The critical and compensation temperatures of the bilayer Bethe lattices with one of the layers having only spin-1/2 atoms and the other having only spin-1 atoms placed symmetrically are studied by using exact recursion relations in a pairwise approach. The Hamiltonian of the model consist of the bilinear intralayer coupling constants of the two layers J 1 and J 2 for the interactions of the atoms in layers with spin-1/2 and spin-1, respectively, and the bilinear interlayer coupling constant J 3 between the adjacent atoms with spin-1/2 and spin-1 of the layers. After obtaining the ground state phase diagram with J 1 > 0, the variations of the order-parameters and the free energy are investigated to obtain the phase diagram of the model by considering only the ferromagnetic ordering of the layers, i.e. J 1 > 0 and J 2 > 0, and ferromagnetic or antiferromagnetic ordering of the adjacent spins of the layers, J 3 > 0 or J 3 < 0, respectively. It was found that the system presents both second- and first-order phase transitions and, tricritical points. The compensation temperatures was also observed for the appropriate values of the system parameters.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
H. J. Elmers, Int. J. Mod. Phys. B 9:3115 (1995).
Digest 13th Int. Colloq. on Magnetic Films and Surfaces, Glasgow (1991).
M. N. Baibich, J. M. Broto, A. Fert, F. Nguyen Van Dau, F. Petroff, P. Eitenne, G. Creuzet, A. Friederich, and J. Chazelas, Phys. Rev. Lett. 61:2472; G. Binasch, P. Grunberg, F. Saurenbach, and W. Zinn, Phys. Rev. B 4828 (1989).
J. Sayama, T. Asahi, K. Mizutani, and T. Osaka, J. Phys. D: Appl. Phys. 37:L1–L4 (2004).
R. Wu and A. J. Freeman, Phys. Rev. B 45:7205 (1992); M. Donath, J. Phys.: Condens. Matter 11:9421 (1999).
R. C. O’Handley and S. W. Sun, Phys. Rev. Lett. 66:2798 (1991); G. Bochi, O. Song, and R. C. O’Handley, Phys. Rev. B 50:2043 (1994).
Y. M. Seidov and G. R. Shaulov, J. Phys.: Condens. Matter 6:9621 (1994); M. Jaščur and T. Kaneyoshi, J. Magn. Magn. Mater 168:47 (1997); B. Laaboudi, M. Saber, and M. Kerouad, Phys. Stat. Sol. (b) 212:153 (1999); T. Bouziane and A. Belaaraj, Phys. Stat. Sol. (b) 214:387 (1999); T. Kaneyoshi and S. Shin, Phys. Stat. Sol. (b) 218:537 (2000).
F. Dujardin, B. Stébé, A. Ainane, and M. Saber, Chinese J. Phys. 37:479 (1999); T. Bouziane, Phys. Stat. Sol. (b) 217:951 (2000); M. Bentaleb, N. El Aouad, and M. Saber, Chinese J. Phys. 40:307 (2002).
G. Wiatrowski, G. Bayreuther, and K. Pruegl, J. Mag. Magn. Mater. 196–197:26 (1999); G. Wiatrowski, Physica A 290:107 (2001).
M. Bengrine, A. Benyoussef, H. Ez-Zahraouy, and F. Mhirech, Physica A 268:149 (1999); H. Ez-Zahraouy and A. Kassou-Ou-Ali, Chinese J. Phys. 40:86 (2002).
L. Bahmad, A. Benyoussef, and H. Ez-Zahraouy, Surf. Sci. 536:114 (2003); X.-G. Wang, N.-N. Liu, S.-H. Pand, and G.-Z. Yang, J. Magn. Magn. Mater. 212:121 (2000).
H. Ez-Zahraouy, L. Bahmad, and A. Benyoussef, Physica A 358:86 (2005).
M. L. Lyra and C. R. da Silva, Phys. Rev. B 47:526 (1993).
J. L. Monroe, Physica A 335:563 (2004).
C.-K. Hu and N. Sh. Izmailian, Phys. Rev. E 59:6489 (1999); E. Albayrak, Phys. Stat. Sol. (b) 244:759 (2007).
L. Bahmad, A. Benyoussef, and H. Ez-Zahraouy, J. Magn. Magn. Mater. 251:115 (2002); A. Benyoussef, H. Ez-Zahraouy, H. Mahboub, and M. J. Ouazzani, Physica A 326:220 (2003).
J. W. Tucker, T. Balcerzak, M. Gzik, and A. Sukiennicki, J. Magn. Magn. Mater. 187:381 (1998); M. Gzik-Szumiata and T. Balcerzak, Acta Physica Slovaca 48:611 (1998).
L. Bahmad, A. Benyoussef, and H. Ez-Zahraouy, Surf. Sci. 552:1 (2004); L. Bahmad, A. Benyoussef, and H. Ez-Zahraouy, M. J. Condensed Matter 5:134 (2004).
E. Albayrak and O. Canko, Physica A 373:363 (2007); O. Canko and E. Albayrak, Phys. Rev. E 75:011116 (2007)
D. Gatteshi, O. Khan, J. S. Miller, and F. Palacio (eds.) Magnetic Molecular Materials (NATO ASI Series) (Dordrecht, Kluwer Academic, 1991); O. Khan, Molecular Magnetism (VCH Publishers, New York, 1993).
H. J. Williams, R. C. Sherwood, F. G. Foster, and E.M. Kelley, J. Appl. Phys. 28:1181 (1957).
M. Bengrine, A. Benyoussef, A. El Kenz, M. Loulidi, and F. Mhirech, J. Magn. Magn. Mater. 183:334 (1998).
K. Htoutou, A. Ainane, and M. Saber, J. Magn. Magn. Mater. 269:245 (2004).
W. Jiang, G.-Z. Wei, and A. Du, J. Magn. Magn. Mater 250:49 (2002).
W. Jiang and G.-Z. Wei, Physica B 362:236 (2005).
M. Jaščur and T. Kaneyoshi, J. Phys.: Condens. Matter 5:6313 (1993).
M. Bengrine, A. Benyoussef, A. El Kenz, and L. Peliti, Physica B 269:34 (1999).
M. Jaščur and T. Kaneyoshi, Physica A 220:542 (1995).
T. Kaneyoshi, Phys. Rev. B 52:7304 (1995).
M. Jaščur and T. Kaneyoshi, J. Phys. Condens. Mater. 5:6313 (1993).
M.-h. Yu and Z.-d. Zhang, J. Magn. Magn. Mater. 195:514 (1999).
C.-K. Hu, N. Sh. Izmailian, and K. B. Oganesyan, Phys. Rev. E 59:6489 (1999); E. Albayrak, S. Yilmaz, and S. Akkaya, J. Magn. Magn. Mater 310:98 (2007).
P. J. Jensen, K. H. Bennemann, K. Baberschke, P. Poulopoulos, and M. Farle, J. Appl. Phys. 87:6692 (2000).
B. Schmittmann and R. K. P. Zia, Phys. Rep. 301:45 (1998).
Author information
Authors and Affiliations
Corresponding author
Additional information
PACS: 05.50.+q 05.70.Fh 64.60.Cn 75.10.Hk
Rights and permissions
About this article
Cite this article
Albayrak, E., Bulut, T. & Yilmaz, S. Critical and Compensation Temperatures of the Ising Bilayer System Consisting of Spin-1/2 and Spin-1 Atoms. J Stat Phys 127, 967–983 (2007). https://doi.org/10.1007/s10955-007-9311-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10955-007-9311-3