Spin waves in the two-dimensional honeycomb lattice XXZ-type van der Waals antiferromagnet ${\mathrm{CoPS}}_3$

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 ∼13 meV. The magnon spectra were fitted using an XXZ-type $J_1\text{−}{J}_2\text{−}{J}_3$ Heisenberg Hamiltonian with single-ion anisotropy assuming no magnetic exchange interaction between the honeycomb layers. The best-fit parameters show ferromagnetic exchange interactions $J_1=-2.08\mathrm{meV}$ and $J_2=-0.26\mathrm{meV}$ for the nearest- and second-nearest neighbors and a sizable antiferromagnetic exchange interaction $J_3=4.21\mathrm{meV}$ for the third-nearest neighbor with the strong easy-axis anisotropy $K=-2.06\mathrm{meV}$. 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 $\alpha =J_z/J_x=0.6$. 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.

Figure 1

(a) The magnetic structure of $\mathrm{CoP}{\mathrm{S}}_3$ with the crystallographic unit cell drawn using vesta [49]. (b) The magnetic exchange paths are shown in the $ab$ plane for the first-, second-, and third-nearest neighbors. The numbers denote the position of spins used for the spin-wave calculation.

Figure 2

(a)–(f) Magnon spectra at different temperatures. (g) Temperature dependence of magnon intensity integrated over the momentum range of $Q=\left[0.3,4\right]{\AA }^{-1}$. (h) Temperature dependence of the overall integrated magnon spectra and (0,1,0) elastic peak. The blue triangle shows the integrated intensity of (0,1,0) magnetic peak in Ref. [27], and the red circle and green square show our data of magnon spectra and (0,1,0) magnetic peak each. The shaded area indicates the signals of spin fluctuations above the $T_{\mathrm{N}}$. The reference data were scaled to compare with our data directly.

Figure 3

(a) The best-fit magnon spectra with the XXZ model. (b) The experimental INS data of $\mathrm{CoP}{\mathrm{S}}_3$ measured at $T=8\mathrm{K}$ with $E_{\mathrm{i}}=71.3\mathrm{meV}$. (c) The best-fit magnon spectra with the isotropic Heisenberg model. An instrumental energy resolution of 3 meV was used to convolute the theoretical results shown in (a) and (c). Horizontal and vertical white boxes denote the integration range for the constant-$E$ and constant-$Q$ cuts in Fig. 3, respectively.

Figure 4

(a), (b) Constant-$Q$ cut at the momentum range of $Q=\left[1.71.8\right]$ and $Q=\left[2.22.3\right]{\AA }^{-1}$ for the measured data with the best-fit simulations. (c), (d) Constant-$E$ cut with the energy range of $E=\left[1316\right]$ and $E=\left[2427\right]\mathrm{meV}$. The XXZ model (solid red line) agrees better with the data.

Figure 5

The spin-wave dispersion along with the Brillouin zone's high-symmetric points for the isotropic Heisenberg model and the XXZ model. All the trajectories are given for the crystallographic unit cell. The Brillouin zone and the relevant positions are shown in the inset.