Skip to main content
SpringerLink
Log in

Magnetic Properties of Mg x Cu1−x Cr2O4 Spinels are Studied by Different Theoretical Methods

  • Original Paper
  • Published:
Journal of Superconductivity and Novel Magnetism Aims and scope Submit manuscript

Abstract

The external magnetic field induced the reorientation of magnetization of a ferromagnetic (or antiferromagnetic) treated within the framework of many-body Green’s function theory by considering all components of the magnetization. We present a new method for the calculation of expectation values in terms of the eigenvalues and eigenvectors of the equations of motion matrix for the set of Green’s functions. Magnetization and magnetic susceptibility are investigated when an external magnetic field is applied in (x-z)-plane. The mean field theory is applied to calculate the nearest neighbour and the next-neighbour super-exchange J 1(Cr−Cr) and J 2(Cr−(Mg(Cu)−O)−Cr), respectively, for the Mg x Cu1−x Cr2O4 in the range of 0 ≤ x ≤ 1. The intra-planar and the inter-planar interactions are deduced. The high-temperature series expansions (HTSEs) are derived for the magnetic susceptibility and two-spin correlation functions for a Heisenberg ferromagnetic model on the B-spinel lattice. The calculations are developed in the framework of the random-phase approximation (RPA). The magnetic-phase diagram is deduced. A spin-glass phase is predicted for intermediate range of concentration. The spin glass is obtained. The obtained results are comparable with those obtained by magnetic measurements. The critical exponents associated with the magnetic susceptibility (γ) and the correlation lengths (ν) have been deduced. The obtained values are comparable to those of 3D Heisenberg model.

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

Similar content being viewed by others

References

  1. Bland, J.A.C., Heinrich, B.: Ultrathin Magnetic Structures. Springer, Berlin (1994)

    Book  Google Scholar 

  2. Lugert, G., Robl, W., Pfau, L., Brockmann, M., Bayreuther, G.: J. Magn. Magn. Mater. 121, 498 (1993)

    Article  ADS  Google Scholar 

  3. Schulte, O., Klose, F., Felsch, W.: Phys. Rev. B 52, 6480 (1995)

    Article  ADS  Google Scholar 

  4. Farle, M., Mirwald-Schulz, B., Anisimov, A.N., Platow, W., Baberschke, K.: Phys. Rev. B 55, 3708 (1997). (and references therein.)

    Article  ADS  Google Scholar 

  5. Bland, J.A.C., Heinrich, B.: Ultrathin Magnetic Structures. Springer, Berlin (1994)

    Book  Google Scholar 

  6. Lugert, G., Robl, W., Pfau, L., Brockmann, M., Bayreuther, G.: J. Magn. Mater. 121, 498 (1993)

    Article  ADS  Google Scholar 

  7. Schute, O., Klose, F., Felch, W.: Phys. Rev. B 52, 6480 (1995)

    Article  ADS  Google Scholar 

  8. Farle, M., Mirwald Schulz, B., Anisimov, A.N., Platow, W., Baberschke, K.: Phys. Rev. B 55, 3708 (1997)

    Article  ADS  Google Scholar 

  9. Lazarev, S.B., Panti, M., Toni, B.S.: Physica A 246, 53 (1997)

    Article  ADS  Google Scholar 

  10. Frobrich, P., et al.: Eur. Phys. J. B 13, 477 (2000)

    ADS  Google Scholar 

  11. Frobrich, P., et al.: Eur. Phys. J. B 18, 579 (2000)

    Article  ADS  Google Scholar 

  12. Wang, H.Y., et al.Int J. Mod. Phys. B 16, 3803 (2002)

    Article  ADS  Google Scholar 

  13. Wang, C.R., Chen, Y.Y., Yao, Y.D., Lin, Y.S., Ou, M.N., Taher, S.M.A., Hamdeh, H.H., Zhang, X., Ho, J.C., Gruber, B., John, J.: Mag. Mag. Mat. 269, 419 (2004)

