Order of Magnetic Transitions in La(Fe1-xSix)13 Induced by Random Anisotropy
Main Article Content
Abstract
The temperature dependence of the magnetic moment in La(Fe1-xSix)13 compounds
reveals the presence of both first-order and second-order magnetic phase transitions. The nature of the transition is governed by variations in the Si concentration, which induce significant
modifications in the FeI–FeII interactions between Fe atoms occupying two non-equivalent sites.
These effects can be effectively modeled as a form of random anisotropy, the resulting behavior of
which is accurately described within the framework of the Blume-Capel model. Monte Carlo simulations demonstrate that the evolution from a first-order to a second-order magnetic transition
in La(Fe1-xSix)13 compounds can be consistently reproduced by maintaining a fixed anisotropy
probability p while systematically reducing the corresponding anisotropy amplitude D, yielding
good agreement with experimental trends.
Keywords:
La(Fe1-xSix)13, Magnetic transition, Random anisotropy, Monte Carlo simulation.
References
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[2] T. J. D. Rose, R. K. Chouhan, A. Doyle, A. K. Pathak, Y. Mudryk, LaFeSi–LaFe13−xSix Composites: Modulating Magnetic and Magnetocaloric Properties Through Inherent Stress Manipulation, Journal of Applied Physics,
Vol. 136, 2024, pp. 035101, https://doi.org/10.1063/5.0212650.
[3] K. Imaizumi, A. Fujita, A. Suzuki, M. Kobashi, K. Ozaki, Improvement of Magnetocaloric Effect in La(FexSi1−x)13 by Dealing With Inhibitory Microstructures at High Fe Concentration, Acta Materialia, Vol. 227, 2022, pp. 117726, https://doi.org/10.1016/j.actamat.2022.117726.
[4] K. Imaizumi, A. Fujita, A. Suzuki, M. Kobashi, K. Ozaki, Microstructure and Magnetocaloric Property of Homogeneous La(FexSi1−x)13 Compounds Fabricated by Laser Fusion Using a Powder Mixture of Fe and La–Si Compounds, Journal of Alloys and Compounds, Vol. 901, 2022, pp. 163706, https://doi.org/10.1016/j.jallcom.2022.163706.
[5] P. I. Kripyakevich, O. S. Zarechnyuk, E. I. Gladyshevsky, O. I. Bodak, Crystal Structure of Compounds With the NaZn13 Type, Zeitschrift für Anorganische Chemie, Vol. 358, 1968, pp. 90, https://doi.org/10.1002/zaac.19683580110.
[6] T. T. M. Palstra, J. A. Mydosh, G. J. Nieuwenhuys, A. M. van der Kraan, K. H. J. Buschow, Critical Behaviour of Magnetization and Electrical Resistivity in Cubic La(Fe,Si)13 Compounds, Journal of Magnetism and Magnetic Materials, Vol. 36, 1983, pp. 290, https://doi.org/10.1016/0304-8853(83)90128-2.
[7] W. Wang, R. Huang, W. Li, J. Tan, Y. Zhao, S. Li, C. Huang, L. Li, Zero Thermal Expansion in NaZn13-Type La(Fe,Si)13 Compounds, Physical Chemistry Chemical Physics, Vol. 17, 2015, pp. 2352-2356, https://doi.org/10.1039/C4CP04672B.
[8] G. J. Wang, F. Wang, N. L. Di, B. G. Shen, Z. H. Cheng, Hyperfine Interactions and Band Structures of LaFe13−xSix Intermetallic Compounds with Large Magnetic Entropy Changes, Journal of Magnetism and Magnetic Materials, Vol. 303, No. 1, 2006, pp. 84-91, https://doi.org/10.1016/j.jmmm.2005.10.231.
[9] X. B. Liu, Z. Altounian, D. H. Ryan, Structure and Magnetic Transition of LaFe13−xSix Compounds, Journal of Physics: Condensed Matter, Vol. 15, 2003, pp. 7385, https://doi.org/10.1088/0953-8984/15/43/020.
[10] D. Givord, R. Lemaire, Magnetic Transition and Anomalous Thermal Expansion in R2Fe17 Compounds, IEEE Transactions on Magnetics, Vol. 10, No. 2, 1974, pp. 109-113, https://doi.org/10.1109/TMAG.1974.1058311.
[11] L. M. M. Ramírez, J. Y. Law, J. M. Borrego, A. Barcza, J. M. Greneche, V. Franco, First-Order Phase Transition in High-Performance La(Fe,Mn,Si)13H Despite Negligible Hysteresis, Journal of Alloys and Compounds,
Vol. 950, 2023, pp. 169883, https://doi.org/10.1016/j.jallcom.2023.169883.
[12] D. T. K. Anh, V. V. Hiep, Samples Preparation, Structure and Magnetic Properties of La(Fe1−xSix)13 Compounds, VNU Journal of Science: Mathematics and Physics, Vol. 28, 2012, pp. 1-5, https://doi.org/10.25073/2588-1124/vnumap.4353.
[13] M. Blume, Theory of the First-Order Magnetic Phase Change in UO2, Physical Review, Vol. 141, 1966,
pp. 517-524, https://doi.org/10.1103/PhysRev.141.517.
[14] H. W. Capel, On the Possibility of First-Order Phase Transitions in Ising Systems of Triplet Ions with Zero-Field Splitting, Physica, Vol. 32, No. 5, 1966, pp. 966-988, https://doi.org/10.1016/0031-8914(66)90027-9.
