (1999)
K.Yu. Gulienko, P. Vavassori, Y. Otani, V. Novosad, M. Grimsditch, S.D. Bader, Phys. Rev. B 66, 052407 (2002)
H. Hauser, J. Hochreiter, G. Stangl, R. Chabicovsky, M. Janiba, K. Riedling, J. Magn. Magn. Mater. 788, 215 (2000)
J. McCord, J. Westwood, IEEE Trans. Magn. 37, 1755 (2001)
A.S. Edelstein, G.A. Fisher, J. Appl. Phys. 91, 7795 (2002)
C. Antoniak, M. Farle, Mod. Phys. Lett. B 21, 1111 (2007)
L. Berger, Y. Labaye, M. Tamine, J.M.D. Coey, Phys. Rev. B 77, 104431 (2008)
L.P. Regnault, P.Burlet, J. Rossat-Mignod, Physica 86–88B, 660 (1977)
D.G. Wiesler, M. Suzuki, H. Zabel, S.M. Shapiro, R.M. Nicklow, Physica 136B, 22 (1986)
D.G. Wiesler, H. Zabel, Phys. Rev. B 36, 7303 (1987)
D.G. Wiesler, H. Zabel, J. Appl. Phys. 63, 3554 (1988)
D.G. Wiesler, H. Zabel, S.M. Shapiro, Physica B 156–157, 292 (1989)
H. Zabel, D.G. Wiesler, S.M. Shapiro, Z. Phys., B Condens. Matter 93, 277 (1994)
M.T. Hutchings, P. Day, E. Janke, R. Pynn, J. Magn. Magn. Mater. 54–57, 673 (1986)
L.M. Castro, J.A. Plascak, A.S.T. Pires, J. Magn. Magn. Mater. 248, 62 (2002)
L.M. Castro, A.S.T. Pires, J.A. Plascak, Phys. Rev., B Condens. Matter Mater. Phys. 75, 024410 (2007)
S. Hikami, T. Tsuneto, Prog. Theor. Phys. 63, 387 (1980)
S. Takeno, S. Homma, Prog. Theor. Phys. 64, 1193 (1980)
M.E. Gouvêa, G.M. Wisyn, A.R. Bishop, F.G. Mertens, Phys. Rev. B 39, 11840 (1989)
J.E.R. Costa, B.V. Costa, Phys. Rev. B 54, 994 (1996)
J.E.R. Costa, B.V. Costa, D.P. Landau, J. Appl. Phys. 81, 5746 (1997)
D. Forster, Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions, 2nd edn. (Perseu Books, Basel, 1999)
B.V. da Costa, A.S.T. Pires, Z. Phys., B Condens. Matter 64, 433 (1986)
H.-J. Mikeska, B. Vaz da Costa, H. Fogedby, Z. Phys., B Condens. Matter 77, 119 (1989)
B.V. Costa, M.E. Gouvea, A.S.T. Pires, Phys. Lett. A 165, 179 (1992)
J. Villain, J. Phys. 35, 27 (1974)
F. Moussa, J. Villain, J. Phys. C. Solid State Phys. 9, 4433 (1976)
D.R. Nelson, D.S. Fisher, Phys. Rev. B 16, 4945 (1977)
A.S.T. Pires, S.L. Menezes, M.E. Gouvea, Phys. Rev. B 47, 12280 (1993)
D.L. Huber, Phys. Lett. A 68, 125 (1978)
D.L. Huber, Phys. Lett. A 76, 406 (1980)
D.L. Huber, Phys. Rev. B 47, 3758 (1993)
F.G. Mertens, A.R. Bishop, G.M. Wysin, C. Kawabata, Phys. Rev. Lett. 59, 117 (1987)
A.R. Pereira, J.E.R. Costa, J. Magn. Magn. Mater. 162, 219 (1996)
N. Papanicolaou, T.N. Tomaras, Nucl. Phys. B 360, 425 (1991)
N. Papanicolaou, T.N. Tomaras, Phys. Lett. A 179, 33 (1993)
H.G. Evertz, D.P. Landau, Phys. Rev. B 54, 12302 (1996)
B.V. Costa, D.P. Landau, J.E.R. Costa, K. Chen, in Computer Simulation Studies in Condensed Matter Physics VIII, ed. by D.P. Landau, K.K. Mon, H.B. Schuettler (Springer, New York, 1995)
J.E.R. Costa, B.V. Costa, D.P. Landau, Phys. Rev. B 57, 11510 (1998)
E.E. Huber Jr., D.O. Smith, J.B. Goodenough, J. Appl. Phys. 29, 294 (1958)
S.-i. Iwasaki, Y. Nakamura, IEEE Trans. Magn. 13, 1272 (1977)
R.L. Compton, P.A. Crowell, Phys. Rev. Lett. 97, 137202 (2006)
