Abstract
The critical behavior for the second-order ferromagnetic paramagnetic phase transition Ni50Mn29Ga20.8Tb0.2 alloy is studied. The values of the critical exponents were found to be \(\gamma =1.05\), \(\beta =0.45\) and are close to the ones described by the mean-field model. Using the Arrott–Noakes equation of state with these \(\gamma \) and \(\beta \) values, the Curie temperature was successfully calculated. The isothermal magnetization \(M\) and magnetic entropy change \(-\Delta {S}_{\mathrm{M}}\) curves were simulated using the Arrott–Noakes equation, the Landau theory and a mean field model.
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References
C. Romero-Muniz, R. Tamura, S. Tanaka, V. Franco, Phys. Rev. B. 94, 134401 (2016)
K. Raju, N. PavanKumar, P.V. Reddy, D.H. Yoon, Phys. Lett. A 379, 1178 (2015)
A. Kitanovski, Adv. Energy Mater. 10, 1903741 (2020)
S.K. Ma, Modern Theory of Critical Phenomena (Addison-Wesley, London, 1976)
K. Huang, Statistical Mechanics (Wiley, New York, 1987)
Z.B. Li, Y.D. Zhang, C.F. Sanchez-Valdes, J.L. Sanchez Llamazares, C. Esling, X. Zhao, L. Zuo, Appl. Phys. Lett. 104, 044101 (2014)
X.Z. Zhou, H. Kunkel, G. Williams, S.H. Zhang, D.S. Xue, J. Magn. Magn. Mater. 305, 372 (2006)
C. Hürrich, S. Roth, M. Pötschke, B. Rellinghaus, L. Schultz, J. Alloys Compd. 494, 40–43 (2010)
I. Karaman, H.E. Karaca, B. Basaran, D.C. Lagoudas, Y.I. Humlyakov, H.J. Maier, Scr. Mater. 55, 403 (2006)
J. Kim, F. Inaba, T. Fukuda, T. Kakeshita, Acta. Mater. 54, 493 (2006)
D. Pal, K. Mandal, J. Phys. D: Appl. Phys. 43, 455002 (2010)
K. Mandal, D. Pal, N. Scheerbaum, J. Lyubina, O. Gutfleisch, J. Appl. Phys. 105, 073509 (2009)
M. Pasquale, C.P. Sasso, L.H. Lewis, L. Giudici, T. Lograsso, D. Schlagel, Phys. Rev. B 72, 094435 (2005)
J. Marcos, L. Mañosa, A. Planes, F. Casanova, X. Batlle, A. Labarta, Phys. Rev. B 68, 094401 (2003)
L. Gao, J.H. Sui, W. Cai, J. Magn. Magn. Mater. 320, 63 (2008)
J.H. Sui, X. Zhang, L. Gao, W. Cai, J. Alloys. Compd. 509, 8692 (2011)
J.M. Lee, Y.M. Oh, K. Euh, S.B. Kang, Met. Mater. Int. 3, 459 (2009)
J.H. Sui, X. Zhang, X.H. Zheng, Z.Y. Yang, W. Cai, X.H. Tian, Scr. Mater. 68, 679 (2013)
