Analytical and numerical Ku-B phase diagrams for cobalt nanostructures: Stability region for a Bloch skyrmion

A. Riveros, N. Vidal-Silva, F. Tejo, Juan E Escrig Murua, Juan E. Escrig Murua

Research output: Contribution to journalArticle

Abstract

In this paper we calculate the energies corresponding to the different magnetic phases present in a ferromagnetic cylinder by means of analytical calculations. From the comparison of these energies, it is possible to construct magnetic phase diagrams as a function of the uniaxial anisotropy of the sample and the applied external magnetic field. As proof of concept, we analyzed the magnetic phase diagrams for a cobalt dot of 240 nm in diameter and 70 nm in length, with an easy axis parallel to the dot axis, and with a magnetic field applied towards or perpendicular to this axis. From these diagrams we have obtained the stability regions for a Bloch skyrmion (Sk), a vortex core (VC) and a ferromagnetic (F) configuration, which can point in any ψ direction. Our results provide a pathway to engineer the formation and controllability of a skyrmion in a ferromagnetic dot to different anisotropy constants and magnetic fields. © 2018 Elsevier B.V.
LanguageEnglish
Pages292-296
Number of pages5
JournalJournal of Magnetism and Magnetic Materials
Volume460
DOIs
Publication statusPublished - 2018

Fingerprint

Cobalt
Phase diagrams
Nanostructures
cobalt
phase diagrams
Magnetic fields
Anisotropy
magnetic fields
anisotropy
controllability
Controllability
engineers
Vortex flow
diagrams
vortices
Engineers
energy
configurations

Keywords

  • Antiferromagnetic materials
  • Cobalt
  • Ferromagnetic materials
  • Ferromagnetism
  • Graphic methods
  • Magnetic fields
  • Phase diagrams
  • Vortex flow
  • Analytical calculation
  • Anisotropy constants
  • External magnetic field
  • Ferromagnetic cylinders
  • Magnetic phase diagrams
  • Proof of concept
  • Stability regions
  • Uniaxial anisotropy
  • Magnetic anisotropy

