The recent introduction of magnetic van der Waals (vdW) materials has opened new and novel opportunities to examine the low-dimensional magnetism in real materials. In particular, TMPS₃ (TM = Mn, Fe, Co, Ni) family has attracted special interests in the community as a class of antiferromagnetic 2D vdW materials. The crystal structure of TMPS₃ is a monoclinic structure with a C 2/m space group, where a weak vdW force couples honeycomb layers with edge-shared TMS₆ octahedra on the ab-plane along the c-axis. Since magnetic structure and exchange interactions in TMPS₃ depend on the TM elements, they provide an excellent playground to validate spin dynamics theory in low dimensions experimentally.

CoPS₃ has been less studied among them due to the difficulty in synthesizing high-purity samples [1]. Therefore, the magnetic Hamiltonian of CoPS₃ has been unknown so far and needs investigation. CoPS₃ has antiferromagnetic phase transition at T_N = 122 K with zig-zag magnetic order. The spins are aligned along the a axis with a small canting to the c axis. The magnetic susceptibility shows a difference between H // ab and H // c in the paramagnetic state, which implies XY-like anisotropy [1].

Moreover, Co²⁺ magnetic systems have recently drawn significant attention because Co compounds may host Kitaev interactions [2]. A spin-orbital entangled state is an essential ingredient to realize the Kitaev interactions, which can be verified by measuring spin excitations. Typically, a spin-orbit exciton, the crystal field excitation between J_eff = 1/2 to 3/2 state, is strong evidence of a spin-orbital entangled state. Most cobalt compounds have such excitation at 20~30meV, proportional to the strength of spin-orbit coupling of cobalt [3].

In this study [4], we examined such a possibility using inelastic neutron scattering at the time-of-flight spectrometer of HRC at J-PARC. Our temperature-dependent measurements show that CoPS₃ does not show the spin-orbit exciton expected near 30 meV at high temperature in stark contrast with initial expectations. Figure 1 shows the temperature dependence of magnetic excitations. Above T_N = 122 K, there is no sign of excitations near 30 meV. This can only be interpreted as evidence for the ground state of CoPS₃ being an S = 3/2 state, not the spin-orbital entangled J_eff = 1/2 state. Figure 2 shows the spin-wave spectrum of CoPS₃ with incident neutron energy E_i = 71 meV. The measured spin-wave spectrum shows two magnon branches over 40 meV with a massive 13 meV spin gap. Also, the spin-wave spectrum shows extra gap-like features at 24~27 meV. Based on the former analysis about temperature dependence of magnetic excitations, we use magnetic Hamiltonian with S = 3/2 system to explain the spin-waves of CoPS₃. This magnon was well-fitted using an anisotropic Heisenberg (XXZ) model with a reasonable anisotropy coefficient α ≡ J_z/J_x = 0.6 and strong easy-axis single-ion anisotropy K = 2.4 meV along the a axis. The magnetic structure from our magnetic Hamiltonian also consistent with the reported magnetic structure. In summary, our experiment and theoretical analysis suggest CoPS₃ as another exciting platform to study anisotropic XXZ-type spin Hamiltonian in the honeycomb antiferromagnet. Moreover, it provides an excellent playground for future investigation of low-dimensional magnetism with magnetic van der Waals materials.

Fig. 1. (a-f) Magnon spectra of CoPS₃ at different temperatures with E_i = 71.3 meV.

Fig. 2. The experimental INS data of CoPS₃ measured at T = 8 K with E_i = 71.3 meV is shown in (b). (a), (c) The best-fit magnon spectra with the XXZ model and 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 (d-g), respectively. (d), (e) Constant-Q cut at the momentum range of Q = [1.7 1.8] and Q = [2.2 2.3] Å-1 for the measured data with the best-fit simulations. (f), (g) Constant-E cut with the energy range of E = [13 16] and E = [24 27] meV

References

• [1] A. R. Wildes et al., J. Phys.: Condens. Matter 29, 455801 (2017).
• [2] H. Liu et al., Phys. Rev. B 97, 014407 (2018).
• [3] K. Tomiyasu et al., Phys. Rev. B 84, 054405 (2011).
• [4] C. Kim et al., Phys. Rev. B 102, 184429 (2020).

Authors

• C. Kim^a, J. Jeong^a, P. Park^a, T. Masuda, S. Asai, S. Itoh^b, H. S. Kim^c, A. Wildes^d, and J. G. Park^a
• ^aSeoul National University
• ^bKEK
• ^cKangwon National University
• ^dInstitut Laue-Langevin