Skip to main content
SpringerLink
Log in

Border effects on the ground state of an ultrathin magnetic film model

  • Regular Article - Solid State and Materials
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

In the study of ultrathin magnetic films, one of the most simple and widely studied model is the two-dimensional Ising model with short-range ferromagnetic exchange and long-range antiferromagnetic dipolar interactions (ILRA model). In substrates with periodic boundary conditions, it is well known that the ground state of this system, depending on the strength parameter \(\delta \), is given by the antiferromagnetic, the irregular checkerboard and the striped states. In this work, we study the border effects on the ground state. We develop a systematic study on square substrates of size \(L\times L\) with open boundary conditions focusing our attention on the range \(0.35\leqslant \delta \leqslant 0.75\). Our results show that, at intermediate values of \(\delta \), none of the configurations present on substrates with periodic boundary conditions correspond to the ground state of the system. Specifically, we find three new kinds of ground states for \( L \le 8 \), which are also our best candidates to be ground state in systems of sizes up to \( L = 100\). Also, by means of the same systematic study on a similar short-range model, we analyze which of these ground states is a consequence of the long-range character of the dipolar interactions in the ILRA model.

Graphical Abstract

Ground states for \(8 \times 8\) lattice in the range of the strength parameter \(0.35\leqslant \delta \leqslant 0.75\)

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

Data availability statement

Any requirement for the data shown in this paper can be requested via email.

References

  1. R. Lavrijsen, J.H. Lee, A. Fernández-Pacheco, D.C.M.C. Petit, R. Mansell, R.P. Cowburn, Magnetic ratchet for three-dimensional spintronic memory and logic. Nature (London) 493, 647 (2013)

    Article  ADS  Google Scholar 

  2. O. Hellwig, A. Berger, J.B. Kortright, E.E. Fullerton, Domain structure and magnetization reversal of antiferromagnetically coupled perpendicular anisotropy film. J. Mag. Mag. Mat. 319, 13 (2007)

    Article  ADS  Google Scholar 

  3. O. Hellwig, A. Berger, E.E. Fullerton, Magnetic reversal and domain structure in perpendicular AF-coupled films. J. Mag. Mag. Mat. 290, 1 (2005)

    Article  ADS  Google Scholar 

  4. Y. Shiroishi, K. Fukuda, I. Tagawa, S. Takenoiri, H. Tanaka, H. Mutoh, N. Yoshicawa, Future options for HDD storage. IEEE Trans. Mag. 45, 3816 (2009)

    Article  ADS  Google Scholar 

  5. R. Reeve, S.L. Chin, K.P. Kooper, A. Ionescu, C.H.W. Barnes, Electron beam tuning of the magnetic anisotropy in Co/Cu(110) films. IEEE Trans. Mag. 47, 1554 (2011)

    Article  ADS  Google Scholar 

  6. T.J. Hayward, B. Hong, K.N. Vyas, J.J. Palfreyman, J.F.K. Cooper, Z. Jiang, J.R. Jeong, J. Llandro, T. Mitrelias, J.A.C. Bland, C.H.W. Barnes, Magnetic micro-barcodes for molecular tagging applications. J. Phys. D 43, 175001 (2010)

    Article  ADS  Google Scholar 

  7. C. Liang, C.P. Gooneratne, Q.X. Wang, Y. Liu, Y. Gianchandani, J. Kosel, Magnetic properties of FeNi-based thin film materials with different additives. Biosensors 4, 189 (2014)

    Article  Google Scholar 

  8. E. Rastelli, S. Regina, A. Tassi, Phys. Rev. B 76, 054438 (2007)

    Article  ADS  Google Scholar 

  9. J.S.M. Fonseca, L.G. Rizzi, N.A. Alves, Stripe-tetragonal phase transition in the two-dimensional Ising model with dipole interactions: Partition function zeros approach. Phys. Rev. E 86, 011103 (2012)

    Article  ADS  Google Scholar 

  10. S.A. Pighín, S.A. Cannas, Phys. Rev. B 75, 224433 (2007)

    Article  ADS  Google Scholar 

  11. L.G. Rizzi, N.A. Alves, Phys. B (Amsterdam, Neth.) 405, 1571 (2010)

    Article  ADS  Google Scholar 

  12. A. Giuliani, J. Lebowitz, E.H. Lieb, Checkerboards, stripes, and corner energies in spin models with competing interactions Phys. Rev. B 84, 064205 (2011)

    Article  Google Scholar 

  13. K. De’Bell, A.B. MacIsaac, J.P. Whitehead, Dipolar effects in magnetic thin films and quasi-two-dimensional systems. Rev Mod. Phys. 72, 225 (2000)

    Article  ADS  Google Scholar 

  14. O. Portmann, A. Vaterlaus, D. Pescia, An inverse transition of magnetic domain patterns in ultrathin films. Nature (London) 422, 701 (2003)

    Article  ADS  Google Scholar 

  15. O. Portmann, A. Vaterlaus, D. Pescia, Observation of stripe mobility in a dipolar frustrated ferromagnet. Phys. Rev. Lett. 96, 047212 (2006)

