Field-dependent anisotropic magnetic coupling in layered ferromagnetic Fe3−xGeTe2

Abstract

Two-dimensional layered itinerant ferromagnetic ${\mathrm{Fe}}_{3\ensuremath{-}x}{\mathrm{GeTe}}_{2}$ is considered as a candidate for applications in heterostructure-based spintronics because of its near-room-temperature Curie temperature and highly tunable characteristic of ferromagnetism. Moreover, the strong anisotropic magnetism of ${\mathrm{Fe}}_{3\ensuremath{-}x}{\mathrm{GeTe}}_{2}$ is another great advantage for fabricating magnetic storage devices. However, many relevant properties of its anisotropy still remain poorly understood, especially the basic mechanism of anisotropic magnetic interaction. In this work, we focus on the study of magnetic coupling in single-crystal ${\mathrm{Fe}}_{3\ensuremath{-}x}{\mathrm{GeTe}}_{2}$ ($x\ensuremath{\approx}0.28$) by the anisotropic magnetization, magnetic entropy change, and critical behavior. Our results confirm that the magnetization is angle dependent $[M(\ensuremath{\varphi})]$, in which the easy magnetic axis is along the $c$ axis while it exhibits absolute isotropic property in the $ab$ plane. The magnetic entropy change $[\mathrm{\ensuremath{\Delta}}{S}_{M}]$ also reveals an anisotropic feature between $H//c$ and $H//ab$. By fitting the field-dependent parameters of $\mathrm{\ensuremath{\Delta}}{S}_{M}(T,H)$, it gives the critical exponents $\ensuremath{\beta}=0.361(3), \ensuremath{\gamma}=1.736(7)$, and $\ensuremath{\delta}=5.806(8)$ for $H//c$, while $\ensuremath{\beta}=0.714(3), \ensuremath{\gamma}=1.243(7)$, and $\ensuremath{\delta}=2.741(1)$ for $H//ab$. The critical exponents with $H//c$ belong to the theoretical prediction of three-dimensional Heisenberg model, which suggest a short-range magnetic coupling. However, the critical exponents with $H//ab$ are close to those of mean-field model, which indicates a long-range magnetic coupling. The determined critical exponents suggest that the anisotropic magnetic coupling of ${\mathrm{Fe}}_{3\ensuremath{-}x}{\mathrm{GeTe}}_{2}$ is strongly dependent on orientations of the applied magnetic field.