R.L. Compton, T.Y. Chen, P.A. Crowell, Phys. Rev. B 81, 144412 (2010)
K. Yu. Guslienko, B.A. Ivanov, V. Novosad, Y. Otani, H. Shima, K. Fukamichi, J. Appl. Phys. 91, 8037 (2002)
J.P. Park, P. Eames, D. M. Engebretson, J. Berezovsky, P.A. Crowell, Phys. Rev. B 67, 020403R (2003)
S.B. Choe, Y. Acremann, A. Scholl, A. Bauer, A. Doran, J. Stohr, H.A. Padmore, Science 304, 420 (2004)
S. Prakash, Phys. Rev. B 42, 6574 (1990)
A.B. MacIsaac, J.P. Whitehead, K. DeB́ell, P.H. Poole, Phys. Rev. Lett. 77, 739 (1996)
A. Hucht, K.D. Usadel, J. Magn. Magn. Mater. 156, 423 (1996)
A.B. MacIsaac, K. DeB́ell, J.P. Whitehead, Phys. Rev. Lett. 80, 616 (1998)
E.Yu. Vedmedenko, A. Ghazali, J.-C.S. Lévy, Phys. Rev. B 59, 3329 (1999)
E.Yu. Vedmedenko, H.P. Oepen, A. Ghazali, J.-C.S. Lévy, J. Kirschner, Phys. Rev. Lett. 84, 5884 (2000)
L. Thompson, arXiv:cond-mat/0510414v1 [cond-mat.mes-hall] 16 Oct 2005
E. Bîrsan, J. Supercond. Novel Magn. 22, 711 (2009)
Y. Labaye, L. Berger, J.M.D. Coey, J. Appl. Phys. 91, 5341 (2002)
Y. Labaye, O. Crisan, L. Berger, J.M. Greneche, J.M.D. Coey, J. Appl. Phys. 91, 8715 (2002)
S.A. Leonel, I.A. Marques, P.Z. Coura, B.V. Costa, J. Appl. Phys. 102, 104311 (2007)
J.C.S. Rocha, P.Z. Coura, S.A. Leonel, R.A. Dias, B.V. Costa, J. Appl. Phys. 107, 053903 (2010)
K. Shigeto, T. Okuno, K. Mibu, T. Shinjo, T. Ono, Appl. Phys. Lett. 80, 4190 (2002)
A. Thiaville1, J.M. García, R. Dittrich, J. Miltat, T. Schrefl, Phys. Rev. B 67, 094410 (2003)
T.Y. Chen, P.A. Crowell, Non-linear dynamics of a magnetic vortex. IEEE Trans. Magn. 46, 1457 (2010)
R.L. Compton, T.Y. Chen, P.A. Crowell, Magnetic vortex dynamics in the presence of pinning. Phys. Rev. B 81, 144412 (2010)
R.L. Compton, P.A. Crowell, Dynamics of a pinned magnetic vortex. Phys. Rev. Lett. 97, 137202 (2006)
J.P. Park, P.A. Crowell, Interactions of spin waves with a magnetic vortex. Phys. Rev. Lett. 95, 167201 (2005)
C. Zaspel, B.A. Ivanov, J.P. Park, P.A. Crowell, Excitations in vortex-state permalloy dots. Phys. Rev. B 72, 024427 (2005)
J.P. Park, P. Eames, D.M. Engebretson, J. Berezovsky, P.A. Crowell, Imaging of spin dynamics in closure domain and vortex structures. Phys. Rev. B 67, 020403R (2003)
B.V. Costa, M.E. Gouvea, A.S.T. Pires, Phys. Lett. A 165, 179 (1992)
R. Hertel, S. Gliga, M. Fa"hnle, C.M. Schneider, Phys. Rev. Lett. 98, 117201 (2007)
A. Vansteenkist, K.W. Chou, M. Weigand, M. Curcic, V. Sackmann, H. Stoll, T. Tyliszczak, G. Woltersdorf, C.H. Back, G. Schütz, Van Waeyenberg, Nat. Phys. 5, 332 (2009)
G.S. Grest, Phys. Rev. B 39, 9267 (1989)
G. Ramirez-Santiago, J.V. José, Phys. Rev. B 49, 9567 (1994)
P. Olsson, Phys. Rev. Lett. 73, 3339 (1994)
P. Olsson, Phys. Rev. B 52, 4526 (1995)
A.B. Lima, B.V. Costa, J. Magn. Magn. Mater. 300, 427 (2006)
A.B. Lima, B.V. Costa, J. Magn. Magn. Mater. 263, 324 (2003)
Acknowledgements
This work was partially supported by CNPq and FAPEMIG (Brazilian Agencies). We are indebt with Dr. Júlio Rocha who patiently produced most of the figures used in this work.