The quantum non-Heisenberg nature of two-dimensional CrI₃ magnets

Higher-order exchange interactions and quantum effects are widely known to play an important role in describing the properties of nano magnets. Here we show that the magnetism of recently discovered 2D CrI₃ cannot be captured at the level of a simple Ising model as initially thought. Using a complementary suite of magneto-optical Kerr effect microscopy, magnetic force microscopy, correlated first-principles methods and Monte Carlo techniques including higher-order exchange interactions, we identify CrI₃ as a quantum non-Heisenberg material. We find that biquadratic exchange interactions are essential to quantitatively describe the magnetism of CrI₃ but requiring quantum scaling corrections to reproduce its thermal properties. The quantization of spin-wave excitations at the low temperature regime is reflected on the fluctuations of the magnetization which follow Bose-Einstein rather than the Boltzmann statistics. These fluctuations induce the formation of metastable magnetic domains stabilizing into a single macroscopic magnetization over large surface areas. Such domains have characteristics of N'eel and Bloch types with a narrow domain wall width (3-5 nm). Similar behavior is expected for the majority of 2D vdW magnets where higher-order exchange interactions are appreciable.