OJAppS  Vol.3 No.3 , July 2013
Mean-Field Solution of the Mixed Spin-2 and Spin-5/2 Ising Ferrimagnetic System with Different Single-Ion Anisotropies
Author(s) Fathi Abubrig
ABSTRACT

The mixed spin-2 and spin-5/2 Ising ferrimagnetic system with different anisotropies (DA/zJ|) for the spin-2 and (DB/zJ|) for the spin-5/2 is studied by the use of the mean-field theory based on the Bogoliubov inequality for the free energy. First, the ground state phase diagram of the system at zero temperature is obtained on the (DA/zJ,DB/zJ|) plane. Topologically, different kinds of phase diagrams are achieved by changing the temperature and the values of the single ion anisotropies DA/zJ and DB/zJ. Besides second-order transition lines, first order phase transition lines terminating at tricritical points, are found. The existence and dependence of a compensation temperature on single-ion anisotropies is also investigated.


Cite this paper
F. Abubrig, "Mean-Field Solution of the Mixed Spin-2 and Spin-5/2 Ising Ferrimagnetic System with Different Single-Ion Anisotropies," Open Journal of Applied Sciences, Vol. 3 No. 3, 2013, pp. 270-277. doi: 10.4236/ojapps.2013.33034.
References
[1]   O. Khan, “Molecular Magnetism,” VCH publishers, New York, 1993.

[2]   T. Kaneyoshi and Y. Nakamura, “A Theoretical Investigation for Low-Dimensional Molecular-Based Magnetic Materials,” Journal of Physics: Condensed Matter, Vol. 10, No. 13, 1998, p. 3003. doi:10.1088/0953-8984/10/13/017

[3]   T. Kaneyoshi, Y. Nakamura and S. Shin, “A Diluted Mixed Spin-2 and Spin-5/2 Ferrimagnetic Ising System; a Study of a Molecular-Based Magnet,” Journal of Physics: Condensed Matter, Vol. 10, No. 31, 1998, p. 7025. doi:10.1088/0953-8984/10/31/018

[4]   L. Néel, “Propriétées Magnétiques des Ferrites; Férrimag nétisme et Antiferromagnétisme,” Annales de Physique (Paris), Vol. 3, 1948, pp. 137-198.

[5]   M. Mansuripur, “Magnetization Reversal, Coercivity, and the Process of Thermomagnetic Recording in Thin Films of Amorphous Rare Earth Transition Metal Alloys,” Journal of Applied Physics, Vol. 61, No. 4, 1987, pp. 1580-1587. doi:10.1063/1.338094

[6]   F. Tanaka, S. Tanaka and N. Imamura, “Magneto-Optical Recording Characteristics of TbFeCo Media by Magnetic Field Modulation Method,” Japan Journal of Applied Physics, Vol. 26, 1987, pp. 231-235. doi:10.1143/JJAP.26.231

[7]   L. L. Goncaloves, “Uniaxial Anisotropy Effects in the Ising Model: An Exactly Soluble Model,” Physica Scripta, Vol. 32, No. 3, 1985, p. 248. doi:10.1088/0031-8949/32/3/012

[8]   L. L. Goncaloves, “Uniaxial Anisotropy Effects in the Ising Model: An Exactly Soluble Model,” Physica Scripta, Vol. 33, No. 2, 1986, p. 192. doi:10.1088/0031-8949/33/2/018

[9]   A. Dakhama and N. Benayad, “On the Existence of Compensation Temperature in 2d Mixed-Spin Ising Ferri magnets: An Exactly Solvable Model,” Journal of Magnetism and Magnetic Materials, Vol. 213, No. 1-2, 2000, pp. 117-125. doi:10.1016/S0304-8853(99)00606-X

[10]   N. R. da Silva and S. R. Salinas, “Mixed-Spin Ising Model on Beth Lattice,” Physical Review, Vol. 44, No. 2, 1991, pp. 852-855. doi:10.1103/PhysRevB.44.852

[11]   J. W. Tucker, “The Ferrimagnetic Mixed Spin-1/2 and Spin-1 Sing System,” Journal of Magnetism and Magnetic Materials, Vol. 195, No. 3, 1999, pp. 733-740. doi:10.1016/S0304-8853(99)00302-9