Cite this

@article{ff9487c5a1274d45a84df33617ed5bc7,
title = "Analytical and numerical Ku-B phase diagrams for cobalt nanostructures: Stability region for a Bloch skyrmion",
abstract = "In this paper we calculate the energies corresponding to the different magnetic phases present in a ferromagnetic cylinder by means of analytical calculations. From the comparison of these energies, it is possible to construct magnetic phase diagrams as a function of the uniaxial anisotropy of the sample and the applied external magnetic field. As proof of concept, we analyzed the magnetic phase diagrams for a cobalt dot of 240 nm in diameter and 70 nm in length, with an easy axis parallel to the dot axis, and with a magnetic field applied towards or perpendicular to this axis. From these diagrams we have obtained the stability regions for a Bloch skyrmion (Sk), a vortex core (VC) and a ferromagnetic (F) configuration, which can point in any ψ direction. Our results provide a pathway to engineer the formation and controllability of a skyrmion in a ferromagnetic dot to different anisotropy constants and magnetic fields. {\circledC} 2018 Elsevier B.V.",
keywords = "Antiferromagnetic materials, Cobalt, Ferromagnetic materials, Ferromagnetism, Graphic methods, Magnetic fields, Phase diagrams, Vortex flow, Analytical calculation, Anisotropy constants, External magnetic field, Ferromagnetic cylinders, Magnetic phase diagrams, Proof of concept, Stability regions, Uniaxial anisotropy, Magnetic anisotropy",
author = "A. Riveros and N. Vidal-Silva and F. Tejo and {Escrig Murua}, {Juan E} and {Escrig Murua}, {Juan E.}",
note = "Export Date: 8 June 2018 CODEN: JMMMD Correspondence Address: Escrig, J.; Departamento de F{\'i}sica, Universidad de Santiago de Chile (USACH), Av. Ecuador 3493, Chile; email: juan.escrig@usach.cl Funding details: 041731EM-POSTDOC, DICYT, Departamento de Investigaciones Cient{\'i}ficas y Tecnol{\'o}gicas, Universidad de Santiago de Chile Funding details: FB0807, FINATEC, Funda{\cc}{\~a}o de Empreendimentos Cient{\'i}ficos e Tecnol{\'o}gicos Funding details: 1150952, FONDECYT, Fondo Nacional de Desarrollo Cient{\'i}fico y Tecnol{\'o}gico Funding details: 3180470, FONDECYT, Fondo Nacional de Desarrollo Cient{\'i}fico y Tecnol{\'o}gico Funding text: We thank V. Salinas-Barrera for his insightful commments. This work was supported by Fondecyt Grant 1150952 and 3180470, DICYT Grant 041731EM-POSTDOC from VRIDEI-USACH, Financiamiento Basal para Centros Cient{\'i}ficos y Tecnol{\'o}gicos de Excelencia FB0807, and Conicyt-PCHA/Doctorado Nacional/2014. References: Skyrme, T.H.R., (1962) Nucl. Phys., 31, p. 556; Nahas, Y., Prokhorenko, S., Louis, L., Gui, Z., Kornev, I., Bellaiche, L., (2015) Nat. Commun., 6, p. 8542; Ackerman, P.J., Trivedi, R.P., Senyuk, B., van de Lagemaat, J., Smalyukh, I.I., (2014) Phys. Rev. E, 90, p. 012505; Nagaosa, N., Yu, X.Z., Tokura, Y., (2012) Philos. Trans. A, 370, p. 5806; Finocchio, G., Buttner, F., Tomasello, R., Carpentieri, M., Klaui, M., (2016) J. Phys. D: Appl. Phys., 49, p. 423001; Muhlbauer, S., Binz, B., Jonietz, F., Pfleiderer, C., Rosch, A., Neubauer, A., Georgii, R., Boni, P., (2009) Science, 323, p. 915; Munzer, W., Neubauer, A., Adams, T., Muhlbauer, S., FRanz, C., Jonietz, F., Georgii, R., Pfleiderer, C., (2010) Phys. Rev. B, 81, p. 041203(R); Yu, X.Z., Onose, Y., Kamazawa, N., Park, J.H., Han, J.H., Matsui, Y., Nagaosa, N., Tokura, Y., (2010) Nature, 465, p. 901; Seki, S., Yu, X.Z., Ishiwata, S., Tokura, Y., (2012) Science, 336, p. 198; Yu, X.Z., Kanazawa, N., Onose, Y., Kimoto, K., Zhang, W.Z., Ishiwata, S., Matsui, Y., Tokura, Y., (2011) Nat. Mater., 10, p. 106; Finazzi, M., Savoini, M., Khorsand, A.R., Tsukamoto, A., Itoh, A., Duo, L., Kirilyuk, A., Ezawa, M., (2013) Phys. Rev. Lett., 110, p. 177205; Jiang, W., Upadhayaya, P., Zhang, W., Yu, G., Jungfleisch, M.B., Fradin, F.Y., Pearson, J.E., Hoffmann, A., (2015) Science, 349, p. 283; Wang, W., Zhang, Y., Xu, G., Peng, L., Ding, B., Wang, Y., Hou, Z., Zhang, X.