Spin wave excitations in van der Waals honeycomb ferromagnets

Recent discoveries of robust two-dimensional magnetism brought about a great research interest in van der Waals ferromagnets [1]. Experimental observations of their spin wave excitations are important because the underlying spin Hamiltonian can provide crucial information regarding thermal stability of their long-range order. In this talk, we focus on honeycomb ferromagnets where linear Dirac crossings in their magnon bands similarly to the electronic band of graphene [2]. We used inelastic neutron scattering to observe spin wave excitations in CrI₃ and Cr₂Ge₂Te₆ single crystals, where robust ferromagnetism was observed in monolayers [1]. The spin wave band of CrI₃ at T = 5 K consisted of two distinctive bands of ferromagnetic excitations separated by a ~ 2 meV gap at the Dirac points [3]. These results can only be understood by considering a Heisenberg Hamiltonian with Dzyaloshinskii-Moriya interaction, thus providing experimental evidence that spin waves in CrI₃ can have robust topological properties. As the temperature was increased to and beyond T_C = 61 K, the anisotropy gap at the zone center vanished following the power law behavior whereas the stiffness of the spin waves remained finite. These results strongly indicate that the magnetic anisotropy plays a decisive role in determining the Curie temperature in CrI₃, which is in contrast with typical three-dimensional Heisenberg ferromagnets where exchange interactions controlling the Curie temperature. In comparison, Cr₂Ge₂Te₆ showed no evidence of Dirac gap but revealed the significant next nearest neighbor exchanges due to Ge ions. Finally, we will report the quantitative estimates of exchange parameters in their spin Hamiltonian, and compared their values with those of CrBr₃ and Cr₂Si₂Te₆.
[1] C, Gong et al., Nature 546, 265 (2017); B. Huang et al., Nature 546, 270 (2017)
[2] J. Fransson et al., Phys. Rev. B 94, 075401 (2016)
[3] L. Chen et al., Phys. Rev. X 8, 041028 (2018)