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Kinetics of the Mixed Spin (1, 3/2) Ising Model in the Presence of an Oscillating Magnetic Field by Using the Path Probability Method

Year 2025, Volume: 46 Issue: 1, 142 - 151, 25.03.2025

Mustafa Gençaslan , Abdulrahma Mohammed Kaif Awwadee

https://doi.org/10.17776/csj.1525584

Abstract

Kinetics of the mixed spin (1, 3/2) Ising ferrimagnetic system on the two interpenetrating square lattices with the bilinear and crystal-field interactions under an oscillating magnetic field were investigated by using the path probability method (PPM). We examined time variations in average dynamic magnetizations and obtained phases and then we investigated the thermal behaviors of dynamic magnetizations to determine the nature of the dynamic phase transitions and find their temperature values. We also constructed the dynamic phase diagrams in (d,T) and (h_0,T) planes. Dynamic phase diagrams display the paramagnetic (p), ferrimagnetic (i), and mixed phases (i+p), and one dynamic tricritical point and dynamic double critical endpoints. We found that the PPM is a more convenient method to investigate the kinetics and dynamics behaviors of ferrimagnetism.

Keywords

Mixed spin-1 and spin-3/2 Ising model Path probability method Dynamic phase transition temperatures Dynamic magnetic phase diagrams