R. Wroblewskia, M. Leonowicza, Z.Q. Zhao, L.P. Jiang, J. Magn. Magn. Mater. 316, e595–e598 (2007)
J. Zhang, Y. Ma, R. Wu, J. Wang, J. Iron. Steel. Res. Int 26, 321–328 (2019)
Y. Wu, J. Wang, H. Hua, C. Jiang, H. Xu, J. Alloys. Compd. 632, 681–685 (2015)
I. Ait Elkoua, R. Masrour, A .Jabar, (2021) J. Cryst. Growth. 576 126381.
S. Amara, S. Labidi, R. Masrour, A. Jabar, M. Ellouze, Chem. Phys. Lett. 787, 139261 (2022)
R. Masrour, A. Jabar, S. Labidib, Y. El Krimi, M. Ellouze, M. Labidi, A. Amara, Mater. Today Commun. 26, 101772 (2021)
Y. El Krimi, R. Masrour, A. Jabar, S. Labidi, M. Bououdina, M. Ellouze, Results Phys. 18, 103252 (2020)
Y. El Krimi, R. Masrour, A. Jabar, J. Mol. Struct. 1220, 128707 (2020)
YEl. Krimi, R. Masrour, A. Jabar, J. Mol. Graph. Model. 114, 108165 (2022)
Y. El Krimi, R. Masrour, A. Jabar, Mater. Today. Energy 20, 100685 (2021)
A. Fujita, K. Fukamichi, IEEE Trans. Magn. 41(10), 3490 (2005)
V.S. Amaral, et al., J. Magn. Magn. Mater. 242–245 (2002)
V.S. Amaral et al., J. Appl. Phys. 93, 7646 (2003)
A. Arrott, J.E. Noakes, Phys. Rev. Lett. 19, 786 (1967)
M.E. Fisher, Rep. Prog. Phys. 30, 615 (1967)
S.K. Banerjee, Phys. Lett. 12, 16 (1964)
J.S. Kouvel, M.E. Fisher, Phys. Rev. 136, 1626–1632 (1964)
V. Franco, A. Conde, V.K. Pecharsky, K.A. Gschneidner Jr., Europhys. Lett. 79, 47009 (2007)
V. Franco, J.S. Blazquez, A. Conde, J. Appl. Phys. 103, 07B316 (2008)
J.Y. Law, V. Franco, L.M. Moreno-Ramírez, A. Conde, D.Y. Karpenkov, I. Radulov, K.P. Skokov, O. Gutfleisch, Nat. Commun. 9, 2680 (2018)
V. Franco, A. Conde, Int. J. Refrig. 33, 465 (2010)
R. Romero-Muniz, S. Tamura, V. Tanaka, Franco. Phys. Rev. B 94, 134401 (2016)
A.K. Pramanik, A. Banerjee, Phys. Rev. B 79, 214426 (2009)
M.E. Fisher, S.K. Ma, B.G. Nickel, Phys. Rev. Lett. 29, 917–920 (1972)
J. Coey, Magnetism and Magnetic Materials (Cambridge University Press, Cambridge, 2009)
J.A. Gonzalo, Effective Field Approach to Phase Transitions and Some Applications to Ferroelectrics (World Scientific, Singapore, 2006)
C. Kittel, Introduction to Solid State Physics, 7th edn. (Wiley, New York, 1996)
J. S. Amaral, S. Das and V. S. Amaral. The mean-field theory in the study of ferromagnets and the magnetocaloric effect, thermodynamics - systems in equilibrium and non-equilibrium, Edited by Dr. Juan Carlos Moreno Pirajá, October (2011)
S.B. Ogale, R. Shreekala, R. Bathe, S.K. Date, S.I. Patil, B. Hannoyer, F. Petit, G. Marest, Phys. Rev. B 57, 7841 (1998)
V.S. Amaral, J.S. Amaral, J. Magn. Magn. Mater. 272–276, 2104–2105 (2004)
Q.Y. Dong, H.W. Zhang, J.L. Shen, J.R. Sun, B.G. Shen, J. Magn. Magn. Mater. 319, 56 (2007)
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SK made the critical behavior analysis. NZ and MH performed the magnetocaloric effect simulation. All authors contributed equally to the writing of the manuscript.
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Hsini, M., Zaidi, N. & Khadhraoui, S. Critical Behavior and Magnetocaloric Effect Simulation in NiMnGaTb Heusler Alloy. J Low Temp Phys 210, 334–346 (2023). https://doi.org/10.1007/s10909-022-02883-w
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DOI: https://doi.org/10.1007/s10909-022-02883-w