-X., (2016) Adv. Mater., 28, p. 6887; Moreau-Luchaire, C., Moutafis, C., Reyren, N., Sampaio, J., Vaz, C.A.F., Van Horne, N., Bouzehouane, K., Fert, A., (2016) Nat. Nanotechnol., 11, p. 444; Woo, S., Litzius, K., Kruger, B., Im, M.-Y., Caretta, L., Richter, K., Mann, M., Beach, G.S.D., (2016) Nat. Mater., 15, p. 501; Romming, N., Hanneken, C., Menzel, M., Bickel, J.E., Wolter, B., von Bergmann, K., Kubetzka, A., Wiesendanger, R., (2013) Science, 341, p. 636; Jonietz, F., Muhlbauer, S., Pfleiderer, C., Neubauer, A., Munzer, W., Bauer, A., Asams, T., Rosch, A., (2010) Science, 330, p. 1648; Nagaosa, N., Tokura, Y., (2013) Nat. Nanotechnol., 8, p. 899; Litzius, K., Lemesh, I., Kruger, B., Bassirian, P., Caretta, L., Richter, K., Buttner, F., Klaui, M., (2017) Nat. Phys., 13, pp. 170-175; Zhang, X., Ezawa, M., Zhou, Y., (2015) Sci. Rep., 5, p. 9400; Sampaio, J., Cros, V., Rohart, S., Thiaville, A., Fert, A., (2013) Nat. Nanotechnol., 8, pp. 839-844; Rohart, S., Thiaville, A., (2013) Phys. Rev. B, 88, p. 184422; Beg, M., Carey, R., Wang, W., Cort{\'e}s-Ortu{\~n}o, D., Vousden, M., Bisotti Albert, M., Chernyshenko, D., Fangohr, H., (2015) Sci. Rep., 5, p. 17137; Dai, Y.Y., Wang, H., Tao, P., Yang, T., Ren, W.J., Zhang, Z.D., (2013) Phys. Rev. B, 88, p. 054403; Guslienko, K., (2015) IEEE Magn. Lett., 6, p. 4000104; Castro, M.A., Allende, S., (2016) J. Magn. Magn. Mater., 417, pp. 344-348; Guslienko, K.Y., Gareeva, Z.V., (2016) IEEE Magn. Lett., 8, p. 4100305; Boulle, O., Vogel, J., Yang, H., Pizzini, S., de Souza Chaves, D., Locatelli, A., Onur Mentes, T., Gaudin, G., (2016) Nat. Nanotechnol., 11, p. 449; Fert, A., Cros, V., Sampaio, J., (2013) Nat. Nanotechnol., 8, p. 152; Sampaio, J., Cros, V., Fert, A., Rohart, S., Thiaville, A., (2013) Nat. Nanotechnol., 8, p. 839; Miao, B.F., Wen, Y., Yan, M., Sun, L., Cao, R.X., Wu, D., You, B., Ding, H.F., (2015) Appl. Phys. Lett., 107, p. 222402; Gilbert, D.A., Maranville, B.B., Balk, A.L., Kirby, B.J., Fischer, P., Pierce, D.T., Unguris, J., Liu, K., (2015) Nat. Commun., 6, p. 8462; Aharoni, A., Introduction to the Theory of Ferromagnetism (1996), Clarendon Oxford; Belavin, A.A., Polyakov, A.M., (1975) JETP Lett., 22, pp. 245-247; Vidal-Silva, N., Riveros, A., Escrig, J., (2017) J. Magn. Magn. Mater., 443, pp. 116-123; Landeros, P., Escrig, J., Altbir, D., Laroze, D., d'Albuquerque e Castro, J., Vargas, P., (2005) Phys. Rev. B, 71; Mejia-Lopez, J., Altbir, D., Landeros, P., Escrig, J., Romero, A.H., roshchin, I.V., Li, C.-P., Schuller, I.K., (2010) Phys. Rev. B, 81, p. 184417; Riveros, A., Vidal-Silva, N., Landeros, P., Altbir, D., Vogel, E.E., Escrig, J., (2016) J. Magn. Magn. Mater., 401, pp. 848-852; Donahue, M.J., Porter, D.G., (1999), OOMMF User's Guide 1.0. Interagency Report NISTIR 6376. National Institute of Standards and Technology, Gaithersburg, MD; Legrand, W., Chauleau, J.-Y., Maccariello, D., Reyren, N., Collin, S., Bouzehouane, K., Jaouen, N., Fert, A., (2018), arXiv:1712.0597v2 [cond-mat.mtrl-sci]; Fang, Y., Magnetic thin Films With Graded or Tilted Anisotropy for Spintronics Devices (2013), PhD thesis University of Gothenburg Sweden; Ono, T., Miyajima, H., Shigeto, K., Shinjo, T., (1999) J. Magn. Magn. Mater., 198-99, pp. 225-227; Krupinski, M., Mitin, D., Zarzycki, A., Szkudlarek, A., Giersig, M., Albrecht, M., Marszalek, M., (2017) Nanotechnology, 28, p. 085302; Michea, S., Oyarzun, S., Vidal, S., Denardin, J.C., (2017) AIP Adv., 7, p. 056310; Lau, J.W., Liu, X., Boling, R.C., Shaw, J.M., (2011) Phys. Rev. B, 84, p. 214427; Lavin, R., Gallardo, C., Palma, J.L., Escrig, J., Denardin, J.C., (2012) J. Magn. Magn. Mater., 324, pp. 2360-2362",
year = "2018",
doi = "10.1016/j.jmmm.2018.04.018",
language = "English",
volume = "460",
pages = "292--296",
journal = "Journal of Magnetism and Magnetic Materials",
issn = "0304-8853",
publisher = "Elsevier Science B.V.",