[12]   T. Kaneyoshi and J. C. Chen, “Mean-Field Analysis of a Ferrimagnetic Mixed Spin System,” Journal of Magnet ism and Magnetic Materials, Vol. 98, No. 1-2, 1991, pp. 201-204. doi:10.1016/0304-8853(91)90444-F

[13]   T. Kaneyoshi, “Curie Temperatures and Tricritical Points in Mixed Ising Ferromagnetic Systems,” The Physical Society of Japan, Vol. 56, 1987, pp. 2675-2680. doi:10.1143/JPSJ.56.2675

[14]   T. Kaneyoshi, “Phase Transition of the Mixed Spin System with a Random Crystal Field,” Physica A, Vol. 153, No. 3, 1988, pp. 556-566. doi:10.1016/0378-4371(88)90240-3

[15]   T. Kaneyoshi, M. Jascur and P. Tomczak, “The Ferri magnetic Mixed Spin-1/2 and Spin-3/2 Ising System,” Journal of Physics: Condensed Matter, Vol. 4, No. 49, 1992, pp. L653-L658. doi:10.1088/0953-8984/4/49/002

[16]   T. Kaneyoshi, “Tricritical Behavior of a Mixed Spin-1/2 and Spin-2 Ising System,” Physica A, Vol. 205, No. 4, 1994, pp. 677-686. doi:10.1016/0378-4371(94)90229-1

[17]   A. Bobak and M. Jurcisin, “Discussion of Critical Behaviour in a Mixed-Spin Ising Model,” Physica A, Vol. 240, No. 3-4, 1997, pp. 647-656. doi:10.1016/S0378-4371(97)00044-7

[18]   S. G. A. Quadros and S. R. Salinas, “Renormalization Group Calculations for a Mixed-Spin Ising Model,” Physica A: Statistical Mechanics and Its Applications, Vol. 206, No. 3-4, 1994, pp. 479-496.

[19]   G.-M. Zhang and C.-Z. Yang, “Monte Carlo Study of the Two-Dimensional Quadratic Ising Ferromagnet with Spins S = 1/2 and S = 1 and with Crystal-Field Interactions,” Physical Review B, Vol. 48, No. 13, 1993, pp. 9452-9455. doi:10.1103/PhysRevB.48.9452

[20]   G. M. Buendia and M. A. Novotny, “Numerical Study of a Mixed Ising Ferrimagnetic System,” Journal of Physics: Condensed Matter, Vol. 9, No. 27, 1997, pp. 5951-5964. doi:10.1088/0953-8984/9/27/021

[21]   G. M. Buendia and J. A. Liendo, “Monte Carlo Simulation of a Mixed Spin-1/2 and Spin-3/2 Ising Ferrimagnetic System,” Journal of Physics: Condensed Matter, Vol. 9, No. 25, 1997, pp. 5439-5448. doi:10.1088/0953-8984/9/25/011

[22]   A. Bobak, “The Effect of Anisotropies on the Magnetic Properties of a Mixed Spin-1 and Spin-3/2 Ising Ferri magnetic System,” Physica A, Vol. 258, No. 1-2, 1998, pp. 140-156. doi:10.1016/S0378-4371(98)00233-7

[23]   O. F. Bobak and D. H. Abubrig, “An Effective-Field Study of the Mixed Spin-1 and Spin-3/2 Ising Ferrimagnetic System,” Journal of Magnetism and Magnetic Materials, Vol. 246, No. 1-2, 2002, pp. 177-183. doi:10.1016/S0304-8853(02)00048-3

[24]   O. F. Abubrig, D. Horvath, A. Bobak and M. Jascur, “Mean-Field Solution of the Mixed Spin-1 and Spin-3/2 Ising System with Different Single-Ion Anisotropies,” Physica A, Vol. 296, No. 3-4, 2001, pp. 437-450. doi:10.1016/S0378-4371(01)00176-5