[15] P. H. Nguyen, N. T. Nguyen, H. D. Nguyen, H. T. L. Nguyen, C. T. Bach, G. H. Bach, Random-Anisotropy Driven Giant Magnetic Entropy Change in First-Order Magnetic Transition Under External Fields, Journal of Alloys and Compounds, Vol. 1017, 2025, pp. 179001, https://doi.org/10.1016/j.jallcom.2025.179001.
[16] P. H. Nguyen, G. H. Bach, Thermodynamic Properties of the First-Order Magnetic Transition in the Highly Anisotropic 2D Blume–Capel Model, Communications in Physics, Vol. 35, No. 3, 2025, pp. 203-212, https://doi.org/10.15625/0868-3166/22722.
[17] G. H. Bach, O. K. T. Nguyen, C. V. Nguyen, C. T. Bach, First-Order Magnetization Process in Polycrystalline Perovskite Manganite, Materials Transactions, Vol. 56, No. 9, 2015, pp. 1320-1322, https://doi.org/10.2320/matertrans.MA201507.
[18] O. K. T. Nguyen, P. H. Nguyen, L. D. Dang, C. T. Bach, G. H. Bach, Fluctuation Inducing Fractional Magnetization Behavior on the Shastry–Sutherland Lattice, Physica B: Condensed Matter, Vol. 583, 2020,
pp. 412012, https://doi.org/10.1016/j.physb.2020.412012.
[19] O. K. T. Nguyen, P. H. Nguyen, N. T. Nguyen, C. T. Bach, H. D. Nguyen, G. H. Bach, Monte Carlo Investigation for an Ising Model with Competitive Magnetic Interactions in the Dominant Ferromagnetic-Interaction Regime, Communications in Physics, Vol. 33, 2023, pp. 205,
https://doi.org/10.15625/0868-3166/18109.
[20] P. H. Nguyen, Q. M. Le, O. K. T. Nguyen, C. T. Bach, G. H. Bach, Effective Field Theory Investigation for a Disordered Ising Model in the Description of Amorphous Magnetic Systems, Journal of Non-Crystalline Solids, Vol. 643, 2024, pp. 123165, https://doi.org/10.1016/j.jnoncrysol.2024.123165.
[21] I. Puha, H. T. Diep, Random-Bond and Random-Anisotropy Effects in the Phase Diagram of the Blume–Capel Model, Journal of Magnetism and Magnetic Materials, Vol. 224, No. 1, 2001, pp. 85-92, https://doi.org/10.1016/S0304-8853(00)01378-0.
[22] N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, E. Teller, Equation of State Calculations by Fast Computing Machines, The Journal of Chemical Physics, Vol. 21, 1953, pp. 1087-1092, https://doi.org/10.1063/1.1699114.
[23] K. Hukushima, K. Nemoto, Exchange Monte Carlo Method and Application to Spin Glass Simulations, Journal of the Physical Society of Japan, Vol. 65, No. 6, 1996, pp. 1604-1608, https://doi.org/10.1143/JPSJ.65.1604.
[24] P. H. Nguyen, C. T. Bach, H. D. Nguyen, H. T. L. Nguyen, H. H. Mai, D. Q. Dao, G. H. Bach, Field-Driven Magnetization Processes, Magnetocaloric Effect and Tunneling Magnetoconductivity in Bilayer CrI3 Thin Films: Insights From Replica-Exchange Monte Carlo Simulations, Acta Materialia, Vol. 307, 2026, pp. 121975, https://doi.org/10.1016/j.actamat.2026.121975.
[25] T. T. M. Palstra, G. J. Nieuwenhuys, J. A. Mydosh, K. H. J. Buschow, Magnetic Properties of Cubic La(Fe,Al)13 Intermetallic Compounds, Journal of Applied Physics, Vol. 55, 1984, pp. 2367, https://doi.org/10.1063/1.333667.
[26] T. T. M. Palstra, G. J. Nieuwenhuys, J. A. Mydosh, K. H. J. Buschow, Mictomagnetic, Ferromagnetic, and Antiferromagnetic Transitions in La(Fe,Al)13, Physical Review B, Vol. 31, 1985, pp. 4622, https://doi.org/10.1103/PhysRevB.31.4622.
[27] A. Fujita, K. Fukamichi, Giant Volume Magnetostriction Due to the Itinerant-Electron Metamagnetic Transition in La(Fe,Si)13, IEEE Transactions on Magnetics, Vol. 35, 1999, pp. 1796, https://doi.org/10.1109/INTMAG.1999.837942.
[28] H. Yamada, K. Fukamichi, T. Goto, Itinerant-Electron Metamagnetism and Pressure Dependence of the Curie Temperature in La(Fe,Si)13, Physical Review B, Vol. 65, 2002, pp. 024413, https://doi.org/10.1103/PhysRevB.65.024413.
[29] E. C. Stoner, Collective Electron Ferromagnetism, Proceedings of the Royal Society A, Vol. 165, 1938,
pp. 372-414, https://doi.org/10.1098/rspa.1938.0066.
[30] K. H. J. Buschow, F. R. de Boer, Physics of Magnetism and Magnetic Materials, Springer, USA, 2003, https://doi.org/10.1007/b100503.
[31] H. Nishimori, G. Ortiz, Elements of Phase Transitions and Critical Phenomena, Oxford University Press, Oxford, 2011, https://doi.org/10.1093/acprof:oso/9780199577224.001.0001.