Revisiting the magnetic ordering through anisotropic magnetic entropy change in quasi-two-dimensional metallic ferromagnet, Fe$_4$GeTe$_2$

We have investigated the nature of ferromagnetic order and phase transitions in two dimensional (2D) van der Waals (vdW) layered material, Fe$_4$GeTe$_2$ through measurements of magnetization, magneto-caloric Effect (MCE), and heat capacity. Fe$_4$GeTe$_2$ hosts a complex magnetic phase with two distinct transitions: paramagnetic to ferromagnetic at around $T_\text{C}$ $\sim$ 266 K and another spin reorientation transition (SRT) at around $T_\text{SRT}$ $\sim $ 100 K. The magnetization measurements shows a prominent thermal hysteresis in proximity to $T_\text{SRT}$ at $H\parallel c$, which implies the first-order nature of SRT. Reasonable MCE has been observed around both transition temperatures ( at around $T_\text{C}$, -$\Delta$S$_M^\text{max}$ = 1.95 and 1.99 J.Kg$^{-1}$K$^{-1}$ and at around $T_\text{SRT}$, -$\Delta$S$_M^\text{max}$= 3.9 and 2.4 J.Kg$^{-1}$K$^{-1}$ along $H\parallel ab$ and $H\parallel c$ respectively) at 50 kOe magnetic field change. The above results reveal higher MCE value at $T_\text{SRT}$ compared to the values of MCE at $T_\text{C}$. The scaling analysis of MCE at $T_\text{C}$, shows that the rescaled $\Delta$S$_M (T, H)$ follow a universal curve confirming the second-order character of the ferromagnetic transition. The same scaling analysis of MCE breaks down at $T_\text{SRT}$ suggesting that SRT is not a second order phase transition. The exponent $n$ from field dependence of magnetic entropy change presents a maximum of $|n|>2$ confirming the first-order nature of SRT.