}

TY - JOUR

T1 - Analytical and numerical Ku-B phase diagrams for cobalt nanostructures: Stability region for a Bloch skyrmion

AU - Riveros, A.

AU - Vidal-Silva, N.

AU - Tejo, F.

AU - Escrig Murua, Juan E

AU - Escrig Murua, Juan E.

N1 - Export Date: 8 June 2018 CODEN: JMMMD Correspondence Address: Escrig, J.; Departamento de Física, Universidad de Santiago de Chile (USACH), Av. Ecuador 3493, Chile; email: juan.escrig@usach.cl Funding details: 041731EM-POSTDOC, DICYT, Departamento de Investigaciones Científicas y Tecnológicas, Universidad de Santiago de Chile Funding details: FB0807, FINATEC, Fundação de Empreendimentos Científicos e Tecnológicos Funding details: 1150952, FONDECYT, Fondo Nacional de Desarrollo Científico y Tecnológico Funding details: 3180470, FONDECYT, Fondo Nacional de Desarrollo Científico y Tecnológico Funding text: We thank V. Salinas-Barrera for his insightful commments. This work was supported by Fondecyt Grant 1150952 and 3180470, DICYT Grant 041731EM-POSTDOC from VRIDEI-USACH, Financiamiento Basal para Centros Científicos y Tecnológicos de Excelencia FB0807, and Conicyt-PCHA/Doctorado Nacional/2014. References: Skyrme, T.H.R., (1962) Nucl. Phys., 31, p. 556; Nahas, Y., Prokhorenko, S., Louis, L., Gui, Z., Kornev, I., Bellaiche, L., (2015) Nat. Commun., 6, p. 8542; Ackerman, P.J., Trivedi, R.P., Senyuk, B., van de Lagemaat, J., Smalyukh, I.I., (2014) Phys. Rev. E, 90, p. 012505; Nagaosa, N., Yu, X.Z., Tokura, Y., (2012) Philos. Trans. A, 370, p. 5806; Finocchio, G., Buttner, F., Tomasello, R., Carpentieri, M., Klaui, M., (2016) J. Phys. D: Appl. Phys., 49, p. 423001; Muhlbauer, S., Binz, B., Jonietz, F., Pfleiderer, C., Rosch, A., Neubauer, A., Georgii, R., Boni, P., (2009) Science, 323, p. 915; Munzer, W., Neubauer, A., Adams, T., Muhlbauer, S., FRanz, C., Jonietz, F., Georgii, R., Pfleiderer, C., (2010) Phys. Rev. B, 81, p. 041203(R); Yu, X.Z., Onose, Y., Kamazawa, N., Park, J.H., Han, J.H., Matsui, Y., Nagaosa, N., Tokura, Y., (2010) Nature, 465, p. 901; Seki, S., Yu, X.Z., Ishiwata, S., Tokura, Y., (2012) Science, 336, p. 198; Yu, X.Z., Kanazawa, N., Onose, Y., Kimoto, K., Zhang, W.Z., Ishiwata, S., Matsui, Y., Tokura, Y., (2011) Nat. Mater., 10, p. 106; Finazzi, M., Savoini, M., Khorsand, A.R., Tsukamoto, A., Itoh, A., Duo, L., Kirilyuk, A., Ezawa, M., (2013) Phys. Rev. Lett., 110, p. 177205; Jiang, W., Upadhayaya, P., Zhang, W., Yu, G., Jungfleisch, M.B., Fradin, F.Y., Pearson, J.E., Hoffmann, A., (2015) Science, 349, p. 283; Wang, W., Zhang, Y., Xu, G., Peng, L., Ding, B., Wang, Y., Hou, Z., Zhang, X.-X., (2016) Adv. Mater., 28, p. 6887; Moreau-Luchaire, C., Moutafis, C., Reyren, N., Sampaio, J., Vaz, C.A.F., Van Horne, N., Bouzehouane, K., Fert, A., (2016) Nat. Nanotechnol., 11, p. 444; Woo, S., Litzius, K., Kruger, B., Im, M.