Scaling and universality in magnetocaloric materials

Abstract

The magnetocaloric effect of a magnetic material is characterized by two quantities, the isothermal entropy change and the adiabatic temperature change, both of which are functions of temperature and applied magnetic field. We discuss the scaling properties of these quantities close to a second-order phase transition within the context of the theory of critical phenomena. Sufficiently close to the critical temperature of a second-order material, the scaling of the isothermal entropy change will be determined by the critical exponents and will be the same as that of the singular part of the entropy itself. However, this is only true in the critical region near T c and for small fields; for finite fields, scaling with constant exponents, in general, break down, even at T c . The field dependence can then be described by field-dependent scaling exponents. We show that the scaling exponents at finite fields are not universal, showing significant variation for models in the same universality class. As regards the adiabatic temperature change, it is not determined exclusively by the singular part of the free energy and its derivatives. We show that the field dependence of the adiabatic temperature change at the critical temperature depends on the nonsingular part of the specific heat. The field dependence can still be fitted to a power-law expression but with nonuniversal exponents, as we show explicitly both within mean-field theory and using the so-called Arrott-Noakes equation of state. Within the framework of the Bean-Rodbell model, we briefly consider the scaling properties of the magnetocaloric effect in first-order materials. Finally, we discuss the implications of our findings for a widely used phenomenological scaling procedure for magnetocaloric quantities.

Magnetocaloric effect of LaFe11.35Co0.6Si1.05 alloy

“…As mentioned in Refs. [36,[41][42][43][44][45], such a shape of the universal scaling curve suggests that LaFe 11.35 Co 0.6 Si 1.05 alloy displays the second-order phase transition. It corresponds with the previous results delivered by the Arrott plots and temperature dependences of the Landau coefficients.…”

High-entropy bulk metallic glasses as promising magnetic refrigerants

“…[1][2][3][4] The magnetocaloric effect can be characterized by the field induced entropy change (DS M ) due to the alignment of its magnetic spins that occurs on exposure to an external magnetic field. 5 In the past decades, extensive efforts have been carried out in exploring the materials with excellent MCE, [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and some materials with large DS M have been fabricated, such as Mn-Fe-P-As, 3 Ni-Mn-In-(Co), 4 Gd 5 Si 2 Ge 2 , 6 LaFe 11.4 Si 1.6 , 7 and La 0.7 Ca 0.3 MnO 3 . 8 According to the magnetic transition style, the magnetic refrigerants can be divided into two classes, the first order magneto-structural phase transition materials (FOMTM) and second order magnetic phase transition materials (SOMTM).…”

“…8 According to the magnetic transition style, the magnetic refrigerants can be divided into two classes, the first order magneto-structural phase transition materials (FOMTM) and second order magnetic phase transition materials (SOMTM). 2,9 For FOMTM, e.g., Gd 5 Si 2 Ge 2 , the magnetization shows an abrupt variation at magnetic ordering temperature T C , leading to a very narrow and large peak of isothermal magnetic entropy change (DS pk M ). However, the thermal and magnetic hysteresis of the FOMTM makes them not suitable for the application of magnetic refrigeration.…”

Applicability of scaling behavior and power laws in the analysis of the magnetocaloric effect in second-order phase transition materials

“…In other cases, like in the Bean-Rodbell model [26], some additional parameters are included, so they can promote the destruction of these critical phenomena or lead to an artificial narrowing of its validity range. This fact has been interpreted by some researches as a proof of the lack of scaling relations in materials [84]. Finally, we want to pay some attention to those equations of state based directly on scaling relations like the Arrott-Noakes equation [28] or the Ho-Litster equation [29].…”