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

Abstract

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.

12 pages, 10 figures + appendix