-Y., Caretta, L., Richter, K., Mann, M., Beach, G.S.D., (2016) Nat. Mater., 15, p. 501; Romming, N., Hanneken, C., Menzel, M., Bickel, J.E., Wolter, B., von Bergmann, K., Kubetzka, A., Wiesendanger, R., (2013) Science, 341, p. 636; Jonietz, F., Muhlbauer, S., Pfleiderer, C., Neubauer, A., Munzer, W., Bauer, A., Asams, T., Rosch, A., (2010) Science, 330, p. 1648; Nagaosa, N., Tokura, Y., (2013) Nat. Nanotechnol., 8, p. 899; Litzius, K., Lemesh, I., Kruger, B., Bassirian, P., Caretta, L., Richter, K., Buttner, F., Klaui, M., (2017) Nat. Phys., 13, pp. 170-175; Zhang, X., Ezawa, M., Zhou, Y., (2015) Sci. Rep., 5, p. 9400; Sampaio, J., Cros, V., Rohart, S., Thiaville, A., Fert, A., (2013) Nat. Nanotechnol., 8, pp. 839-844; Rohart, S., Thiaville, A., (2013) Phys. Rev. B, 88, p. 184422; Beg, M., Carey, R., Wang, W., Cortés-Ortuño, D., Vousden, M., Bisotti Albert, M., Chernyshenko, D., Fangohr, H., (2015) Sci. Rep., 5, p. 17137; Dai, Y.Y., Wang, H., Tao, P., Yang, T., Ren, W.J., Zhang, Z.D., (2013) Phys. Rev. B, 88, p. 054403; Guslienko, K., (2015) IEEE Magn. Lett., 6, p. 4000104; Castro, M.A., Allende, S., (2016) J. Magn. Magn. Mater., 417, pp. 344-348; Guslienko, K.Y., Gareeva, Z.V., (2016) IEEE Magn. Lett., 8, p. 4100305; Boulle, O., Vogel, J., Yang, H., Pizzini, S., de Souza Chaves, D., Locatelli, A., Onur Mentes, T., Gaudin, G., (2016) Nat. Nanotechnol., 11, p. 449; Fert, A., Cros, V., Sampaio, J., (2013) Nat. Nanotechnol., 8, p. 152; Sampaio, J., Cros, V., Fert, A., Rohart, S., Thiaville, A., (2013) Nat. Nanotechnol., 8, p. 839; Miao, B.F., Wen, Y., Yan, M., Sun, L., Cao, R.X., Wu, D., You, B., Ding, H.F., (2015) Appl. Phys. Lett., 107, p. 222402; Gilbert, D.A., Maranville, B.B., Balk, A.L., Kirby, B.J., Fischer, P., Pierce, D.T., Unguris, J., Liu, K., (2015) Nat. Commun., 6, p. 8462; Aharoni, A., Introduction to the Theory of Ferromagnetism (1996), Clarendon Oxford; Belavin, A.A., Polyakov, A.M., (1975) JETP Lett., 22, pp. 245-247; Vidal-Silva, N., Riveros, A., Escrig, J., (2017) J. Magn. Magn. Mater., 443, pp. 116-123; Landeros, P., Escrig, J., Altbir, D., Laroze, D., d'Albuquerque e Castro, J., Vargas, P., (2005) Phys. Rev. B, 71; Mejia-Lopez, J., Altbir, D., Landeros, P., Escrig, J., Romero, A.H., roshchin, I.V., Li, C.-P., Schuller, I.K., (2010) Phys. Rev. B, 81, p. 184417; Riveros, A., Vidal-Silva, N., Landeros, P., Altbir, D., Vogel, E.E., Escrig, J., (2016) J. Magn. Magn. Mater., 401, pp. 848-852; Donahue, M.J., Porter, D.G., (1999), OOMMF User's Guide 1.0. Interagency Report NISTIR 6376. National Institute of Standards and Technology, Gaithersburg, MD; Legrand, W., Chauleau, J.-Y., Maccariello, D., Reyren, N., Collin, S., Bouzehouane, K., Jaouen, N., Fert, A., (2018), arXiv:1712.0597v2 [cond-mat.mtrl-sci]; Fang, Y., Magnetic thin Films With Graded or Tilted Anisotropy for Spintronics Devices (2013), PhD thesis University of Gothenburg Sweden; Ono, T., Miyajima, H., Shigeto, K., Shinjo, T., (1999) J. Magn. Magn. Mater., 198-99, pp. 225-227; Krupinski, M., Mitin, D., Zarzycki, A., Szkudlarek, A., Giersig, M., Albrecht, M., Marszalek, M., (2017) Nanotechnology, 28, p. 085302; Michea, S., Oyarzun, S., Vidal, S., Denardin, J.C., (2017) AIP Adv., 7, p. 056310; Lau, J.W., Liu, X., Boling, R.C., Shaw, J.M., (2011) Phys. Rev. B, 84, p. 214427; Lavin, R., Gallardo, C., Palma, J.L., Escrig, J., Denardin, J.C., (2012) J. Magn. Magn. Mater., 324, pp. 2360-2362

