Extended Bloch’s law description of two-dimensional dilute magnetic semiconductors

Abstract

The recent discoveries of intrinsic ferromagnetism (FM) in two-dimensional (2D) dilute magnetic semiconductors with high Curie temperature (> 300 K) capable of spintronic applications are among the most impressive tour de force achieved by theoretical and experimental physicists in the field [1,2]. However, the origin of FM in these systems has remained an open issue. The power function proposed by Bloch, M(T) = M(0)[1 - (T/TC)α] with α = 3/2, has successfully described the temperature dependence of saturation magnetization MS(T) for bulk ferromagnetic materials [3]. The extended Bloch’s law for ferromagnetic nanoparticles (α-Fe) embedded in a non-magnetic matrix (SiO2) has yielded higher values of α associated with the reduced dimensionality effect [4]. In this study, we demonstrate that V doping into WS2 monolayer induces ferromagnetic couplings between the vanadium and its tungsten neighbors, forming nanosized ferromagnetic clusters that behave like ferromagnetic nanoparticles. The MS(T) dependence of the nanoclusters in V-WS2 monolayer samples with different V concentrations (0, 0.4, 2, and 8 at.%) is well described by the modified Bloch’s law at temperatures higher than the blocking temperature. Relative to the Bloch coefficient (α = 3/2), the higher values of α (up to 5.96) and its dopant concentration dependence reveal the dimensional effect and the magnetic interaction between the nanoclusters. This method has been successfully applied to describe the M(T) dependence of other 2D magnetic systems such as VSe2 monolayers that exhibit similar magnetic behavior. Our findings also offer a new way to predict the Curie temperatures of low-dimensional magnetic materials that may not be measured experimentally.