Spin waves in the two-dimensional honeycomb lattice XXZ-type van der Waals antiferromagnet CoPS 3

The magnetic excitations in $\mathrm{CoP}{\mathrm{S}}_{3}$, a two-dimensional van der Waals (vdW) antiferromagnet with ${\mathrm{Co}}^{2+}$ ion on a honeycomb lattice, have been measured using powder inelastic neutron scattering. The absence of spin-orbit exciton around 30 meV indicates that ${\mathrm{Co}}^{2+}$ ions in $\mathrm{CoP}{\mathrm{S}}_{3}$ have an $S=3/2$ state rather than a spin-orbital entangled ${J}_{\mathrm{eff}}=1/2$ ground state. And, clear dispersive spin waves are observed with a large spin gap of \ensuremath{\sim}13 meV. The magnon spectra were fitted using an XXZ-type ${J}_{1}\text{\ensuremath{-}}{J}_{2}\text{\ensuremath{-}}{J}_{3}$ Heisenberg Hamiltonian with single-ion anisotropy assuming no magnetic exchange interaction between the honeycomb layers. The best-fit parameters show ferromagnetic exchange interactions ${J}_{1}=\ensuremath{-}2.08\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$ and ${J}_{2}=\ensuremath{-}0.26\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$ for the nearest- and second-nearest neighbors and a sizable antiferromagnetic exchange interaction ${J}_{3}=4.21\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$ for the third-nearest neighbor with the strong easy-axis anisotropy $K=\ensuremath{-}2.06\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$. The anisotropic XXZ-type Hamiltonian could only achieve a suitable fitting. The exchange interaction for the out-of-plane spin component is smaller than that for the in-plane one by a ratio $\ensuremath{\alpha}={J}_{z}/{J}_{x}=0.6$. Our result directly shows that $\mathrm{CoP}{\mathrm{S}}_{3}$ is an experimental realization of the XXZ model with a honeycomb lattice in two-dimensional vdW magnets.