Spin stiffness of chromium-based van der Waals ferromagnets.

Low temperature magnetization of CrI, CrSiTeand CrGeTesingle crystals were systematically studied. Based on the temperature dependence of extrapolated spontaneous magnetization from magnetic isotherms measured at different temperatures, the spin stiffness constant () and spin excitation gap (Δ) were extracted according to Bloch's law. For spin stiffness,is estimated to be 27 ± 6 meV Å, 20 ± 3 meV Åand 38 ± 7 meV Åfor CrI, CrSiTeand CrGeTerespectively. Spin excitation gaps determined via Bloch's formulation have larger error bars yielding 0.59 ± 0.34 meV (CrI), 0.37 ± 0.22 meV (CrSiTe) and 0.28 ± 0.19 meV (CrGeTe). Among all three studied compounds, larger spin stiffness value leads to higher ferromagnetic transition temperature.