Abstract
It is shown using model calculations that Maxwell’s relation is exactly satisfied for ferromagnets with one species of magnetic atoms and for two-component ferromagnets and ferrimagnets. This allows one to confidently use this relation for calculating the main characteristics of the magnetocaloric effect in these cases. A conclusion is made that the proposed model of a ferrimagnet is self-consistent and correct from the viewpoint of thermodynamics. It is also shown that the formulas similar to Maxwell’s relation for the derivatives of magnetization and entropy for magnetic sublattices are valid only approximately.
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REFERENCES
A. M. Tishin and Y. I. Spichkin, The Magnetocaloric Effect and Its Application (Bristol Institute of Physics Publishing, 2003).
V. Franco, J. S. Blazquez, J. J. Ipus, J. Y. Law, L. M. Moreno-Ramires, A. and Conde, “Magnetocaloric effect: From material research refrigeration devices,” Prog. Mater. Sci. 93, 112–232 (2018).
N. V. Baranov, A. V. Proshkin, C. Czternasty, M. Meibner, A. Podlesnyak, and S. M. Podgornykh, “Butterflylike specific heat, magnetocalorical effect and itinerant metamagnetism in (Er,Y)Co2 compound,” Phys. Rev. B 79, 184420 (2009).
I. Chaaba, S. Othmani, S. Haj-Khlifa, de Rando, D. Fruhart, W. Cheikhrouhou-Koubaa, and A. Cheikhrouhow, “Magnetic and magnetocaloric properties of Er(Co1 – xFex)2 intrmetallic compounds,” J. Magn. Magn. Mater. 439, 269–280 (2017).
P. J. Von Ranke, N. A. De Oliveira, B. P. Alho, E. J. R. Plaza, V. S. R. De Sousa, L. Caron, and M. S. Reis, “Understanding the inverse magnetocalorical effect in antiferro- and ferromagnetic arrangements,” J. Phys.: Condens. Matter 21, 056004 (2009).
E. Z. Valiev, “Entropy and magnetocaloric effect in ferrimagnets RCo2,” J. Exp. Theor. Phys. 124, 968–974 (2017).
S. V. Tyablikov, Methods of Quantum Theory of Magnetism (Nauka, Moscow, 1975) [in Russian].
G. M. Nedlin, Physics of Magnetic Dielectrics, Ed. by G.A. Smolenskii (Nauka, Leningrad, 1974) [in Russian].
E. Z. Valiev, “Isotropic magnetoelastic interaction in two-sublattice ferri- and antiferromagnets: mean field approximation for the Heisenberg model,” Fiz. Met. Metalloved. 96, 4–11 (2003).
C. Bean and D. Rotbell, “Magnetic disorder as first-order phase transition,” Phys. Rev. 126, 104–115 (1962).
E. Z. Valiev, “Entropy and magnetocaloric effects in ferromagnets undergoing first- and second-order magnetic phase transitions,” J. Exp. Theor. Phys. 108, 279–285 (2009).
E. Z. Valiev and V. A. Kazantsev, “Magnerocaloric effect in La(FexSi1 – x)13 ferromagnetics,” J. Exp. Theor. Phys. 113, 1000–1005 (2011).
Funding
This work was carried out using the Unique Research Facility “NMK UFM” (Neutron Materials Science Complex) under the auspices of the Ministry of Education and Science of the Russian Federation (topic “Flux” no. AAAA-A18-118020190112-8) and was supported in part by grant no. 18-10-2-22-22 under the auspices of the program of fundamental research of the Ural Branch of the Russian Academy of Sciences.
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Translated by E. Chernokozhin
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Valiev, E.Z. On Maxwell’s Relation in Ferromagnets and Ferrimagnets. Phys. Metals Metallogr. 121, 717–720 (2020). https://doi.org/10.1134/S0031918X2008013X
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DOI: https://doi.org/10.1134/S0031918X2008013X