Spin stiffness of chromium-based van der Waals ferromagnets

Magnetic van der Waals materials attracted much interest after the discovery of long-range magnetic ordering in two-dimensional limit. Measuring and understanding the underlying magnetic exchange and anisotropy energy scales is the key to future material design. In this work, we systematically measure the low temperature magnetization of CrI3, CrGeTe3, CrSiTe3 bulk single crystals. We extracted the spin stiffness constant and spin excitation gap according to revised Bloch's law. Our results are quantitatively consistent with data from inelastic neutron scattering experiments. Among all three studied compounds, larger spin stiffness value leads to higher ferromagnetic transition temperature. Our work provides a fast and reliable way to characterize magnetic excitation gap and spin stiffness using bulk magnetization measurements.