Fig. 1
From: Role of dimensional crossover on spin-orbit torque efficiency in magnetic insulator thin films
Dimensional crossover of magnetism in TmIG thin films. a Atomic force microscopy image of a 10 nm-thick TmIG film. b Magnetic moment as a function of out-of-plane magnetic field for TmIG thin films with different thicknesses at room temperature. c Saturation magnetization as a function of TmIG thickness at room temperature. The inset shows the areal magnetic moment as a function of TmIG thickness, which indicates a negligible magnetic dead layer. d Total magnetic moment as a function of temperature for different TmIG thicknesses. The solid lines are power-law fits to M = M0(1 − T/TC)β. e log10 (M) vs log10 (1 − T/TC) plots from (d) showing the thickness dependence of the β values. f Critical exponent β vs TmIG thickness showing a dimensional crossover from 2D to 3D. The dashed lines are theoretical values for 2D Ising (β = 0.125), 3D Ising (β = 0.325), and 3D Heisenberg (β = 0.365) models. The error bars in (c–e) stand for the measurement uncertainty, and the error bar in (f) stands for the fitting uncertainty
