Estimating of the magnetocaloric effect and spontaneous magnetization within critical behavior in GdGaAl alloys

In this paper, we present a novel calculation approach that emerges from the combination of the Landau theory with the Arrott–Noakes equation. Using an innovative formulation, we simulate the magnetic entropy change, -∆S_M within a random ferromagnetic system. This novel integration represents a significant advancement in accurately simulating the magnetocaloric effect (MCE) in GdGa1−xAlx alloys (x = 0; 0.3 and 0.5) near 180 K. These alloys could be potential for MCE close to 180 K and essential for a range of applications, notably for magnetic resonance imaging (MRI) systems employed in both medical diagnostics and scientific investigations. Initially, the critical exponents (𝛾; 𝛽) of these compounds were estimated to be (1.42; 0.49), (1.3; 0.51) and (1.25; 0.5) for GdGa1−xAlx alloys with x = 0; 0.3 and 0.5, respectively. Subsequently, these exponents were exploited to generate the isothermal magnetization M(H,T) and -∆S_M (H,T) curves. The magnetocaloric performances of the present samples were optimized by high temperature averaged entropy change (TEC). The TEC with two different temperature lifts (3 / 10 K) under 7 T magnetic field are 6.1/6.0, 7.6/7.4 and 9.4/9.10 J.kg-1.K-1 for the three alloys with x = 0; 0.3 and 0.5, respectively. Additionally, an effective new method was employed to calculate spontaneous magnetization by scaling the dependence of -∆S_M on M and using critical exponent values.