References

  • [1]Stanica N., Stager C. V., Cimpoesu M., Andruh M., Synthesis and magnetic properties a of new oxalato-bridged heterotrinuclear complex, [NiCr2 (bipy)2 (µ-C2O4)2(C2O4 )2 (H2O)2 ].H2O. A rare case of antiferromagnetic coupling between Cr(III) and Ni(II) ions, Polyhedron 17 (1998) 1787-1789.
  • [2] Kantar E., Ertaş M., Frequency-Dependent Dynamic Phase Diagrams in Ising System with Fe4N Structure, Journal of Superconductivity and Novel Magnetism 29 (2016) 2319-2326.
  • [3] Numata Y., Inoue K., Baranov N., Field-induced ferrimagnetic state in a molecule-based magnet consisting of a Co (II) ion and a chiral triplet bis(nitroxide) radical, Kurmoo M., Kikuchi K., Journal of the AmericanNChemical Society 129 (2007) 9902-9909.
  • [4] Jiang W., Wei G.-z, Zhang Z.-d,Tricritical behavior and magnetic properties for a mixed spin-1 and spin- 3/2 transverse Ising model with a crystal field, Phys. Rev. B 68 (2003) 134432.
  • [5] Madani M., Gaye A., El Bouziani M., Migdal–Kadanoff solution of the mixed spin-1 and spin-3/2 Blume–Capel model with different single-ion anisotropies, Alrajhi A., Physica A 437 (2015) 396-404.
  • [6] Htoutou K., Oubelkacem A., Benhouria Y., Htoutou K., Oubelkacem A., Benhouria Y., Essaoudi I., Ainane A., Ahuja R., The Magnetic Properties of the Mixed Ferrimagnetic Ising System with Random Crystal Field, Journal of Superconductivity and Novel Magnetism, 30 (2017) 1247-1256.
  • [7] Motlagh H. N., Rezaei G., Monte Carlo simulation of magnetic properties of mixed spin (3/2, 1) ferromagnetic and ferrimagnetic disordered binary alloys with amorphous structure, J. Magn. Magn. Mater., 445 (2018) 26-36.
  • [8] Lafhal A., El Antari A., Hachem N., Al-Rajhi A., Aharrouch R., Saadi H., Madani M., El Bouziani M., Renormalization Group Study of the Mixed Spin-1 and Spin-3/2 Blume-Emery-Griffiths Model with Attractive Biquadratic Coupling, International Journal of Theoretical Physics, 59 (2020) 1165-1178.
  • [9] Zaim A., Kerouad M., Monte Carlo simulation of the compensation and critical behaviors of a ferrimagnetic core/shell nanoparticle Ising model, Physica A, 389 (2010) 3435-3442.
  • [10] Feraoun A., Kerouad M., The mixed spin-(1,3/2) Ising nanowire with core/inter-shell/outer-shell morphology, Applied Physics A-Materials Science & Processing, 124 (2018) 124:735.
  • [11] Vatansever E., Polat H., Monte Carlo investigation of a spherical ferrimagnetic core–shell nanoparticle under a time dependent magnetic field, J. Magn. Magn. Mater., 343 (2013) 221-227.
  • [12] Yang M., Wang W., Li Bo-chen, Wu H. J., Yang Shao-qing, Yang J., Magnetic properties of an Ising ladder-like graphene nanoribbon by using Monte Carlo method, Physica A, 539 (2020) 122932.
  • [13] Keskin M., Kantar E., Canko O., Kinetics of a mixed spin-1 and spin-3/2 Ising system under a time-dependent oscillating magnetic field, Phys. Rev. E, 77 (2008) 051130.
  • [14] Keskin M., Kantar E., Dynamic compensation temperatures in a mixed spin-1 and spin-3/2 Ising system under a time-dependent oscillating magnetic field, J. Magn. Magn. Mater., 322 (2010) 2789-2796.
  • [15] Shi X., Qi Y., Existence of a dynamic compensation temperature of the mixed spin-1 and spin-3/2 Ising model within the effective-field theory, Physica A, 430 (2015) 93-100.
  • [16] Ertaş M., Keskin M., Dynamic hysteresis features in a two-dimensional mixed Ising system, Phys. Letts. A, 379 (2015) 1576-1583.
  • [17] Benhouria Y., Oubelkacem A., Essaoudi I., Ainane A., Ahuja R., Dynamic Magnetic Properties of a Mixed Spin Ising Double-Walled Ferromagnetic Nanotubes: A Dynamic Monte Carlo Study, Journal of Superconductivity and Novel Magnetism, 30 (2017) 839-844.
  • [18] Kikuchi R., The Path Probability Method, Progress of Theoretical Physics Supplement, 3 (1966) 1–64.
  • [19] Gençaslan M., Keskin M., Dynamic magnetic hysteresis loop features of a mixed spin (1/2, 1) Ising system on a hexagonal lattice using path probability method, Modern Phys. Letters, B 35 (2021) 2150221.