    Article  ADS  Google Scholar 

  14. Tyablikov, S.V.: Ukr. Mat. Zh. 11, 289 (1959)

    Google Scholar 

  15. Tyablikov, S.V.: Methods in the Quantum Theory of Magnetism. Plenum, New York (1967)

    Book  Google Scholar 

  16. Kemei, M.C., Moffitt, S.L., Shoemaker, D.P., Seshadri, R.: J. Phys. Condens. Matter. 24, 46003 (2012)

    Article  Google Scholar 

  17. Elk, K., Gasser, W.: Die Methode der Greenschen Funktionen in der Festkorperphysik. Akademie, Berlin (1978)

    Google Scholar 

  18. Nolting, W.: Quantentheorie des Magnetismus, vol. 2. B.G. Teubner, Stuttgart (1986)

    Book  Google Scholar 

  19. Narath, A.: Phys. Rev 140, A854 (1965)

    Article  ADS  Google Scholar 

  20. Lines, M.E.: Phys. Rev. 156, 534 (1967)

    Article  ADS  Google Scholar 

  21. Anderson, F.B., Callen, H.B.: Phys. Rev. 136, A1068 (1964)

    Article  MathSciNet  ADS  Google Scholar 

  22. Bloch, F.: Z. Phys 61, 206 (1930)

    Article  ADS  MATH  Google Scholar 

  23. Elk, K., Gasser, W.: Die Methode der Greenschen Funktionen in der Festk orperphysik. Akademie, Berlin (1978)

    Google Scholar 

  24. Nolting, W.: Quantentheorie des Magnetismus, vol. 2. B.G. Teubner, Stuttgart (1986)

    Book  Google Scholar 

  25. Callen, H.B.: Phys. Rev. 130, 890 (1963)

    Article  ADS  MATH  Google Scholar 

  26. Holland, W.E., Broun, H.A.: Phys-Stat. Sol (a) 10, 249 (1972)

    Article  ADS  Google Scholar 

  27. Hamedoun, M., Rachadi, A., Hourmatallah, A., El Allam, D., Benyoussef, A.: Phys. Stat Sol (b) 191, 503 (1995)

    Article  ADS  Google Scholar 

  28. Hachimi, M., Hamedoun, M., Rachadi, A., Benzakour, N.: Physica B 229, 256 (1997)

    Article  ADS  Google Scholar 

  29. Kant, C.H., Deisenhofer, J., Tsurkan, V., Loidl, A.: J. Phys.: Conf. Ser. 200, 032032 (2010)

    ADS  Google Scholar 

  30. Young, A.P., Shastry, B.S.: J. Phys. C15, 4547 (1982)

    ADS  Google Scholar 

  31. Lines, M.E.: Phys. Rev. 139, A1304 (1965)

    Article  ADS  Google Scholar 

  32. Weisselinowa, J.M.: Phys. Stat. Sol. 120, 585 (1983)

    Article  ADS  Google Scholar 

  33. Weisselinowa, J.M., Apostolov, A.T.: J. Phys.: Condens. Matter. 8, 473 (1996)

    ADS  Google Scholar 

  34. Hamedoun, M., Houssa, M., Cherriet, N.Y., Bakkali, F.Z.: Phys. Stat. Sol. (b) 214, 403 (1999)

    Article  ADS  Google Scholar 

  35. Hamedoun, M., Houssa, M., Benzakour, N., Hourmatallah, A.: Physica B 270, 384 (1999)

    Article  ADS  Google Scholar 

  36. Shoemaker, D.P., Sshadri, R.: Phys. Rev. B 82, 214107 (2010)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory of Materials, Processes, Environment and Quality, National School of Applied Sciences, Cady Ayyed University, PB 63, 46000, Safi, Morocco

    R. Masrour

  2. LMPHE (URAC-12), Faculté des Sciences, Université Mohamed V-Agdal, Rabat, Morocco

    R. Masrour & A. Benyoussef

  3. Laboratoire de Physique du Solide, Faculté des Sciences, Université Sidi Mohammed Ben Abdellah, BP 1796, Fès, Morocco

    A. Elgrini, N. Benzakour & K. Bouslykhane

  4. Institute for Nanomaterials and Nanotechnologies, MAScIR, Rabat, Morocco

    M. Hamedoun, A. Benyoussef, O. Mounkachi & H. El Moussaoui

  5. Academie Hassan II des Sciences et Techniques, Rabat, Morocco

    A. Benyoussef

  6. Equipe de Physique du Solide, Ecole Normale Supérieure, BP 5206, Bensouda, Fes, Morocco

    A. Hourmatallah

Authors
  1. R. Masrour
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Elgrini
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Hamedoun
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. Benyoussef
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. A. Hourmatallah
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. N. Benzakour
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. K. Bouslykhane
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. O. Mounkachi
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. H. El Moussaoui
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. Masrour.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Masrour, R., Elgrini, A., Hamedoun, M. et al. Magnetic Properties of Mg x Cu1−x Cr2O4 Spinels are Studied by Different Theoretical Methods. J Supercond Nov Magn 27, 2073–2082 (2014). https://doi.org/10.1007/s10948-014-2545-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10948-014-2545-9

Keywords

Search

Navigation