Generalized model of the magnetostructural phase transition in La(Fe,Si)$_{13}$ compounds under the simultaneous action of temperature, magnetic field and pressure

R. A. Makaryin ; M. V. Zhelezny ; D. Yu. Karpenkov

Čelâbinskij fiziko-matematičeskij žurnal, Tome 8 (2023) no. 2, pp. 280-291.

Résumé

The paper presents a phenomenological generalized model of a first-order metamagnetic phase transition for the La(Fe,Si)$_{13}$ compounds in the approximation of localized moments under the simultaneous action of temperature, field and pressure. To achieve the maximum cooling power of magnetic solid-state cooling devices, the Curie temperature of the working bodies should be fine-tuned by two external generalized forces: a magnetic field and pressure. The thermodynamic phenomenological models presented in the literature are mostly focused on the description of the behavior of magnetocaloric materials in the vicinity of phase transition in the absence of external pressure. In turn, the latter provide a significant reduction in the field hysteresis effect by shifting the Curie temperature and expand the working temperature range of the refrigerant. To estimate the required pressure value, a new generalized model was developed that excludes the linear dependence of the phase transition temperature on the volume change and modernizes the form of the magnetic and phonon entropy, taking into account anharmonism. In addition, the equations of state describing the behavior of working bodies underwent a multistimuli cooling cycle were obtained. The model allows estimating the upper limit of the temperature and field hysteresis and predicting the required external pressure to reduce the field hysteresis.

Détail

Keywords: magnetocaloric effect, Brillouin function, phonon entropy, phenomenological model, itinerant metamagnetic transition.

Bibliographie

[1] Balli M., Jandl S., Fournier P., et al., “Advanced materials for magnetic cooling: Fundamentals and practical aspects”, Applied Physics Reviews, 4:2 (2017), 021305 | DOI

[2] Kitanovski A., “Energy applications of magnetocaloric materials”, Advanced Energy Materials, 10:10 (2020), 1903741 | DOI

[3] Brück E., Tegus O., Thanh D.T.C., et al., “Magnetocaloric refrigeration near room temperature (invited)”, Journal of Magnetism and Magnetic Materials, 310:2 (3) (2007), 2793–2799 | DOI

[4] Scheibel F., Gottschall T., Taubel A., et al., “Hysteresis design of magnetocaloric materials — from basic mechanisms to applications”, Energy Technology, 6:8 (2018), 1397–1428 | DOI

[5] Greco A., Aprea C., Maiorino A., et al., “A review of the state of the art of solid-state caloric cooling processes at room-temperature before 2019”, International Journal of Refrigeration, 106 (2019), 66–88 | DOI

[6] Silva D.J., Ventura J., Araujo J.P., “Caloric devices: A review on numerical modeling and optimization strategies”, International Journal of Energy Research, 45:13 (2021), 18498–18539 | DOI

[7] Liu J., Gottschall T., Skokov K.P., et al., “Giant magnetocaloric effect driven by structural transitions”, Nature Materials, 11:7 (2012), 620–626 | DOI

[8] Lovell E., Bez H.N., Boldrin D.C., et al., “The La(Fe,Mn,Si)$_{13}$H$_{z}$ magnetic phase transition under pressure”, Physica Status Solidi — Rapid Research Letters, 11:10 (2017), 1700143 | DOI

[9] Cohen L.F., “Contributions to hysteresis in magnetocaloric materials”, Physica Status Solidi B, 225 (2018), 1700317 | DOI

[10] Stern-Taulats E., Castan T., Manosa L., et al., “Multicaloric materials and effects”, MRS Bulletin, 43:4 (2018), 295–298 | DOI

[11] Jia L., Sun J.R., Wang F.W., et al., “Volume dependence of the magnetic coupling in LaFe$_{13-x}$Si$_{x}$ based compounds”, Applied Physics Letters, 92:10 (2008), 101904 | DOI