  • [20] Gençaslan M., Keskin M., Influences of the interaction parameters on the dynamic hysteresis of a mixed spin (1/2, 3/2) Ising model under the presence of an oscillating magnetic field, Int. J. Modern Phys., B 35 (2021) 2150217.
  • [21] Gençaslan M., Keskin M., Dynamic hysteresis features of a mixed spin (1/2,3/2) Ising system within the path probability method, Phase Transitions, 95 (2022) 372-386.
  • [22] Gençaslan M., Keskin M., Dynamic magnetic hysteresis features of a mixed spin (2, 5/2) Ising system on a hexagonal lattice under an oscillating magnetic field within the path probability method, Int. J. Modern Phys. B, 38 (2024) 2450198.
  • [23] Gençaslan M., AWWADEE A. M. K., Effect of Cooling Rate on Dynamic Magnetic Hysteresis Loop Behaviors of Magnetic Materials by Using as a Model Mixed Spin (1, 3/2) Ising System Under an Oscillating Magnetic Field, Journal of Superconductivity and Novel Magnetism, 37 (2024) 1105-1117.
  • [24] AWWADEE A. M. K., Dynamic Magnetic Properties of a Mixed Spin (1, 3/2) Ferrimagnetic Ising System in an Oscilating Magnetic Field Within the Path Probability Method, M. Sc. Thesis, Erciyes University (2024), Kayseri, Türkiye.
  • [25] İnce O., Gençaslan M., Keskin M., Magnetic features and compensation behaviors of a mixed spin (1/2, 1) Ising ferrimagnetic system on a hexagonal lattice, Physica A, 583 (2021) 126270.
  • [26] Gençaslan M., Keskin M., Dynamic magnetic properties of the mixed spin (1/2, 3/2) Ising system in the presence of magnetic field within the path probability method, Physica A, 559 (2020) 125013.
  • [27] İnce O., Gençaslan M., Keskin M., Dynamic phase of transitions of the mixed spin (1/2, 3/2) Ising model in the presence of a time-varying magnetic field by using the path probability method, Phys. Letters A, 390 (2021) 127107.
  • [28] Alhameri M. F. İ., Dynamic phase transitions and compensation behaviors in a mixed spin (1/2,3/2) Ising model on a hexagonal lattice by path probability method, Gençaslan M., Keskin M., Indian J. Physics, 96 (2022) 3775-3786.
  • [29] Gençaslan M., Keskin M., Nonequlibrium magnetic features in a mixed spin (2, 5/2) Ising system driven by the external oscillating magnetic field by path probability method, Physica Scripta, 97 (2022) 085803.
  • [30] Gençaslan M., Özlü M., Keskin M., Dynamic Magnetic Features of a Mixed-Spin-2 and Spin-5/2 Ising Ferrimagnetic System under a Time-Dependent Oscillating Magnetic Field: Path Probability Method Approach, Phys. Status Solidi, B 260 (2023) 2200425.
  • [31] Chakrabarti K., Acharyya M., Dynamic transitions and hysteresis, Rev. Mod. Phys., 71 (1999) 847-859.
  • [32] Yunus Ç., Renklioğlu B., Keskin M., Stepwise positional-orientational order and the multicritical- multistructural global phase diagram of the 𝑠=3/2 Ising model from renormalization-group theory, Berker A. N., Phys. Rev. E, 93 (2016) 062113.
  • [33] Deviren B., Keskin M., Canko O., Kinetics of a mixed spin-1/2 and spin-3/2 Ising ferrimagnetic model, J. Magn. Magn. Mater., 321 (2009) 458-466.
  • [34] Ertaş M., Keskin M., Dynamic magnetic behavior of the mixed spin (2, 5/2) Ising system with antiferromagnetic/antiferromagnetic interactions on a bilayer square lattice, Chin. Phys. B, 22 (2013) 120507.
  • [35] Ertaş M., Deviren B., Nonequilibrium magnetic properties in a two-dimensional kinetic mixed Ising system within the effective-field theory and Glauber-type stochastic dynamics approach, Keskin M., Phys. Rev. E, 86 (2012) 051110.
  • [36] Deviren Ş. A., Deviren B., Dynamic magnetic properties of a mixed-spin (1, 3/2) Ising nanotube: a dynamic mean-field study, Eur. Phys. J. Plus, 137 (2022) 1067.
  • [37] Ertaş M., Deviren B., Dynamic magnetic properties of multilayer mixed spin-1 and spin-3/2 Ising model, Eur. Phys. J. Plus, 137 (2022) 1031.