PY - 2018

Y1 - 2018

N2 - In this paper we calculate the energies corresponding to the different magnetic phases present in a ferromagnetic cylinder by means of analytical calculations. From the comparison of these energies, it is possible to construct magnetic phase diagrams as a function of the uniaxial anisotropy of the sample and the applied external magnetic field. As proof of concept, we analyzed the magnetic phase diagrams for a cobalt dot of 240 nm in diameter and 70 nm in length, with an easy axis parallel to the dot axis, and with a magnetic field applied towards or perpendicular to this axis. From these diagrams we have obtained the stability regions for a Bloch skyrmion (Sk), a vortex core (VC) and a ferromagnetic (F) configuration, which can point in any ψ direction. Our results provide a pathway to engineer the formation and controllability of a skyrmion in a ferromagnetic dot to different anisotropy constants and magnetic fields. © 2018 Elsevier B.V.

AB - In this paper we calculate the energies corresponding to the different magnetic phases present in a ferromagnetic cylinder by means of analytical calculations. From the comparison of these energies, it is possible to construct magnetic phase diagrams as a function of the uniaxial anisotropy of the sample and the applied external magnetic field. As proof of concept, we analyzed the magnetic phase diagrams for a cobalt dot of 240 nm in diameter and 70 nm in length, with an easy axis parallel to the dot axis, and with a magnetic field applied towards or perpendicular to this axis. From these diagrams we have obtained the stability regions for a Bloch skyrmion (Sk), a vortex core (VC) and a ferromagnetic (F) configuration, which can point in any ψ direction. Our results provide a pathway to engineer the formation and controllability of a skyrmion in a ferromagnetic dot to different anisotropy constants and magnetic fields. © 2018 Elsevier B.V.

KW - Antiferromagnetic materials

KW - Cobalt

KW - Ferromagnetic materials

KW - Ferromagnetism

KW - Graphic methods

KW - Magnetic fields

KW - Phase diagrams

KW - Vortex flow

KW - Analytical calculation

KW - Anisotropy constants

KW - External magnetic field

KW - Ferromagnetic cylinders

KW - Magnetic phase diagrams

KW - Proof of concept

KW - Stability regions

KW - Uniaxial anisotropy

KW - Magnetic anisotropy

U2 - 10.1016/j.jmmm.2018.04.018

DO - 10.1016/j.jmmm.2018.04.018

M3 - Article

VL - 460

SP - 292

EP - 296

JO - Journal of Magnetism and Magnetic Materials

T2 - Journal of Magnetism and Magnetic Materials

JF - Journal of Magnetism and Magnetic Materials

SN - 0304-8853

ER -