Low-energy magnon excitations and emerging anisotropic nature of short-range order inCrI3

We report on the low-energy magnetic excitations and the evolution of local magnetic fields in ${\mathrm{CrI}}₃$ in a broad frequency regime of 30--330 GHz and in magnetic fields up to 15 T. Modeling the magnon branches by means of a domain-based ferromagnetic resonance model provides the microscopic parameters describing the magnetic excitations in the two-dimensional ferromagnet. Our data reveal the anisotropy gap of $\mathrm{\ensuremath{\Delta}}=80$ GHz at 2 K, which remarkably remains finite at ${T}_{\mathrm{C}}$ and vanishes only above ${T}_{\mathrm{\ensuremath{\Delta}}}\ensuremath{\simeq}80$ K, i.e., for $T\ensuremath{\gtrsim}1.3{T}_{\mathrm{C}}$. Concomitantly, anisotropic local magnetic fields are probed by a shift of the resonance lines in the same temperature regime. Well above ${T}_{\mathrm{C}}$, we detect short-range magnetic correlations up to 200 K. The observed changing nature of the short-range correlations at ${T}_{\mathrm{\ensuremath{\Delta}}}$ confirms the importance of spin-orbit coupling for the evolution of long-range ferromagnetism which develops from magnetically anisotropic short-range order. In addition, our analysis of the macroscopic magnetization enables to estimate the number of correlated spins well above ${T}_{\mathrm{C}}$ as well as the in-plane magnetic correlation length ${\ensuremath{\xi}}_{\mathrm{ab}}$.