Year 2025, Volume: 46 Issue: 1, 142 - 151, 25.03.2025

Mustafa Gençaslan , Abdulrahma Mohammed Kaif Awwadee

https://doi.org/10.17776/csj.1525584

Abstract

References

  • [1]Stanica N., Stager C. V., Cimpoesu M., Andruh M., Synthesis and magnetic properties a of new oxalato-bridged heterotrinuclear complex, [NiCr2 (bipy)2 (µ-C2O4)2(C2O4 )2 (H2O)2 ].H2O. A rare case of antiferromagnetic coupling between Cr(III) and Ni(II) ions, Polyhedron 17 (1998) 1787-1789.
  • [2] Kantar E., Ertaş M., Frequency-Dependent Dynamic Phase Diagrams in Ising System with Fe4N Structure, Journal of Superconductivity and Novel Magnetism 29 (2016) 2319-2326.
  • [3] Numata Y., Inoue K., Baranov N., Field-induced ferrimagnetic state in a molecule-based magnet consisting of a Co (II) ion and a chiral triplet bis(nitroxide) radical, Kurmoo M., Kikuchi K., Journal of the AmericanNChemical Society 129 (2007) 9902-9909.
  • [4] Jiang W., Wei G.-z, Zhang Z.-d,Tricritical behavior and magnetic properties for a mixed spin-1 and spin- 3/2 transverse Ising model with a crystal field, Phys. Rev. B 68 (2003) 134432.
  • [5] Madani M., Gaye A., El Bouziani M., Migdal–Kadanoff solution of the mixed spin-1 and spin-3/2 Blume–Capel model with different single-ion anisotropies, Alrajhi A., Physica A 437 (2015) 396-404.
  • [6] Htoutou K., Oubelkacem A., Benhouria Y., Htoutou K., Oubelkacem A., Benhouria Y., Essaoudi I., Ainane A., Ahuja R., The Magnetic Properties of the Mixed Ferrimagnetic Ising System with Random Crystal Field, Journal of Superconductivity and Novel Magnetism, 30 (2017) 1247-1256.
  • [7] Motlagh H. N., Rezaei G., Monte Carlo simulation of magnetic properties of mixed spin (3/2, 1) ferromagnetic and ferrimagnetic disordered binary alloys with amorphous structure, J. Magn. Magn. Mater., 445 (2018) 26-36.
  • [8] Lafhal A., El Antari A., Hachem N., Al-Rajhi A., Aharrouch R., Saadi H., Madani M., El Bouziani M., Renormalization Group Study of the Mixed Spin-1 and Spin-3/2 Blume-Emery-Griffiths Model with Attractive Biquadratic Coupling, International Journal of Theoretical Physics, 59 (2020) 1165-1178.
  • [9] Zaim A., Kerouad M., Monte Carlo simulation of the compensation and critical behaviors of a ferrimagnetic core/shell nanoparticle Ising model, Physica A, 389 (2010) 3435-3442.
  • [10] Feraoun A., Kerouad M., The mixed spin-(1,3/2) Ising nanowire with core/inter-shell/outer-shell morphology, Applied Physics A-Materials Science & Processing, 124 (2018) 124:735.
  • [11] Vatansever E., Polat H., Monte Carlo investigation of a spherical ferrimagnetic core–shell nanoparticle under a time dependent magnetic field, J. Magn. Magn. Mater., 343 (2013) 221-227.
  • [12] Yang M., Wang W., Li Bo-chen, Wu H. J., Yang Shao-qing, Yang J., Magnetic properties of an Ising ladder-like graphene nanoribbon by using Monte Carlo method, Physica A, 539 (2020) 122932.
  • [13] Keskin M., Kantar E., Canko O., Kinetics of a mixed spin-1 and spin-3/2 Ising system under a time-dependent oscillating magnetic field, Phys. Rev. E, 77 (2008) 051130.
  • [14] Keskin M., Kantar E., Dynamic compensation temperatures in a mixed spin-1 and spin-3/2 Ising system under a time-dependent oscillating magnetic field, J. Magn. Magn. Mater., 322 (2010) 2789-2796.
  • [15] Shi X., Qi Y., Existence of a dynamic compensation temperature of the mixed spin-1 and spin-3/2 Ising model within the effective-field theory, Physica A, 430 (2015) 93-100.
  • [16] Ertaş M., Keskin M., Dynamic hysteresis features in a two-dimensional mixed Ising system, Phys. Letts. A, 379 (2015) 1576-1583.
  • [17] Benhouria Y., Oubelkacem A., Essaoudi I., Ainane A., Ahuja R., Dynamic Magnetic Properties of a Mixed Spin Ising Double-Walled Ferromagnetic Nanotubes: A Dynamic Monte Carlo Study, Journal of Superconductivity and Novel Magnetism, 30 (2017) 839-844.
  • [18] Kikuchi R., The Path Probability Method, Progress of Theoretical Physics Supplement, 3 (1966) 1–64.
  • [19] Gençaslan M., Keskin M., Dynamic magnetic hysteresis loop features of a mixed spin (1/2, 1) Ising system on a hexagonal lattice using path probability method, Modern Phys. Letters, B 35 (2021) 2150221.
  • [20] Gençaslan M., Keskin M., Influences of the interaction parameters on the dynamic hysteresis of a mixed spin (1/2, 3/2) Ising model under the presence of an oscillating magnetic field, Int. J. Modern Phys., B 35 (2021) 2150217.
