Three-dimensional magnetic critical behavior in CrI${}_3$

CrI${}_3$ is a promising candidate for the van der Waals bonded ferromagnetic devices since its ferromagnetism can be maintained upon exfoliating of bulk crystals down to single layer. In this work we studied critical properties of bulk CrI${}_3$ single crystals around the paramagnetic to ferromagnetic phase transition. Critical exponents $\beta$ = 0.260(4) with a critical temperature $T_c$ = 60.05(13) K and $\gamma$ = 1.136(6) with $T_c$ = 60.43(4) K are obtained by the Kouvel-Fisher method, whereas $\delta$ = 5.32(2) is obtained by a critical isotherm analysis at $T_c$ = 60 K. The critical exponents determined in bulk CrI${}_3$ single crystals suggest a three-dimensional long-range magnetic coupling with the exchange distance decaying as $J(r)\approx r^{-4.69}$.