[12] Basso V., “The magnetocaloric effect at the first-order magneto-elastic phase transition”, Journal of Physics: Condensed Matter, 23:22 (2011), 226004 | DOI

[13] Basso V., Piazzi M., Bennati C., et al., “Hysteresis and phase transition kinetics in magnetocaloric materials”, Physica Status Solidi B, 255:2 (2017), 1700278 | DOI

[14] Valiev E.Z., “Simulation of the magnetic and magnetocaloric properties of hydrides of the La(Fe$_{0.88}$Si$_{0.12}$)$_{13}$ compound by applying a negative pressure”, Physics of the Solid State, 56:1 (2014), 47–50 | DOI

[15] Valiev E.Z., Kazantsev V.A., “Magnetocaloric effect in La(Fe$_{x}$Si$_{1 ? x}$)$_{13}$ ferromagnets”, Journal of Experimental and Theoretical Physics, 113:6 (2011), 1000–1005 | DOI

[16] Van Dijk N.H., “Landau model evaluation of the magnetic entropy change in magnetocaloric materials”, Journal of Magnetism and Magnetic Materials, 529 (2021), 167871 | DOI

[17] Yamada H., Goto T., “Magneto-volume coupling constant in itinerant-electron metamagnets”, Journal of Magnetism and Magnetic Materials, 272–276 (2004), 460–461 | DOI

[18] Bean C.P., Rodbell D.S., “Magnetic disorder as a first-order phase transformation”, Physical Review, 126:1 (1962), 104–115 | DOI

[19] Valiev E.Z., “Entropy and magnetocaloric effects in ferromagnets undergoing first- and second-order magnetic phase transitions”, Journal of Experimental and Theoretical Physics, 108:2 (2009), 279–285 | DOI

[20] Karpenkov D.Yu., Karpenkov A.Yu., Skokov K.P., et al., “Pressure dependence of magnetic properties in La(Fe,Si)$_{13}$: Multistimulus responsiveness of caloric effects by modeling and experiment”, Physical Review Applied, 13:3 (2020), 034014 | DOI | MR

[21] Gruner M.E., Keune W., Landers J., et al., “Moment-volume coupling in La(Fe$1_{?x}$Si$x_{}$)$_{13}$”, Physica Status Solidi B, 255:2 (2018), 1700465 | DOI

[22] Yamada H., Fukamichi K., Goto T., “Itinerant-electron metamagnetism and strong pressure dependence of the Curie temperature”, Physical Review B, 65:2 (2001), 024413 | DOI

[23] Yako H., Fujieda S., Fujita A., et al., “ressure effect on the Curie temperature of La(Fe$_{0.88}$Si$_{0.12?y}$Al$_{y}$)$_{13}$”, Journal of Physics: Conference Series, 266:1 (2011), 012023 | DOI

[24] Giannozzi P., Baroni S., Bonini N., et al., “Approximations for Brillouin and its reverse function”, COMPEL — The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 35:6 (2016), 2095–2099 | DOI

[25] Zhang H., Wang F., Zhao T., et al., “Thermally activated itinerant metamagnetic transition in LaFe$_{11.7}$Si$_{1.3}$”, Physical Review B, 70:21 (2004), 212402 | DOI

[26] Yako H., Fujieda S., Fujita A., et al., “Influence of demagnetization effect on the kinetics of the itinerant-electron metamagnetic transition in magnetic refrigerant La(Fe$_{0.88}$Si$_{0.12}$)$_{13}$”, IEEE Transactions on Magnetics, 47:10 (2011), 2482–2485 | DOI

[27] Moreno-Ramirez L.M., Blazquez J.S., Radulov I.A., et al., “Combined kinetic and Bean — Rodbell approach for describing field-induced transitions in LaFe$_{11.6}$Si$_{1.4}$ alloys”, Journal of Physics D: Applied Physics, 54:13 (2021), 135003 | DOI