  • [21] Gençaslan M., Keskin M., Dynamic hysteresis features of a mixed spin (1/2,3/2) Ising system within the path probability method, Phase Transitions, 95 (2022) 372-386.
  • [22] Gençaslan M., Keskin M., Dynamic magnetic hysteresis features of a mixed spin (2, 5/2) Ising system on a hexagonal lattice under an oscillating magnetic field within the path probability method, Int. J. Modern Phys. B, 38 (2024) 2450198.
  • [23] Gençaslan M., AWWADEE A. M. K., Effect of Cooling Rate on Dynamic Magnetic Hysteresis Loop Behaviors of Magnetic Materials by Using as a Model Mixed Spin (1, 3/2) Ising System Under an Oscillating Magnetic Field, Journal of Superconductivity and Novel Magnetism, 37 (2024) 1105-1117.
  • [24] AWWADEE A. M. K., Dynamic Magnetic Properties of a Mixed Spin (1, 3/2) Ferrimagnetic Ising System in an Oscilating Magnetic Field Within the Path Probability Method, M. Sc. Thesis, Erciyes University (2024), Kayseri, Türkiye.
  • [25] İnce O., Gençaslan M., Keskin M., Magnetic features and compensation behaviors of a mixed spin (1/2, 1) Ising ferrimagnetic system on a hexagonal lattice, Physica A, 583 (2021) 126270.
  • [26] Gençaslan M., Keskin M., Dynamic magnetic properties of the mixed spin (1/2, 3/2) Ising system in the presence of magnetic field within the path probability method, Physica A, 559 (2020) 125013.
  • [27] İnce O., Gençaslan M., Keskin M., Dynamic phase of transitions of the mixed spin (1/2, 3/2) Ising model in the presence of a time-varying magnetic field by using the path probability method, Phys. Letters A, 390 (2021) 127107.
  • [28] Alhameri M. F. İ., Dynamic phase transitions and compensation behaviors in a mixed spin (1/2,3/2) Ising model on a hexagonal lattice by path probability method, Gençaslan M., Keskin M., Indian J. Physics, 96 (2022) 3775-3786.
  • [29] Gençaslan M., Keskin M., Nonequlibrium magnetic features in a mixed spin (2, 5/2) Ising system driven by the external oscillating magnetic field by path probability method, Physica Scripta, 97 (2022) 085803.
  • [30] Gençaslan M., Özlü M., Keskin M., Dynamic Magnetic Features of a Mixed-Spin-2 and Spin-5/2 Ising Ferrimagnetic System under a Time-Dependent Oscillating Magnetic Field: Path Probability Method Approach, Phys. Status Solidi, B 260 (2023) 2200425.
  • [31] Chakrabarti K., Acharyya M., Dynamic transitions and hysteresis, Rev. Mod. Phys., 71 (1999) 847-859.
  • [32] Yunus Ç., Renklioğlu B., Keskin M., Stepwise positional-orientational order and the multicritical- multistructural global phase diagram of the 𝑠=3/2 Ising model from renormalization-group theory, Berker A. N., Phys. Rev. E, 93 (2016) 062113.
  • [33] Deviren B., Keskin M., Canko O., Kinetics of a mixed spin-1/2 and spin-3/2 Ising ferrimagnetic model, J. Magn. Magn. Mater., 321 (2009) 458-466.
  • [34] Ertaş M., Keskin M., Dynamic magnetic behavior of the mixed spin (2, 5/2) Ising system with antiferromagnetic/antiferromagnetic interactions on a bilayer square lattice, Chin. Phys. B, 22 (2013) 120507.
  • [35] Ertaş M., Deviren B., Nonequilibrium magnetic properties in a two-dimensional kinetic mixed Ising system within the effective-field theory and Glauber-type stochastic dynamics approach, Keskin M., Phys. Rev. E, 86 (2012) 051110.
  • [36] Deviren Ş. A., Deviren B., Dynamic magnetic properties of a mixed-spin (1, 3/2) Ising nanotube: a dynamic mean-field study, Eur. Phys. J. Plus, 137 (2022) 1067.
  • [37] Ertaş M., Deviren B., Dynamic magnetic properties of multilayer mixed spin-1 and spin-3/2 Ising model, Eur. Phys. J. Plus, 137 (2022) 1031.
There are 37 citations in total.

Details

Primary Language English
Subjects Statistical Physics
Journal Section Natural Sciences
Authors

Mustafa Gençaslan 0000-0002-5726-1733

Abdulrahma Mohammed Kaif Awwadee 0009-0009-7377-7877

Publication Date March 25, 2025
Submission Date July 31, 2024
Acceptance Date January 12, 2025
Published in Issue Year 2025Volume: 46 Issue: 1

Cite

APA Gençaslan, M., & Awwadee, A. M. K. (2025). Kinetics of the Mixed Spin (1, 3/2) Ising Model in the Presence of an Oscillating Magnetic Field by Using the Path Probability Method. Cumhuriyet Science Journal, 46(1), 142-151. https://doi.org/10.17776/csj.1525584
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