    Article  ADS  Google Scholar 

  16. N. Bergeard, S. Schaffert, V. López-Flores, N. Jaouen, J. Geilhufe, C.M. Günther, M. Schneider, C. Graves, T. Wang, B. Wu, A. Scherz, C. Baumier, R. Delaunay, F. Fortuna, M. Tortarolo, B. Tudu, O. Krupin, M.P. Minitti, J. Robinson, W.F. Schlotter, J.J. Turner, J. Lüning, S. Eisebitt, C. Boeglin, Irreversible transformation of ferromagnetic ordered stripe domains in single-shot infrared-pump/resonant-x-ray-scattering-probe experiments. Phys. Rev. B 91, 054416 (2015)

    Article  ADS  Google Scholar 

  17. A.B. MacIsaac, J.P. Whitehead, M.C. Robinson, K. De’Bell, Phys. Rev. B 51, 16033 (1995)

    Article  ADS  Google Scholar 

  18. A.B. MacIsaac, J.P. Whitehead, K. De’Bell, and K. S. Narayanan Phys. Rev. B 46, 6387 (1992)

    Article  ADS  Google Scholar 

  19. M.B. Taylor, B.L. Gyorffy, J. Phys. Condens. Matter 5, 4527 (1993)

    Article  ADS  Google Scholar 

  20. E. Rastelli, S. Regina, A. Tassi, Phys. Rev. B 73, 144418 (2006)

    Article  ADS  Google Scholar 

  21. I. Booth, A.B. MacIsaac, J.P. Whitehead, K. De’Bell, Phys. Rev. Lett. 75, 950 (1995)

    Article  ADS  Google Scholar 

  22. P.M. Gleiser, F.A. Tamarit, S.A. Cannas, Metastable states in a two-dimensional Ising model with dipolar interactions. Physica D 168, 73 (2002)

    Article  ADS  Google Scholar 

  23. P.M. Gleiser, F.A. Tamarit, S.A. Cannas, M.A. Montemurro, Slow dynamics in a two-dimensional Ising model with competing interactions. Phys. Rev. B 68, 134401 (2003)

    Article  ADS  Google Scholar 

  24. S.A. Cannas, D.A. Stariolo, F.A. Tamarit, Stripe-tetragonal first-order phase transition in ultrathin magnetic films. Phys. Rev. B 69, 092409 (2004)

    Article  ADS  Google Scholar 

  25. S.A. Cannas, M.F. Michelon, D.A. Stariolo, F.A. Tamarit, Ising nematic phase in ultrathin magnetic films: a Monte Carlo study. Phys. Rev. B 73, 184425 (2006)

    Article  ADS  Google Scholar 

  26. M.E.J. Newman, G.T. Barkema, Monte Carlo Methods in Statistical Physics (Oxford University Press, Oxford, 1999)

    Book  Google Scholar 

  27. C.M. Horowitz, M.A. Bab, M. Mazzini, M.L. Rubio Puzzo, G.P. Saracco, Phase transitions and critical phenomena in the two-dimensional Ising model with dipole interactions: a short-time dynamics study. Phys. Rev. B 92, 042127 (2015)

  28. M.A. Bab, C.M. Horowitz, M.L. Rubio Puzzo, G.P. Saracco, Phase transitions and multicritical behavior in the Ising model with dipolar interactions. Phys. Rev. B 94, 042104 (2016)

    Article  MathSciNet  ADS  Google Scholar 

  29. P.P. Ewald, Ann. Phys. (Berlin, Ger.) 369, 253 (1921)

    Article  ADS  Google Scholar 

  30. S. Curilef, Int. J. Mod. Phys. C 11, 629 (2000)

    ADS  Google Scholar 

  31. Due to the simplicity of the short-range model, once the configurations are given, the phase diagram of Fig. 13 can be determined by means of analytical expressions

Download references

Acknowledgements

This work was financially supported by CONICET, UNLP, and ANPCyT (Argentina). We thank UnCaFiQT (SNCAD) for computational resources.

Author information

Authors and Affiliations

  1. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas (INIFTA), UNLP, CCT La Plata-CONICET, Sucursal 4, Casilla de Correo 16, 1900, La Plata, Argentina

    C. M. Horowitz

  2. Instituto de Física de Líquidos y Sistemas Biológicos (IFLYSIB), UNLP, CCT La Plata-CONICET, Calle 59 no. 789, B1900BTE, La Plata, Argentina

    E. S. Loscar

  3. Departamento de Física, Universidad Nacional de La Plata c.c. 67, 1900, La Plata, Argentina

    E. S. Loscar

Authors
  1. C. M. Horowitz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. S. Loscar
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed equally to the theoretical and numerical aspects of this paper. Also, all authors contributed equally to its writing.

Corresponding author

Correspondence to C. M. Horowitz.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Horowitz, C.M., Loscar, E.S. Border effects on the ground state of an ultrathin magnetic film model. Eur. Phys. J. B 97, 33 (2024). https://doi.org/10.1140/epjb/s10051-024-00674-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/s10051-024-00674-8

Search

Navigation