[25]   J. W. Tucker, “Mixed Spin-1 and Spin-3/2 Blume-Capel Ising Ferromagnet,” Journal of Magnetism and Mgnetic Materials, Vol. 237, No. 2, 2001, pp. 215-224. doi:10.1016/S0304-8853(01)00691-6

[26]   Y. Nakamura and J. W. Tucker, “Monte Carlo Study of a Mixed Spin-1 and Spin-3/2 Ising Ferromagnet,” IEEE Transactions on Magnetics, Vol. 38, No. 5, 2002, pp. 2406-2408. doi:10.1109/TMAG.2002.803598

[27]   A. Bobak and J. Dely, “Phase Transitions and Multicriti cal Points in the Mixed Spin-3/2 and Spin-2 Ising System with a Single-Ion Anisotropy,” Journal of Magnetism and Magnetic Materials, Vol. 310, No. 2, 2007, pp. 1419-1421. doi:10.1016/j.jmmm.2006.10.427

[28]   E. Albayrak, “The Critical and Compensation Temperatures of the Mixed Spin-3/2 and Spin-2 Ising Model,” Physica B: Condensed Matter, Vol. 391, No. 1, 2007, pp. 47-53. doi:10.1016/j.physb.2006.08.045

[29]   B. Deviren, E. Kantar and M. Keskin, “Magnetic Proper ties of a Mixed Spin-3/2 and Spin-2 Ising Ferrimagnetic System within the Effective-Field Theory,” Journal of the Korean Physical Society, Vol. 56, No. 6, 2010, pp. 1738-1747. doi:10.3938/jkps.56.1738

[30]   Y. Nakamura, S. Shin and T. Kaneyoshi, “The Effects of Transverse Field on the Magnetic Properties in a Diluted Mixed Spin-2 and Spin-5/2 Ising System,” Physica B, Vol. 284-288, 2000, pp. 1479-1480. doi:10.1016/S0921-4526(99)02668-X

[31]   Y. Nakamura, “Monte Carlo Study of a Mixed Spin-2 and Spin-5/2 Ising System on a Honeycomb Lattice,” Journal of Physics: Condensed Matter, Vol. 12, No. 17, 2000, pp. 4067-4074. doi:10.1088/0953-8984/12/17/312

[32]   Y. Nakamura, “Existence of a Compensation Temperature of a Mixed Spin-2 and Spin-5/2 Ising Ferrimagnetic System on a Layered Honeycomb Lattice,” Physical Re view B, Vol. 62, No. 17, 2000, pp. 11742-11746. doi:10.1103/PhysRevB.62.11742

[33]   J. Li, A. Du and G. Z. Wei, “Green Function Study of a Mixed-Spin-2 and Spin-5/2 Heisenberg Ferrimagnetic System on a Honeycomb Lattice,” Physica Status Solidi (b), Vol. 238, No. 1, 2003, pp. 191-197.

[34]   J. Li, A. Du and G. Z. Wei, “The Compensation Behavior of a Mixed-Spin-2 and Spin-5/2 Heisenberg Ferrimagnetic System on a Honeycomb Lattice,” Physica B, Vol. 348, No. 1-4, 2004, pp. 79-88. doi:10.1016/j.physb.2003.11.074

[35]   G. Wei, Q. Zhang, Z. Xin and Y. Liang, “Internal Energy and Initial Susceptibility of Mixed Spin-2 and Spin-5/2 Ferrimagnetic Ising System with Interlayer Coupling,” Journal of Magnetism and Magnetic Materials, Vol. 277, No 1-2, 2004, pp. 1-15. doi:10.1016/j.jmmm.2003.06.001

[36]   E. Albayrak, “Mixed-Spin-2 and Spin-5/2 Blume-Emery Griffiths Model,” Physica A: Statistical Mechanics and Its Applications, Vol. 375, No. 1, 2007, pp. 174-184.

[37]   M. Keskin and M. Ertas, “Existence of a Dynamic Compensation Temperature of a Mixed Spin-2 and Spin-5/2 Ising Ferrimagnetic System in an Oscillating Field,” Physical Review E, Vol. 80, No. 6, 2009, Article ID: 061140. doi:10.1103/PhysRevE.80.061140

 
 
Top